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Papakonstantinidis prototype draft

NEW: CHAPTER VIII+ The win-win-win papakonstantinidis mode: the Comm!nity"s key-roe in #ar$ainin$ pro#em:

Poiti%a &ame as a f!n%tion of '(ar$ainin$) )Prin%ipa-A$ent) and '*timat!m) $ame : The 'rain#ow%on%ept) in the Poiti%a (ar$ain

PAPA,N.TANTINI/I. 01A

In this improved and completed work2 we3 try to 4nd the function )( i x f of “Political game)

and:

1. The bargaining individual pro#em2. The Principal-Agent” pro#em and23. the “take-it-or-leave it” Ultimatum #ar$ainin$ pro#em

This work introd!%es poiti%a #ar$ainin$2 a pro%ess at the heart of a poiti%a and e%onomi%

e5%han$es in %ontemporary so%iety and the 6ery essen%e of poiti%s itsef2 to pro6ide a new framework

and fresh insi$hts to modern poiti%a s%ien%e1

The way to ha6e Power is to take it7 - Wiiam 7(oss7 Tweed

Bargaining Poer and Political Bargain

!A"#$ &ame theory is 7the st!dy of mathemati%a modes of con%ict and cooperationbeteen intelligent rational deci&ion-maker&17 &ame theory is mainy !sed in e%onomi%s2political &cience2 and psy%hoo$y2 as we as o$i%2 %omp!ter s%ien%e2 #ioo$y and poker1 ri$inay2 itaddressed 8ero-s!m $ames2 in whi%h one person9s $ains res!t in osses for the other parti%ipants1 Today2 $ame theory appies to a wide ran$e of #eha6iora reations2 and is now an !m#rea term forthe s%ien%e of o$i%a de%ision makin$ in h!mans2 animas2 and %omp!ters1

The bargaining poer of the 6i%e president of R/ was hi$h as he had many toos of ne$otiation at

his disposa1 In ne$otiatin$2 %apa%ity of one party to dominate the other d!e to its in;!en%e2 power2

si8e2 or stat!s2 or thro!$h a %om#ination of di

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rom the histori%a 6iew2 'poiti%a $ame) is %om#ined with the '%ompetition poi%y as poiti%a #ar$ain2

espe%iay with the anti-tr!st poi%yB): Candidates for President on%e de#ated antitr!st poi%y1 /isp!tes

a#o!t re$!atin$ tr!sts took %enter sta$e in the fo!r-way = ee%tion %ampai$n amon$ President

Wiiam Howard Taft2 former President Theodore Roose6et2 f!t!re President Woodrow Wison2 and

so%iaist %andidate E!$ene /e#s1 Doreo6er2 antitr!st enfor%ement in the de%ades #efore Word War II

was marked #y sharp pend!!m swin$s1 In the eary =@th %ent!ry2 the .!preme Co!rt iss!ed de%isions

#reakin$ !p .tandard i and Ameri%an To#a%%o1 Two de%ades ater2 d!rin$ the B@s2 the antitr!st

aws were eDodern $ame theory #e$an with the idea re$ardin$ the e5isten%e of mi5ed-strate$y eG!ii#ria in two-

person 8ero-s!m $ames and its proof #y Fohn 6on Ne!mann1 Von Ne!mann9s ori$ina proof !sed

(ro!wer 45ed-point theorem on %ontin!o!s mapping& into compact conve &et&4 whi%h #e%ame a

standard method in $ame theory and mathemati%a e%onomi%s1 His paper was foowed #y the

#ook Theory of &ames and E%onomi% (eha6ior2 %o-written with skar Dor$enstern2 whi%h %onsidered

%ooperati6e $ames of se6era payers1 The se%ond edition of this #ook pro6ided an a5iomati% theory of

e5pe%ted !tiity2 whi%h aowed mathemati%a statisti%ians and e%onomists to treat de%ision-makin$

!nder !n%ertainty1

ny some of the detais of ea%h %o!ntry are modeed2 s!%h as the e6e of !nempoyment2 the nationade#t and in%ome2 and the Co!ntries pop!ation As president2 there is nothin$ to stop yo! t!rnin$Ameri%a into a so%iaist state2 or to stop yo! e$ai8in$ ma%hine $!ns and heroin as (ritish primeminister111

The ee%torate in the $ame are we-informed rationa and aways t!rn !p to %ast their 6ote1 Thepoiti%a system is proportiona representation and its ass!med there is ony one opposin$ party1 This isa #i$ di1 Ha6in$ saidthat we do mode a h!$e amo!nt2 ots of sim!ation detai2 a h!$e n!m#er of totay independent6oters2 ots of poi%ies2 e6ents and poi%y diemmas2 p!s 6oters hodin$ $r!d$es and e6en 6oter%yni%ism and an$er

E5tensi6e $ame

B 5onathan B. Baker /200 'CDPETITIN P0ICJ A. A P0ITICA0 (AR&AIN) Antitrust Law JournalVo1 KB2 No1 = =@@L>2 pp1 MB-B@ P!#ished #y: Ameri%an (ar Asso%iation

Brouer . #. 5. 1623$ 7n the si$ni4%an%e of the prin%ipe of e5%!ded midde in mathemati%s2

espe%iay in f!n%tion theory17 With two Addenda and %orri$enda2 BB- (ro!wer $i6es #rief synopsis

of his #eief that the aw of e5%!ded midde %annot #e 7appied witho!t reser6ation e6en in the

mathemati%s of in4nite systems7 and $i6es two e5ampes of fai!res to i!strate his assertion1

papakonstantinidis Pa$e =

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/!rin$ the ate M@s and eary @s the ;owerin$ of transitiona and %onsoidatin$ third wa6edemo%ra%ies aro!nd the $o#e $enerated a wa6e of instit!tion #!idin$1 Internationa a$en%ies ike the

Word (ank %ame to !nderstand that $ood $o6ernan%e was not a !5!ry that %o!d #e deayed whie

more #asi% so%ia needs were #ein$ met2 ike the pro6ision of %ean water2 #asi% heath %are and

s%hooin$1 Instead the esta#ishment of demo%ra%y was !nderstood as an essentia pre-%ondition for

e Ee%tora En$ineerin$: Votin$ R!es and Poiti%a (eha6ior

RDAT Paper#a%kformat>L Boardgamegeek *tore: .ID*0ATIN &ADE.

papakonstantinidis Pa$e B

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#a%k to shorty after its fo!ndin$2 when2 in the ate @s2 it o#ser6ed ee%tions on the ,oreanPenins!a1 /!rin$ the s!#seG!ent era of tr!steeship and de%ooni8ation2 it s!per6ised and o#ser6edpe#is%ites2 referenda and ee%tions wordwide1 Today2 the *nited Nations %ontin!es to #e a tr!stedimpartia a%tor pro6idin$ ee%tora assistan%e to appro5imatey L@ %o!ntries ea%h year2 either at thereG!est of Dem#er .tates or #ased on a .e%!rity Co!n%i or &enera Assem#y mandate1

Ee%tora assistan%e is #ased on the prin%ipe esta#ished in the *ni6ersa /e%aration of H!man Ri$hts

that the wi of the peope2 as e5pressed thro!$h periodi% and $en!ine ee%tions2 sha #e the #asis of $o6ernment a!thority1 Ee%tora assistan%e aso re%o$ni8es the prin%ipes of state so6erei$nty andnationa ownership of ee%tions2 and that there is no sin$e mode of demo%ra%y1

The main $oa of *nited Nations ee%tora assistan%e is to s!pport Dem#er .tates in hodin$ periodi%2in%!si6e and transparent ee%tions that are %redi#e and pop!ary per%ei6ed as s!%h and esta#ishin$nationay s!staina#e ee%tora pro%esses1

The pro6ision of ee%tora assistan%e #y the *nited Nations is a team e2 s!pport sho!d #e pro6ided in aninte$rated manner

*nited Nations ee%tora assistan%e has #een a %r!%ia and s!%%essf! %omponent in pea%ekeepin$2pea%e #!idin$2 and in esta#ishin$ and deepenin$ demo%rati% $o6ernan%e1 As demo%ra%y has spread2so has the roe of ee%tions as the means to esta#ish e$itimate $o6ernment1 The *nited Nations has#een en$a$ed in ee%tions in a re$ions of the word2 with assistan%e pro6ided re%enty in theAf$hanistan2 Dai2 .omaia2 Fordan2 Nepa2 (an$adesh and IraG22 to name Q!st a few1 In T!nisia fore5ampe2 the *N s!pported %i6i so%iety in the %to#er =@ Nationa Constit!ent Assem#y ee%tionsand %ontin!es to pro6ide te%hni%a assistan%e to the nationa a!thorities1 In 0i#ya2 an inte$rated *Nteam s!pported the 0i#yan a!thorities in or$ani8in$ and %ond!%tin$ the &enera Nationa Con$ress

K /emo%ra%y and Ee%tions *N &o#a Iss!es

papakonstantinidis Pa$e

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ee%tions on K F!y =@=1 In =@B2 the *nited Nations pro6ided te%hni%a and o$isti%a s!pport toDaian a!thorities in the %ond!%t of Presidentia ee%tions1 In addition2 the *nited Nations is %!rrenty inthe pro%ess of s!pportin$ ee%tora reform in Af$hanistan1

The *nited Nations aso has esta#ished reations with re$iona and inter$o6ernmenta or$ani8ationsin6o6ed in ee%tora assistan%e2 in%!din$ the Afri%an *nion2 the E!ropean *nion2 the InternationaInstit!te for /emo%ra%y and Ee%tora Assistan%e2 the r$ani8ation of Ameri%an .tates2 the

r$ani8ation for .e%!rity and Co-operation in E!rope2 0ea$!e of Ara# .tates 0A.> and ther$ani8ation of the Isami% Conferen%e IC>2 and the .o!thern Afri%an /e6eopment Comm!nity2 aswe as with s!#-re$iona or$ani8ations ike E%onomi% Comm!nity f West Afri%an .tates ECWA.>1ther partners are the many internationa non-$o6ernmenta or$ani8ations workin$ in the 4ed of ee%tora assistan%e1 These in%!de instit!tions s!%h as the Carter Center2 the Ee%tora Instit!te for the.!staina#iity of /emo%ra%y in Afri%a2 and the Internationa o!ndation for Ee%tora .ystems1 Thesereationships pro6ide opport!nities for %oa#oration on ee%tora s!pport a%ti6ities as we as forsharin$ essons and e5perien%es1

It is re%o$ni8ed that addressin$ the %apa%ity of an ee%tora mana$ement #ody in isoation wi notne%essariy prod!%e %redi#e ee%tions1 There aso needs to #e a fo%!s on the o6era poiti%aen6ironment in whi%h the ee%tions take pa%e1 The *nited Nations therefore aso makes e #ar$ainers #y a tripe roe #eow> and2the G!estion is:7At what e6e the '%omm!nity inter6ention)2 or more soft '%omm!nity in6o6ement)> s!%%eeds thema5im!m satisfa%tion for a the #ar$ainers of the entire %omm!nity in%!din$2 aso2 the Comm!nity>UIn other words2 at whi%h point the additiona mar$ina satisfa%tion of #oth (ar$ainers and theComm!nity is e5a%ty eG!a to ER-@U

I think it"s time for a s%ienti4% dis%!ssion on Comm!nity roe2 the .tate roe> and its poi%ies mi5m!st re-open2 espe%iay today2 as a the i#eraism aternati6es faied to eiminate the h!$e !n-eG!aities a o6er the word th!s res!ted the war2 the hate2 the inQ!sti%e This G!estion m!st #e %om#ined with:

.tartin$ from &er$ey 0akatos2 (enedek Na$y =@@> 'Xor a non %onstant-s!m $ames %an #ee5tend to 8ero s!m $ames addin$ a new payer who has no rea %hoi%e2 #!t $et a pay-o< to et the$ame 8ero45>-s!m11) we de4ne o!r proposa on this: The /i &ames with few payers L th Internationa Conferen%e onAppied Informati%s E$er2 H!n$ary2 Fan!ary =KYB2 =@@1@ Thomas Ho##s" '0e6iathan): It may sho!d #e somethin$ ike There is an essentia di was one of the 4rst thinkers-fo!nders of the modern state and fo!nder of poiti%aphiosophy1


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in6o6ed in any #ar$ain #etween = it represents the 'other) e5%ept of the two main #ar$ainers

2−n > and at the same time2 'take %are) for the #ar$ain itsef as a> an independent B rd part of ne$otiations2 #> as an A$ent in the 'Prin%ipa-A$ent reation with its %iti8ens2 and %> as the ar#itratorin any #ar$ain #etween =It %o!d #e somethin$ ike the '0e6iathan) of Thomas Ho##es L> #!t o!r proposa introd!%es the

%on%ept of %are1 rather than imitin$ the freedom of the indi6id!a e5presses the 7%oe%ti6e7 the%oe%ti6e e ee%ted demo%rati%ay #y thepeope2 this means that the 7Comm!nity7 a%%o!nta#e for its a%tions !nder a its responsi#iities inthe fa%e of a 7#ar$ain7 #etween any two>In this frame2 the 'introd!%ed) CDD*NITJ #y the 'win-win-win papakonstantinidis mode) is a newpayer whi%h has m!%h more '%hoi%es) and responsi#iities: it is ikened to the 'rain#ow)2 whi%h is 'a%oor more) and at the same time as a 'synthesis of a the other %oors)

We start with the 'papakonstantinidis %onQe%t!res) that Comm!nity parti%ipates and m!st do> in any#ar$ain #etween = or more payers2 #y the B-di

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'we pass from the a#stra%t form of the %omm!nity2 into the pra%ti%a iss!e of the 'poi%ies mi5) andthe poiti%a pro$rams

In an aternati6e e5pression we are to st!dy the ser6i%es #ar$ainin$ pa%ka$es) whi%h are s%hed!ed inpoiti%a pro$rams that #e presented for #een 6oted #y the 7Comm!nity7 pop!ation or the maQorityof them>

In a '%oored) e5pression2 Comm!nity %o!d #e ike the white %oor2 whi%h in%!des a the other %oorsof the rain#ow"s phasma

,)-,)-,)$ +he :A,)B(

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The :ainbo concept) $i6es !s an idea on ho the

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o !A"#: Any set of %ir%!mstan%es that has a res!t dependent on the a%tions of two of more de%ision

makers 7payers7> A $ame is a forma des%ription of a strate$i% sit!ation1

o !A"# +9#(:F #D,),+,()*$ &ame theory is the forma st!dy of de%ision-makin$ where se6era payers

m!st make %hoi%es that potentiay a of those a$ents2 where the o!t%omes in G!estion mi$ht ha6e #een intended #y

none of the a$ents1 The meanin$ of this statement wi not #e %ear to the non-e5pert !nti ea%h of the

itai%i8ed words and phrases has #een e5pained and feat!red in some e5ampes1 /oin$ this wi #e the

main #!siness of this arti%e irst2 howe6er2 we pro6ide some histori%a and phiosophi%a %onte5t in order to

moti6ate the reader for the te%hni%a work ahead Aso2 !ame theor7 is the forma st!dy of %on;i%t and

%ooperation1 &ame theoreti% %on%epts appy whene6er the a%tions of se6era a$ents are interdependent1

These a$ents may #e indi6id!as2 $ro!ps2 4rms2 or any %om#ination of these1 The %on%epts of $ame theory

pro6ide a an$!a$e to form!ate str!%t!re2 anay8e2 and !nderstand strate$i% s%enarios1

o )()- form of a $ame1

o PAF#:*$ A strate$i% de%ision maker within the %onte5t of the $ameo ,)D(:"A+,() *#+: The information a6aia#e at a $i6en point in the $ame1 The term information set is

most !s!ay appied when the $ame has a seG!entia %omponent1o *+:A+#!F : A %ompete pan of a%tion a payer wi take $i6en the set of %ir%!mstan%es that mi$ht arise

within the $ame A $ame %an ha6e a pure-&trateg7 or a mied )a&h #>uilibrium. In the atter a p!restrate$y is %hosen sto%hasti%ay with a 45ed pro#a#iity>1 *+:A+#!F In a $ame in strate$i% form2 astrate$y is one of the $i6en possi#e a%tions of a payer1 In an e5tensi6e $ame2 a strate$y is a %ompetepan of %hoi%es2 one for ea%h de%ision point of the payer1

o *+:A+#!,< P:(D,#: We wi de4ne a strate$i%-form $ame in terms of its %onstit!ent parts: payers2

a%tions2 and preferen%es1 We wi introd!%e the notion of mi5ed strate$ies2 whi%h are randomi8ations o6era%tions1 !r 4rst step in the anaysis of these $ames wi #e to so6e the Easy Part of &ame Theory2 6i81 thepro#em of what %hoi%e a rationa payer wo!d make $i6en her #eiefs a#o!t the %hoi%es of her opponents10ater we wi t!rn to the Hard Part of &ame Theory: what #eiefs the payers %an rationay hod %on%ernin$the %hoi%es of their opponents1

o *+:A+#!,< D(:" A $ame in strate$i% form2 aso %aed norma form2 is a %ompa%t representation of a$ame in whi%h payers sim!taneo!sy %hoose their strate$ies1 The res!tin$ payo

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it2 and so on1 The str!%t!re of the $ame is often ass!med to #e %ommon knowed$e amon$ the payers1

o #I+#)*,@# !A"# An e5tensi6e $ame or e5tensi6e form $ame> des%ri#es with a tree how a $ame is

payed1 It depi%ts the order in whi%h payers make mo6es2 and the information ea%h payer has at ea%h

de%ision point1

o P#:D#

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) su su sun

....()(1

≡

i1 e n RS u →:

o +he outcome$ somethin$ that foows from an a%tion2 disp!te2 sit!ation2 et% res!t %onseG!en%e1 In agame theory2 an outcome is a set of mo6es or &trategie& taken b7 the pla7er&2 or it is their payo

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o P:(BAB,,+F$ The a of +otal Probabilit7 states that the pa7oK for a &trateg7 is the s!m of thepayo2 ea%h with its own pro#a#iity1 A%%ordin$ to the 0aw of TotaPro#a#iity2 the payo< is:

( ) ( ) ( LOSI OF Y PROBABILIT WIN YOU IF PAYOFF WINNINGOF Y PROBABILIT .............. +×

To make this easier to write2 we" represent the pro#a#iity of an e6ent as event P so now we ha6e:

( )loss for paoff P !in for paoff P loss!in ....)....( ×+×

How do we know the pro#a#iity of ea%h o!t%omeU .in%e we want to 4nd the a6era$e payo< for a payers of the

strate$y2 we ima$ine the pro#a#iity for an a6era$e mem#er of the pop!ation2 that is2 one who is of a6era$e si8e2

4$htin$ a#iity2 and so on1 In this simpe e5ampe2 that means that the pro#a#iities of winnin$ and osin$ are eG!a2

at j1 Jo! %o!d aso reason that ea%h intera%tion has a winner and a oser2 so there are eG!a n!m#ers of winners

and osers in the pop!ation2 makin$ the pro#a#iity of ea%h o!t%ome the same1> When there are more than two

possi#e o!t%omes2 there are more terms in the s!m=:

N out"o#e for paoff P out"o#e for paoff P N out"o#eout"o#e ..........1...... ..1.. ×++×

+he &trategic /or “normal” form of a game is a nat!ra and adeG!ate des%ription of a sim!taneo!s mo6e$ame1 It is aso a !sef! patform on whi%h to perform at east some of o!r anaysis of $ames whi%h ha6e a more%ompi%ated tempora and information str!%t!re than a sim!taneo!s-mo6e $ame has1

A &trateg7 need not refer to a &ingle4 simpe2 eementa a%tion in a $ame with tempora str!%t!re a strate$y%an #e a 6ery comple &e>uence of action& whi%h depend on the histories of simpe a%tions taken #y a otherpayers1 The name 'strate$i% form) deri6es pre%isey #e%a!se the present formaism i$nores a this potentia

%ompe5ity and %onsiders the strate$ies as primiti6es of the theory i1e1 as !nits whi%h %annot #e de%omposed intosimper %onstit!ents>1

Indi6id!a strate$ies: We ha6e a nonempty2 4nite set ,...}2,1{.... ≡∈ N nof I payers)1}...(,...2,1{ n I = The I i plaer t$i ∈− ,.... has a nonempty set of strate$iesher &trateg7 &pace iS

a6aia#e to her2 from whi%h she %an %hoose one strate$y

ii S s ∈ Noteas indi%ated #y the i s!#s%riptthat ea%h payer has her own strate$y spa%e iS Therefore ea%hpayer has a%%ess to her own possi#y !niG!e set of strate$ies1 We wi ass!me that ea%h payer"s strate$y spa%e is4nite1 When ne%essary we wi refer to the&e a& pure &trategie& in order to distin$!ish them from mied&trategie&2 whi%h are randomi8ations o6er p!re strate$ies=11

E5ampe: Consider a two-payer $ame #etween Eias and Daria

.!ppose #lia& has two a%tions a6aia#e to her: *p and /own1 Then his strate$y spa%e E S wo!d #e

},{ %o!nUpS E =

When she pays the $ame she %an %hoose ony one of these a%tions1

= CRNE0 *NIVER.ITJ-http:SSess1n##1%orne1ed!Spro#1htm= :atliK 5im /166E .trate$i%-orm &ames Fames Rati< is an Ameri%an poiti%ian and a /emo%rati%mem#er of the Arkansas Ho!se of Representati6es


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.o his strate$y E S wo!d #e either UpS E = or %o!nS E =

0ikewise2 s!ppose that "aria %an mo6e eft2 midde2 or ri$ht1 Then her strate$y spa%e is

},,{ ri&$t #i''ieleft S ( =

the notion of mi5ed strate$ies2 whi%h are randomiHation& over action& /P:(BAB,,+,#*>1

.trate$y pro4esor the time #ein$ it wi #e !sef! to ima$ine that a payers pi%k their strate$ies at the same time:

Pla7er 1 pi%ks some11 S s ∈

Pla7er 2 pi%ks some22 S s ∈ et%1 We %an des%ri#e the &et of &trategie& %hosen #y the n payers as the

ordered tuplen − :

)..,( 21 n s s s s = Thisn -dimensiona 6e%tor of indi6id!a strate$ies is %aed a strate$y pro4e or sometimes a strate$y%om#ination>1 or e6ery di with peope

o The Comm!nity and its roe at any =-person ultimatum game: Comm!nity is the a#sor#er of #oth feein$s

and indi6id!a strate$ies In parti%!ar2 feein$s of fairness2 an$er and en6y are ikey %andidates as a

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i$!re : The %anoni%a two-payer2 two-a%tion-per-payer strate$i%-form $ame=L1

We %onsider the two-payer strate$i%-form $ame in i$!re 1 We assi$n rows to payer A

and %o!mns to payer B 1 s A' strate$y spa%e is { } %U S A ,= and { }r l s B ,' =

(e%a!se ea%h payer has ony two a%tions2 ea%h of her mi5ed strate$ies %an #e des%ri#ed #y a sin$e

n!m#er B for *an' A for p ............ #eon$in$ to the !nit inter6a [ ]1,0

A mi5ed-strate$y pro4e for this $ame2 then2 is an ordered pair ( ) [ ] [ ]1,01,0, ×∈* p We denote thepayers" payo ma5im!m o6er a of s A'

payoindin$ Di5ed .trate$y Nash EG!ii#ria in =g= 2 Qiml6irt!aperfe%tion1%om[2 1


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s A' payo< as a f!n%tion of the mi5ed-strate$y pro4e: To 4nd s A' #est-response%orresponden%e we 4rst %omp!te her e5pe%ted payo< for an ar#itrary mi5ed-strate$ypro4e #y wei$htin$ ea%h of s A' p!re-strate$y pro4e payouilibrium4 is a ist of strate$ies2 one for ea%h payer2 whi%h has the property that no payer %an !niateray %han$e

his strate$y and $et a #etter payo

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+9# “,)-,)” "(#$ “)A*9 #NU,,B:,U"”-)A*9 BA:!A,),)! *(U+,()

0et the game ),( f S

Ea%h of i #ar$ainers2 de6eops .trate$y pro4es d!rin$ the #ar$ain2 0et iS #e a strate$y pro4e for

i payer2 and n s s sS ××= ...21 the set of strate$y pro4es and ))(),......(()( 1 x f x f x f n= ispayo< f!n%tion2 i1 e a strate$y pro4e2 #y its pro#a#iity Pa7oK i& a linear function of &trateg7pro8le$

) su su su n....()( 1≡

Now2 .tartin$ from the 'win-win) NE =-payers $ame>:

0et ),( f S G #e a $ame with n payers in a %ompetiti6e reation where iS is the strate$y set for ipayers

n s s sS ××= ...21 the set of strate$y pro4es and ))(),......(()( 1 x f x f x f n= is payo

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'h!mans ha6e attit!de to %ooperation #y nat!re and the same person may a%t more or ess%ooperati6ey dependin$ on the parti%!ar payo strate$y2 #!t aso on the mi5ed see at7pro#a#iities7> strate$ies of the opponents> A 'rea%ti6e reation) %hara%teri8es the #ar$ain in its%omponents It pres!pposes that '%ompete information) #etween #ar$ainers e5ists and this

information does not in;!en%ed #y 'feein$s)

7Rationaity72 7Information7 and 7Indi6id!aity7 in hi$hest e6e 2 are the #ase of #ar$ainers9 a%tions inorder to ma5imi8e their persona satisfa%tion from this #a8aar otherwise wo!d not ha6e the in%enti6eto start #ar$ainin$ inay2 we sho!d re%o$ni8e the Payouilibrium /).#

E6ery possi#e eG!ii#ri!m Nash EG!ii#ri!m> is wei$hted with the %orrespondin$ pro#a#iity of it 6onNe!mann forms a 7possi#e rankin$7 a these 7e5pe%tations7 that are re;e%ted in n!m#ers !tis> In

the e6ent that the random potentia %assi4ed in 5 and @@ -5> then the 7shares7 they e5pe%t thene$otiators of parti%!ar eG!ii#ria of potentia2 i1 e a$reement> foow a #inomia distri#!tion Y a“lotter7 over di&tribution”4 or “a lotter7 over po&&ible outcome& / isa strate$y pro4e with the property that no sin$e payer %an2 #y de6iatin$ !niateray to anotherstrate$y2 ind!%e a ottery that he or she 4nds stri%ty prefera#e1 In @ the mathemati%ian Fohn Nash

pro6ed that e6ery $ame with a 4nite set of payers and a%tions has at east one EG!ii#ri!m)

In e5pe%ted !tiity theory2 a ottery is a dis%rete distri#!tion of pro#a#iityB@ on a set of states of nat!re1 The element& of a lotter7 %orrespond to the pro#a#iities that ea%h of the states of nat!re wi o%%!rIn e%onomi%s2 indi6id!as are ass!med to rank otteriesB a%%ordin$ to a rationa system of preferen%es2

=M 9an&-:Odiger P8&ter 4and !i&ela Bhm /2012> Responder eein$s in a Three-Payer Three-ption *timat!m&ame: A CHAPTER: )DIgE/ .TRATE&J)INTERNATINA0 ENCJC0PE/IA THE .CIA0 .CIENCE.2 =N/ E/ITINiess(at%hAA-D S=BS@K=:B PD Pa$e =@B@ "a&-

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atho!$h it is now a%%epted that peope make irrationa %hoi%es systemati%ay1 (eha6iora e%onomi%sst!dies what happens in markets in whi%h some of the a$ents dispay h!man %ompi%ations andimitationsB=

A possi#e ob=ection say from #ar$ainer (> de4nes a simpe a%tion in '#ar$ainin$)

ne of the payers2 say payer 2 can rai&e an ob=ection. An o#Qe%tion is an aternati6e a$reement1

Pro#a#y2 the aternati6e a$reement is #etter for payer 2 and worse for payer1 2 Then2 /A.Raisin$s!%h an o#Qe%tion has some pro#a#iity of endin$ the ne$otiation1 This pro#a#iity %an #e see%ted #y

payer2 e1 $2 #y the amo!nt of press!re he p!ts on payer 1 to a$ree>1 +he ob=ection i&

eKective onl7 if4 i.e4 pla7er 2 prefer& the alternative agreement with a %han%e2 o6er the

ori$ina a$reement for s!re1 /B Payer 1%an then raise a %o!nter-o#Qe%tion #y %aimin$ that for him

This means that payer1 prefers to insist on the ori$ina a$reement e6en if this mi$ht #ow !p the

ne$otiation payer 1prefers the ori$ina a$reement with a %han%e2 o6er the aternati6e a$reement

for s!re1

Here2 howe6er2 we ha6e the third and most powerf! ne$otiator who is the Comm!nity The proposawe p!t forward with this proQe%t2 the distri#!tion of possi#e eG!ii#ria is trinomia and the $enera#!d$et 7#7 trise%tedBB

This2 introd!%e to the pro#a#iity of two o#Qe%tions at the same time instead of one

In this %ase2 the %on%ept '!timat!m) seems to ha6e $reater !tiity2 as we as the %on%eptof the risk of disa$reement whi%h are e5amined #eow

▲

???????????????????????????????????????????????????

,*A!:##"#)+

A two person #ar$ain pro#em %onsists of a disa$reement2 or threat2 point 2 where

and are the respe%ti6e payo 7*tiity2 risk2 and inearity7 Fo!rna of poiti%a e%onomy LK >: BM1BB Papakon&tantinidi& A/2002 'win-win-win mode) E*RACA/EDJ2 THEDATIC &*I/E2 *ni6ersity of Vis#y2 &otand-.W =@@=-@M-


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other payer>1 The prod!%t of the two e5%ess !tiities is $eneray referred to as the Nash prod!%t1Int!iti6ey2 the so!tion %onsists of ea%h payer $ettin$ her stat!s G!o payo< i1e12 non-%ooperati6epayo in addition to an eG!a share of the #ene4ts a%%r!in$ from %ooperationB

)a&hR& #i&tence +heorem

Nash pro6es that if we aow mi5ed strate$ies then e6ery $ame with a 4nite n!m#er of payers inwhi%h ea%h payer %an %hoose from 4nitey many p!re strate$ies has at east one Nash

eG!ii#ri!mB1 Theodore (er$strom =@@=> BLpro6ides !s with the %hara%teristi% $raph in a possi#e

sit!ation #etween 'Cri##a$e)BK and 'Temperat!re)2 for A and ( #ar$ainers:

In fa%t2 he pro6ides !s with a 'D!t!a Pro4t C!r6e)2 for A and ( #ar$ainers or a 'win-win %!r6e)WWC>2 or !n%tion

We sha speak of ea%h %om#ination of a 'room temperat!re) and a n!m#er of '&ames of Cri##a$e) as'a sit!ation) If e6ery#ody ikes sit!ation 'a) as we as sit!ation '#) and someone ikes 'a) #etter2 wesay that 'a) is a Pareto s!perior to '#) A sit!ation is said to #e Pareto optima if there are no possi#esit!ations that are Pareto s!perior to it

:,*' v& uence& of agentL& action& are alternative ell-de8ned “probabilit7

di&tribution” over the random variable& the7 face

B "uthoo4 Abhina7 /1666. (ar$ainin$ theory with appi%ations Cam#rid$e *ni6ersity PressB 'uhn 9arold4 )a&ar *7lvia =@@=> The essentia Fohn Nash) Prin%eton *ni6ersity Press edition=@@=>BL +heodore Berg&trom /20020e%t!re YA Primiti6e P!#i% E%onomy *C.( Dar%h B2 =@@= % MBK

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0et9s %onsiderBMthe !tiity f!n%tions of A and (:

)(),...( & u x f u B A ==

a&ree#ents possi+leof ea"$at strate&ies possi+le x u xu n B A ....10............,,....,... ==

fun"tionnonlinear u fun"tionlinear xu n

B A ...:...,....: ==

)eutral :i&k /blue line A) the ri&k aver&ion /red line

:...............exp".." B for "onfli"t of fear t$eressesn

Cases:

When 1=n 2 then #ar$ainer ( is ne!tra either #ar$ain eads to a$reement or no

When 1n 2 then ( the #etter the o

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)o4

A%%ordin$ to 'Pareto EO%ien%y) %riterion the a$reement is eO%ient if and ony if there is no #etterdistri#!tion2 or de%ision whi%h %o!d eads the 'A) sit!ation in a #etter position2 witho!t the '()position to #e%ome worst

.o if there are ony two e6ents in a #inomia distri#!tion with ony = possi#iities2 i1 e to '#e) Ye6ent 5>or 'not to #e)e6ent @@-5> .o2 the tota 'to #e) and 'not to #e) e6ents m!st #e @@ %ertainty>

#IA"P# (D )A*9 BA:!A,),)! *(U+,()

Reation f!n%tion> #etween payers" strate$i% pro4es and their e5pe%ted payo

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L @ @ = =B L

K @ L@ @ B =@ ma5

M B@ K@ = @ L@

=@ M@ = @ L@@

@ @ @ L =

@ @@ @ M@ @

@aroufaki& Fani&4 “!ame +heor7”-ardano&4 2002

T,EORY GA(E BARGAIN ..⊆

Di5ed .trate$ies Pro#a#iity /istri#!tion and their %orresponded e5pe%ted payoof a possi#e so!tion eG!ii#ri!m>

A and ( m!st de6eop %oaitions in a 'non-%ooperati6e $ame) if they want a #ar$ainin$ so!tion

A and ( m!st de6eop instant re;e%tion winnin$ strate$ies2 for #etter payo< indi6id!a 3s f!n%tions2a%%ordin$ to their e5pe%tations

(oth of them know the r!es of the $ame2 and ha6e the same %ommon ,nowed$e of RationaityC1,1R>

(oth of them work in a 'rea%tion) f!n%tion

(oth of them %reate e5pe%tations from the $ame and for this reason they ha6e to %orrespond ea%hpayo< to its pro#a#iity the tota of these form a 'pro#a#iities distri#!tion)

inay2 the 's!staina#iity) meas!rement %o!d #e res!ted from the '!88y set theory) %om#inin$

eements of di

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In a %ompetiti6e e%onomy2 any ao%ation o6er the !tiityYpossi#iity frontier is a Pareto optim!m2 asthe *P is a representation of the Pareto %ontra%t %!r6e in a di1 The set of points2 whi%h for a $i6en e6e of !tiity of person 2 !tiity of person = is ma5imi8eds!#Qe%t to reso!r%e a6aia#iity>1 (e%a!se a points aon$ the *PC represent di is the !pper frontier of the !tiity possi#iities set2 whi%h is the set

of !tiity e6es of a$ents possi#e for a $i6en amo!nt of o!tp!t2 and th!s the !tiity e6es possi#e in a$i6en %ons!mer Ed$eworth #o5 The *P is the %ontra%t %!r6e of the Ed$eworth #o5

0et A and ( ead Yafter hard> #ar$ainin an a$reement or this2 they mast %oa#orate d!rin$ the#ar$ainin$ time a non-%ooperati6e $ame>

The Nash" %on%ept: the strate$i% asked shares #y #ar$ainers A2 (> %orrespond - to 'e6es) ofsatisfa%tion or '!tiity !nits)> for ea%h of the #inomia p2 -p> distri#!tion

or this2 it is important to 'dis%o6er) the ma5 'e6e) that satisfy #oth #ar$ainers2 so no one has anin%enti6e to %han$e his strate$y de%ision and one %annot impro6e its sit!ation witho!t worsenin$ theposition of the other atho!$h #oth -ea%h one for himsef-seek the opposite to impose on ea%h other>

@1 Albou74 avid /200C .prin$> 7Pareto ptimaity and P!#i% &oods with Two A$ents7 1 (erkeey*ni6ersity Y E%onomi%s @ 0e%t!re Note2 0esson SS Harsanyi2 Fohn MK>1 The New Pa$ra6e: A/i%tionary of E%onomi%s1 pp1 YM

Ed$eworth #o5 is a way of representin$ 6ario!s distri#!tions of reso!r%es1 Ed$eworth madehis presentation in his #ook Dathemati%a Psy%hi%s: An Essay on the Appi%ation of Dathemati%s to theDora .%ien%es2 MM


http://emlab.berkeley.edu/users/webfac/card/e101a_s05/paretopublicgoods.pdfhttp://emlab.berkeley.edu/users/webfac/card/e101a_s05/paretopublicgoods.pdfhttp://en.wikipedia.org/wiki/Resource_(economics)http://en.wikipedia.org/wiki/Resource_(economics)http://emlab.berkeley.edu/users/webfac/card/e101a_s05/paretopublicgoods.pdfhttp://en.wikipedia.org/wiki/Resource_(economics)

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*9A# *U:DA

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NA.H .0*TIN: Dathemati%a Approa%h

The %on%ept:⇒≈⇒≈ 0)'*(max* B A B A U U U U

0et the !tiity f!n%tion of two 'payers) A2 and ( with *tiities B A U U ,...

n

B A xU an' xU )100(...... −== X fun"tionsutilitt in'epen'enU an' U B A ...........

)....(.................. )riterion ParetoUPF t$eon E N +e#ust U an' U B A

B A B A xU U U U =∩

The 'n) fa%tor

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

We s!ppose 'mi5ed strate$ies) for payers2 who ha6e 'perfe%t information) a#o!t the $ame and itsr!es: mi5ed strate$ies ask possi#iities to #e %hosen amon$ other strate$ies>

The fear of non-a$reement2 #etween = indi6id!as2 that is the 'n) fa%tor and its !tiity in wefaree%onomi%s2 it is printed in the form of the *tiity-Pro#a#iity rontier*P> of A and ( satisfa%tion"spossi#iity

*tiity-Possi#iity rontier *P> of D and &

D and & are eG!a afraid of the possi#iity of disa$reement disp!te>

& s%ared more

D s%ared more

(ar$ainin$ is fa6or to those2 who are ess s%ared on possi#e disa$reement

papakonstantinidis Pa$e =L

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in the %ase of 2=n and D in the %ase of 2

1=n are afraid a#o!t the disp!tenon a$reement> in a

%orrespond -> reation the more 'n)2 the ess of fear for D : In that %ase2 there is the possi#iity D to%aim and take more payo< strate$ySpayo from & D is not afraid of disa$reement as & does>

NA.H .0*TIN: Nash .o!tion: the ma52 amon$ Nash EG!ii#ria2 on *P:

Hyper#oa denotes the B A B A uuuu f P *),( ==

THE (AR&AININ& NA.H .0*TIN

n

B A xU an' xU )100(...... −== 2 where %= x that2 ' A) e5pe%ts to deri6e from the #ar$ain 2after a$reement with the '() Y .o2 A m!st #e %oordinated2 Q!st in #ar$ainin$ instant re;e%tion> with'() therwise2 there is no possi#iity for a$reement: A strate$ies form the #inomiadistri#!tion as it

Hyper#oa 2 XXXX1 Para#oa2

)eumann4 P. /16. 7#er den Dedian der (inomia- and Poisson6ertei!n$71 Wissens%hafti%heeits%hrift der Te%hnis%hen *ni6ersitut /resden in &erman> : =YBB)XIn pro#a#iity

theory and statisti%s2 the #inomia distri#!tion with parameters n and p is the dis%rete pro#a#iitydistri#!tion of the n!m#er of s!%%esses in a seG!en%e of n independent yesSno e5periments2 ea%h of whi%h yieds s!%%ess with pro#a#iity p:

papakonstantinidis Pa$e =K

http://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Discrete_probability_distributionhttp://en.wikipedia.org/wiki/Discrete_probability_distributionhttp://en.wikipedia.org/wiki/Discrete_probability_distributionhttp://en.wikipedia.org/wiki/Statistical_independencehttp://en.wikipedia.org/wiki/Statistical_independencehttp://en.wikipedia.org/wiki/Probabilityhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Probability_theoryhttp://en.wikipedia.org/wiki/Statisticshttp://en.wikipedia.org/wiki/Discrete_probability_distributionhttp://en.wikipedia.org/wiki/Discrete_probability_distributionhttp://en.wikipedia.org/wiki/Statistical_independencehttp://en.wikipedia.org/wiki/Probability

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has #een de4ned #y Fohn 6on Ne!mann LL>L as:

for k @2 2 =2 1112 n2 where K

)A*9 #NU,,B:,U"$

Nash .o!tion is the 6a!e of 5 5> whi%h ma5imi8es the 'prod!%t) B A uu P *=

of the = !tiity

f!n%tions max)100( =−= n

x x P

max* = B A U U

n

B A xU xU )100(...,. −==

))(max(%*max B A U U x =

n

B A x xU U )100(maxmax −=

(!tX

0)('...max,....)(........

0)('...max,...)(..

→→

==

x f t$en x f approa"$evenor

x f t$en x f If

[ ] 0')100(

max)100(

=−

=−n

n

x x

x x

0])100([)100(max =′−⇒− nn x x x x

0]')100([ =− n x x

(!t2

0)100()100(1 1 =−+− −nn x xn x

L Ne!mann2 P1 LL>1 7#er den Dedian der (inomia- and Poisson6ertei!n$71 Wissens%hafti%heeits%hrift der Te%hnis%hen *ni6ersitut /resden in &erman>K ,n general4 if the random 6aria#e g foows the #inomia distri#!tion with parameters n and p2 we

write g v (n2 p>1 The pro#a#iity of $ettin$ e5a%ty k s!%%esses in n trias is $i6en #y the pro#a#iitymass f!n%tion:

papakonstantinidis Pa$e =M

http://en.wikipedia.org/wiki/Probability_mass_functionhttp://en.wikipedia.org/wiki/Probability_mass_functionhttp://en.wikipedia.org/wiki/Probability_mass_functionhttp://en.wikipedia.org/wiki/Probability_mass_functionhttp://en.wikipedia.org/wiki/Probability_mass_function

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11 )100()1()100()100)(1( −− −−=−− nn x x- x x

IfX10)#100( x−

1

1

1

1

)100(

)100()1(

)100(

)100()100(−

−

−

−

−−−

=−

−−n

n

n

n

x

x xn

x

x x

xn x )1()100( −=−

nx x −=100

)1(100 += n x

xn =+1100

]%1

100[%*+

=n

x

When 1=n the A2 ( ha6e the identi%a inear f!n%tions #ene4t S !tiity @-@>

When 1

When2 1n !tiity $rowth rate of A is ess than that of ( -in e5ampe sef is aways eG!a to >

▲

,DD#:#)

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''')...(... x x x fro# startin& +=

0)100()100(1

1

=−+− −nn

x xn x

'

2

'

1

2

1'

22

'

11

'

22

'

11 **0**u

u

u

uuuuuuuuu =⇒−=⇒=+

The reati6e #ar$ainin$ power depends on reati6e sopes of their !tiity f!n%tions

(ar$ainin$ power of payer 2 in reation with #ar$ainin$ power of payer =2 depends on the reati6erates of sopes that denote 'risk a6ersion): the more in%rease rate in e5pe%ted payo a& the arbitrator in the&e game& in the whoe %omm!nity so to win

.o2 'a$en%y theory) introd!%es !s to the do!#e thinkin$ eadin$ th!s2 in imit2 to a tripe

poe win in-in-in> !rthermore2 the 7a$en%y theory7 prod!%es '#eha6iors) of a

do!#e dire%tion: one for himSherSsef and the other for the 7prin%ipe7 The third part of

ne$otiations e6en !nder-informed> %an ind!%e the other party to re6ea their information1

They %an pro6ide a men! of %hoi%es in s!%h a way that the %hoi%e depends on the pri6ate

information of the other partyM1 I96e tried to 7see7 the in-in-in papakon&tantinidi&

model methodoo$i%a too2 thro!$h the 7Prin%ipa-A$ent Theory) with the asymmetri%

information eadin$ either in 7mora ha8ard72 or 7ad6erse see%tion7 %o!d #e seen #y a

three poe #ar$ainin$ so!tion A2 ( and the Comm!nity as the third poe>

M *tiglitH 5o&eph #. /16EC> The Theory of 7.%reenin$27 Ed!%ation2 and the /istri#!tion of In%ome- The Ameri%an E%onomi% Re6iew V o1 L2 No1 B F!n12 K>2 pp1 =MB-B@@

papakonstantinidis Pa$e B@

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#D,),+,()$ +he principalSagent problem aso known as agenc7 dilemma or theoryof a$en%y> o%%!rs when one person or entity the 'a$ent) is a#e to make de%isions on#ehaf of2 or that impa%t2 another person or entity: the 'prin%ipa) The diemma e5ists#e%a!se sometimes the a$ent is moti6ated to a%t in his own #est interests rather thanthose of the prin%ipa1 The a$ent-prin%ipa reationship is a !sef! anayti% too in poiti%as%ien%e and e%onomi%s #!t may aso appy to other areas1 Common e5ampes of thisreationship in%!de %orporate mana$ement a$ent> and sharehoders prin%ipa>2 orpoiti%ians a$ent> and 6oters prin%ipa> The pro#em arises where the to partie& havediKerent intere&t& and a&7mmetric information the a$ent ha6in$ more information>2s!%h that the prin%ipa %annot dire%ty ens!re that the a$ent is aways a%tin$ in its theprin%ipa9s> #est interestsparti%!ary when a%ti6ities that are !sef! to the prin%ipa are%osty to the a$ent2 and where eements of what the a$ent does are %osty for the prin%ipato o#ser6e1

An agenc7 per&pective wo!d aow the parties more freedom in stip!atin$ e$a $ro!nds

for re6iew1 If parties want a de%ision that is a%%!rate2 they %o!d reG!ire that ar#itrators not

make %ear errors of aw1 Hi$h G!aity ar#itratorxa$ents %o!d trade on their a#iity to

interpret aw #y promisin$ not to Comm!nity as a '%omm!nity a$ent) and 'ar#itrator)@

(!t2 the point is to st!dy the Principal-Agent Pro#em with Adver&e *election Ad6erse

see%tion is the tenden%y of those in dan$ero!s Qo#s or hi$h risk ifestyes to $et ifeins!ran%e =1 A sit!ation where seers ha6e information that #!yers don9t or 6i%e 6ersa>

a#o!t some aspe%t of prod!%t G!aity In order to 4$ht ad6erse see%tion2 ins!ran%e

%ompanies try to red!%e e5pos!re to ar$e %aims #y imitin$ %o6era$e or raisin$ premi!ms

Ad6erse see%tion o%%!rs when there9s a a%k of symmetri% information prior to a dea

#etween a #!yer and a seer2 whereas mora ha8ard o%%!rs when there is asymmetri%

information #etween two parties and %han$e in #eha6ior of one party after a dea is str!%k1

Dora ha8ard and ad6erse see%tion are two terms !sed in e%onomi%s2 risk mana$ement

and ins!ran%e to des%ri#e sit!ations where one party is at a disad6anta$e1 An a$en%y2 in

$enera terms2 is the reationship #etween two parties2 where one is a prin%ipa and the

other is an a$ent who represents the prin%ipa in transa%tions with a third part71 A$en%y

reationships o%%!r when the prin%ipas hire the a$ent to perform a ser6i%e on theprin%ipas9 #ehaf1 Prin%ipas %ommony dee$ate de%ision-makin$ a!thority to the a$ents1

A$en%y pro#ems %an arise #e%a!se of ineO%ien%ies and in%ompete information1 In

4nan%e2 two important a$en%y reationships are those #etween sto%khoders and

mana$ers2 and sto%khoders and %reditors=

Thro!$h .ti$it89s work No#e Pri8e2 =@@>2 asymmetri% information was pa%ed into

%ontained $enera eG!ii#ri!m modes to des%ri#e ne$ati6e e5ternaities that pri%e o!t the

#ottom of markets1 F1 .ti$it8 pioneered the theory of s%reenin$1 In this way the !nder

informed party %an ind!%e the other party to re6ea their information1 They %an pro6ide a

men! of %hoi%es in s!%h a way that the %hoi%e depends on the pri6ate information of the

other party: 'Prin%ipa-A$ent Theory): A s!pposition that e5pains the reationship#etween principal& and agent& in #!siness A$en%y theory is %on%erned with reso6in$

pro#ems that %an e5ist in a$en%y reationships that is2 #etween prin%ipas s!%h as

sharehoders> and a$ents of the prin%ipas for e5ampe2 %ompany e5e%!ti6es>1 The two

pro#ems that a$en%y theory addresses are$

ucian Bebchuk and 5e&&e Dried4 /200; Pay Witho!t Performan%e #y Har6ard *ni6ersity Press=@@@ +om !in&burg2006 'The Ar#itrator as A$ent: Why /eferentia Re6iew Is Not Aways Pro-Ar#itration) FHN D1 0IN 0AW ECNDIC. WR,IN& PAPER N1 @= =/ .ERIE.> INVE.TPE/IA= *tiglitH4 5o&eph #. /16G64 7Prin%ipa and a$ent72 in atwe Fohn2 Di$rate D!rray2Ne!man Peter ,1 The New Pa$ra6e: ao%ation2 information2 and markets2 New Jork: Norton2


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1 the pro#ems that arise when the desires or $oas of the prin%ipa and a$ent are in

%on;i%t2 and the prin%ipa is !na#e to 6erify #e%a!se it diO%!t andSor e5pensi6e to do

so> what the a$ent is a%t!ay doin$ and

=1 the pro#ems that arise when the prin%ipa and a$ent ha6e di

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Indeed2 Z!aity *n%ertainty and the Darket De%hanism7 is a K@ paper #y the e%onomist&eor$e Akerof whi%h e5amines how the G!aity of $oods traded in a market %an de$rade inthe presen%e of information asymmetry #etween #!yers and seers2 ea6in$ ony 7emons7#ehind1

A 'emon) is an Ameri%an san$ term for a %ar that is fo!nd to #e defe%ti6e ony after it has

#een #o!$ht1

.!ppose #!yers %an9t distin$!ish #etween a G!aity %ar a 7pea%h7> from a 7emon71 Thenthey are ony wiin$ to pay a 45ed pri%e for a %ar that a6era$es the 6a!e of a 7pea%h7 and

7emon7 to$ether )( av& p (!t seers know whether they hod a pea%h or a emon1 &i6en

the 45ed pri%e whi%h #!yers are wiin$ to #!y at2 seers are ony wiin$ to se when they

hod 7emons7 sin%e )( av& le#on p p and ea6e the market when they hod 7pea%hes7 sin%e

)( av& pea"$ p p > Th!s the !ninformed #!yer9s pri%e %reates an ad6erse see%tion pro#em

whi%h dri6es the G!aity %ars from the market1 Ad6erse see%tion is the market me%hanismthat eads to a market %oapse1

Akerof9s paperL shows how pri%es %an determine the G!aity $oods #ein$ traded on the

market 0ow pri%es dri6es away seers with G!aity $oods ea6in$ ony the emons #ehind

(!yers sometimes ha6e #etter information a#o!t how m!%h #ene4t they %an e5tra%t froma ser6i%e in whi%h %ase the 7#ad7 %!stomers are more ikey to appy for the ser6i%e1 ore5ampe2 an a-yo!-%an-eat #! %!stomers1Another e5ampe is in o

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,nformation a&7mmetr7 model

Information asymmetry modes ass!me that at east one party to a transa%tion has

ree6ant information2 whereas the others> do not1 .ome asymmetri% information modes

%an aso #e !sed in sit!ations where at east one party %an enfor%e2 or e %annot1

In adver&e &election modes2 the i$norant party a%ks information whie ne$otiatin$ an

a$reed !nderstandin$ of or %ontra%t to the transa%tion2 whereas in mora ha8ard the

i$norant party a%ks information a#o!t performan%e of the a$reed-!pon transa%tion or

a%ks the a#iity to retaiate for a #rea%h of the a$reement1 An e5ampe of ad6erse see%tion

is when peope who are hi$h-risk are more ikey to #!y ins!ran%e #e%a!se the ins!ran%e

%ompany %annot e

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predi%tions often hin$e on spe%i4% ass!mptions from the mode1 If the mode wi #e appiedin one parti%!ar en6ironment s!%h as a G!e!in$ mode des%ri#in$ the ines at theRefresher Co!rse2 or the (a%k-.%hoes mode for option pri%in$> then the spe%i4%ass!mptions need to mat%h the en6ironment fairy %osey2 otherwise the G!antitati6epredi%tions wi not #e !sef! in that en6ironment1 ne mi$ht %a this 7en$ineerin$modein$7 rather than 7e%onomi% modein$17 Nualitative predi%tions are often morero#!st2 in two senses1 irst2 G!aitati6e predi%tions may %ontin!e to hod if one makes sma%han$es in the mode9s spe%i4% ass!mptions1 or e5ampe2 a mode9s G!antitati6epredi%tions mi$ht depend on whether a parti%!ar pro#a#iity distri#!tion is norma2e5ponentia2 or !niform2 #!t the mode9s G!aitati6e predi%tions mi$ht hod for any sin$e-peaked i1e12 hi-shaped> distri#!tion2 in%!din$ the three mentioned a#o6e as we asothers1

PAF D(: P#:D(:"A)

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T

A@#:*# *##L@ INVE.TPE/IA

papakonstantinidis Pa$e BL

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orders a food with G!aity # R*+

∈ and pays a monetary transfer +∈ Rt for the pri%e of the

food1 0et ),( *$ θ denote the satisfa%tion of the %!stomer of typeθ #!yin$ the food with

G!aity * Then the elfare or utilit7 of this a$ent

de4ned here #y “a” is:

)())(,()( θ θ θ θ t *$U a −=

&enerai8ationL: 0et )(θ aU G!anti4es how m!%h a %!stomer with taste θ enQoys the

food with G!aity * knowin$ that he spends the amo!nt t for it1 If )(*) represents the%ost of prod!%in$ the food with G!aity * 2 then the !tiity of the prin%ipa de4ned here#y "" p is

))(()()( θ θ θ *) t U p −=

Here )(θ pU %an #e 6iewed as the pro4t that the owner of the resta!rant makes in sein$

the food with G!aity * to the %!stomer with taste θ .in%e the $oa of the owner is tomake more pro4t2 then he tries to anti%ipate the %!stomers" %hoi%es so that ea%h %!stomerre6eas his taste #y %hoosin$ the food that is tar$eted for him1 Therefore2 the prin%ipa"s

!tiity )(θ pU is s!#Qe%t to some %onstraints2 %aed in%enti6e %ompati#e %onstraints2

meanin$ that the %!stomers are $i6en in%enti6e to re6ea their rea tastes1 Dathemati%ay2the in%enti6e %ompati#e %onstraints %an #e represented as

Θ∈′∀′−′≥− θ θ θ θ θ θ θ θ ,),...())(,()()(,( t *$t *$

.o2 the prin%ipa-a$ent pro#em %an #e form!ated as foows:

∫ Θ

− θ θ θ θ θ θ

' f *) t A P (AX t *

)())(()()..()(),(

the ob=ective function

under the con&traint&$

),....2,..1,...0),( nit *$ iii =∀≥−θ

n .it *$t *$ . .iiii ,...2,..1,......),(),( =∀−≥− θ θ

Now2 the 'Prin%ipa-A$ent Theorem) m!st #e distin$!ished #etween two $reat s%hoos of tho!$ht1 i1e

iberali&m and *tati&m

L"o=deh *hadnam /201; THE DATHEDATIC. PRINCIPA0-A&ENT PR(0ED WITH A/VER.E

.E0ECTIN Y Atanti% Ee%troni% Fo!rna of Dathemati%s http:SSaeQm1%aSrema Vo!me L2 N!m#er 2

.!mmer =@ pp1 -=

papakonstantinidis Pa$e BK

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a1 *tati&m2 In poiti%a s%ien%e2 statism is the #eief that the state sho!d %ontro either

e%onomi% or so%ia poi%y2 or #oth2 to some de$ree1 .tatism is e %!stomer2 there %an #e no 7a$reement7 #etween third parties these a$reements are simpy

7%ontra%ts17 perationa-e6e a$reements or 0As2 howe6er2 may #e !sed #y interna $ro!ps to

s!pport .0As1 If some aspe%t of a ser6i%e has not #een a$reed with the %!stomer2 it is not an 7.0A71

*A& %ommony in%!de se$ments to address: a de4nition of ser6i%es2 termination of a$reement1 To

ens!re that .0As are %onsistenty met2 these a$reements are often desi$ned with spe%i4% ines of

demar%ation and the parties in6o6ed are reG!ired to meet re$!ary to %reate an open for!m for

L= :and4 A7n4 /162 'Introd!%in$ #Qe%ti6ism2) The #Qe%ti6ist Newsetter2 A!$1 L=2 p1 B AN/

:and4 A7n4 'War and Pea%e2) The #Qe%ti6ist Newsetter2 %t1 L=2 p1 LB 7liberali&m ,n $enera2 the #eief that it is the aim of poiti%s to preser6e indi6id!a ri$hts and toma5imi8e freedom of %hoi%e17 Con%ise 5ford /i%tionary of Poiti%s2 Iain "cean and Ali&tair"c"illan4 +hird edition 20064L unn 5ohn4/1663 Western Poiti%a Theory in the a%e of the !t!re72 Cam#rid$e *ni6ersity Press2B>

papakonstantinidis Pa$e BM

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%omm!ni%ation1 Contra%t enfor%ement rewards and penaties> sho!d #e ri$idy enfor%ed2 #!t most

.0As aso ea6e room for ann!a re6isitation so that it is possi#e to make %han$es #ased on new

information1 Parti%!ary a ser6i%e-e6e a$reement .0A> is a part of a standardi8ed ser6i%e %ontra%t

where a ser6i%e is formay de4ned1 Parti%!ar aspe%ts of the ser6i%e Y s%ope2 G!aity2 responsi#iities Y

are a$reed #etween the ser6i%e pro6ider and the ser6i%e !ser1 A %ommon feat!re of an .0A is a

%ontra%ted dei6ery time of the ser6i%e or performan%e>1 As an e5ampe2 Internet ser6i%e pro6iders

and te%osL wi %ommony in%!de ser6i%e e6e a$reements within the terms of their %ontra%ts with

%!stomers to de4ne the e6es> of ser6i%e #ein$ sod in pain an$!a$e terms

▲Win-win-win papakonstantinidis mode the math

per%eption

The 'Comm!nity) in a key-roe of #ar$ain

+he “bargaining in-in-in papakon&tantinidi& &olution$ the &ames with few payers L th Internationa Conferen%eon Appied Informati%s E$er2 H!n$ary2 Fan!ary =KYB2 =@@1


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third payer in a =-payers #ar$ain2 #>the 7A$ent7 in the Prin%ipa- A$ent reations with the %iti8ens and%> as a fair a#ritrator #etween the two #ar$ainers

+9# and at the same time2 'take %are) for the #ar$ain itsef as a> an independent B rdpart of ne$otiations2 #> as an A$ent in the 'Prin%ipa-A$ent reation with its %iti8ens2 and %> as thear#itrator in any #ar$ain #etween =

It %o!d #e somethin$ ike the '0e6iathan) of Thomas Ho##es L> #!t o!r proposa introd!%es the

%on%ept of %are1 rather than imitin$ the freedom of the indi6id!a e5presses the 7%oe%ti6e7 the

%oe%ti6e e

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The central idea #ehind the Principal-Agent model is that the Prin%ipa is too #!sy to do a $i6en Qo# and so hires the A$ent2 #!t #ein$ too #!sy aso means that the Prin%ipa %annot monitor the A$entperfe%ty1 There are a n!m#er of ways that the Prin%ipa mi$ht then try to moti6ate the A$ent: this noteanay8es in%enti6e %ontra%ts simiar to pro4t sharin$ or share%roppin$> ater notes dis%!ss ri%her andmore reaisti% modesK@1

.tate is the Agent of

rom this point of 6iew we e5tend the pro#em as to in%!de a pair of any #ar$ainers and the

0e%t!re Note : A$en%y Theory D(A Co!rse 1@B: r$ani8ationa E%onomi%sand Corporate .trate$y> DIT edition


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▲

#I(!#)(U*

#ogenou& variable&$ orld Population trend&

As re6eaed #y the s!r6ey of nationa ser6i%e of *. Cens!s2 peope a$ed o6er L in the ne5t few years

wi s!rpass %hidren a$ed and !nder1 This is a phenomenon not seen in the history a$ain A%%ordin$

to the $raph2 the two a$e $ro!ps wi foow the %orrespondin$ path for the %omin$ de%ades2 the

edery now far o!twei$h the sma1

Dore spe%i4%ay2 in 20C0 peope o6er C make !p 1C.W of the word pop!ation2 more than twi%e

the per%enta$e of %hidren !nder C wi rea%h E.2W. 7This !niG!e demo$raphi% phenomenon is

!npre%edented27 said the s!r6ey1

This wi %a!se 7!pside-down7 in so%ia str!%t!res #!t aso to pension f!nds aro!nd the word

This means two iss!es:

1 ewer and fewer peope wi #e workin$ for more and more peope o6er time and

=1 A and more peope wi ask reG!ire> shares of word weath2 whi%h has a imit theoreti%ay at

east>

It therefore means that2 the 7#ar$ainin$ pro#em7 is more %ompi%ated now2 !nder the new 4ndin$s:

for e5ampe2 that %o!d mean 7di

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on the ori$inaity of win-win-win %on%ept We refer to the 7so%ia state7 as 7stron$ ne$otiator7 who

interfere in any ne$otiations in three forms inter6ention>:

1 as a third part of the dea

2. as the A$ent7 of the 7 Citi8en- Prin%ipe7 whi%h hire .tate ser6i%es i1e Independent

(road%astin$ A!thority2 Citi8en Independent A!thority2 Cons!mption Independent A!thority

et%> %annot do the same2 or work that the state does #etter than him

3. as an ar#itrator in the ne$otiations #etween two

At any %ase2 the '.tate) or $eneray speakin$ the '

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that e6ery %iti8en of this the .tate pay2 and whi%h #eon$s to some #o!nded domain p R⊂Γ (esides

#ar$ainers e5pe%t payo makes in

'sein$) the safety and its ser6i%es2 to the Citi8ens in ne$otiations with another or with G!aity #*+to the CITIEN with2 a 'e6e of a%%epted state Spoiti%a #ar$ainin$ ser6i%es) γ .in%e the $oa of theowner is to make more pro4t2 then he tries to anti%ipate the %!stomers" %hoi%es so that ea%h %!stomerre6eas his taste #y %hoosin$ the food that is tar$eted for him1 Therefore2 the prin%ipa"s CITIEN>

!tiity )(γ pU is s!#Qe%t to some %onstraints2 %aed in%enti6e %ompati#e %onstraints2 meanin$ that

the CITIEN. are $i6en in%enti6e to re6ea their rea a%%epted e6e of '#ar$ainin$ .tate ser6i%es)Dathemati%ay2 the in%enti6e %ompati#e %onstraints %an #e represented as

Γ ∈′∀′−′≥− γ γ γ γ γ γ γ γ ,),...())(,()()(,( t *$t *$

.o2 the prin%ipa-a$ent pro#em2 or2 pro#em2 espe%iay2 as for stateser6i%es G!aity e6e2 %an #e form!ated as foows:

∫ Γ

− γ γ γ γ γ γ

' f *) t A P (AX t *

)())(()()..()(),(

i& the ob=ective function

level +ar servi"es state preferre' of "$an&einitesi#al t$e' !$ere ........'........inf ....,... γ

under the con&traint&$

),....2,..1,...0),( nit *$ iii =∀≥−γ

n .it * & t *$ . .iiii ,...2,..1,......),(),( =∀−≥− γ γ

.o2 the prin%ipa-a$ent pro#em %an #e form!ated as foows:


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∫ Γ

− γ γ γ γ γ γ

' f *) t A P (AX t *

)())(()()..()(),(

etL& .ia , #e the o!t%omes of the #ar$ain or in a DATRIg form 22× witho!t in%!de the 'C)in;!en%e

str A str A=

str ( a2 a2=

str (= a=2 a=2=

A2 ( strate$iesX a2Xa=2=Xthe o!t%omes of A and (2 payers %orrespondy

,n game theor74 an outcome is a set of mo6es or strate$ies taken #y the payers2 or it is theirpayo

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and detaied te%hniG!es for reasonin$ thro!$h these e5ampes2 after we ha6e des%ri#ed a sit!ation we%an !se a tree to mode

*F)+9#*,*$ )A*9 #>uilibrium *trateg7 v& P:,)uilibrium$

Now2 0et

t$e#+et!eenresponse+est are strate&all #e*uili+riu In

strate&ot$er an'enote' S

!$ereS S S S P S S S S P

i plaersall for if E N aisS S S S

t$en

paoff t$e'enote' P an'

i plaer for strate&#e*uili+riut$eS

i

nini

ni

i

..............,.....

.........

,...)...,...,...,...()...,...,..(

........,........)...,....,..,...(

.....(.).....

....,.........

**

2

*

1

***

2

*

1

***

2

*

1

*

−

−≥

0et the o!t%ome .i ,α is the #est for #oth payers in a #ar$ain ),( f S where the o!t%ome .i,α is a

f!n%tion of .trate$ies and payo

In the EG!ii#ri!m points2 and2 espe%iay2 in (ar$ainin$ .o!tion> the o!t%ome for the two #ar$ainers-

e5%ept %omm!nity pro4t- the o!t%ome .i ,α m!st #e the be&t

(!t .i,α is the o!t%ome or rea n!m#ers> of the f!n%tion

"....".........),( ,, strate&in'ivi'ual /ARIABLE t$eis x!$ere x f .i .i =α

That means2 that the 4rst derivative of the o!t%ome" f!n%tion of a sin$e 6aria#e x is ER

BARGAINERS t$eof t!ot$e+et!eenon'istri+uti+est x f (AX .i .i ..3..................[0)(,..... ,, =′→=α

Now2 .i ,α is the o!t%ome or rea n!m#ers> of the f!n%tion

"....".........),( ,, strate&in'ivi'ual /ARIABLE t$eis x!$ere x f .i .i =α

.o2 it %o!d #e that )....()......(, fun"tion paoff x f nu#+ersreal inout"o#es ii .i ≠α andthisdi

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more and more s!re2 that they wi #e satis4ed from their ea%h-other #ar$ainin$ pro%ess

SER/I)ES STATE BARGAINING BSS

SER/I)ES BARGAINING)O((UNITY )BS

BSS an' )BS ex"ellent "aseuni*uet$e If

x f x f a nni. x

.....

........

.."....."........0..

)](.....)([

1

111im....

==

=

=−−∞→

ε

ε

That means that the 'or$ani8ationa str!%t!re and e6e of (ar$ainin$ .tate .er6i%es) is estimated as

6ery $ood2 as1ε

$ets smaer and smaer2 as #ar$ainers %onstanty !pdate more and more often in

fa%t 7s!$$est7 o6er and o6er> e5pe%tations The more times 7re6ise7 their e5pe%tations in anen6ironment of se%!rity2 Q!sti%e and sta#iity ens!re a we-or$ani8ed state2 the #etter o!t%ome That"str!e:

If there is a 45ed re$ime 4nan%ia2 4s%a and e$a pro6isions !nder> so as to ens!re the hi$hestpossi#e de$ree2 the sense of Q!sti%e then2 ea%h part of the dea wi #e in front of a 6ery spe%i4% andimited s%ope to de6eop its own a%tion in the ne$otiation is not statism2 i#eraism is indeed within theoperatin$ framework of a we-or$ani8ed2 we-$o6erned2 sef-$o6ernin$ entity

It is e5%eent)2 ony in the uni>ue ca&e of 01 =ε

(!t2 the .tate asks from #ar$ainers to pay ta5es i1 e the fee for the ser6i%es pro6ided to #ar$ainers forthe se%!rity and sta#iity of their ne$otiations.tate #ar$ainin$ #eha6ior is de4ned from #oth the 'ar#itrator roe) and the 'A$ent roe)

.pe%i4%ay2

The 7#eha6ior7 of the .tate determined on:

1 poiti%a pro$rams presentin$ #y poiti%a parties seekin$ the 6ote of the peope at theee%tion day e6ery 2 years>

=1 the) poiti%a %onseG!en%e 7 2 for e5ampe2 the de6iation $rade #etween poiti%a pro$ramand $o6ernment a%tion

B1 Its so%ia and safety roe

ni

t$en x If

x f x f a nni. x

,....2...,1.,.

0...,......

)](.....)([

1

111im

=

→∞→

=−−∞→

ε

ε

&i6en2 that

[ ]

alsoi#prove' +e!ill tension BARGAININGt$et$eni#prove'

)o##unit t$et$at N EXPE)TATIOt$eist$ereif oppositet$e In

$i&$l in"re#enta+e!ill x f a'eviationt$e

)SW Wea-nessStrate&i")o##unitainre#ain)o##unit As

x f x f a

t$et$en

t$eof strate&ononl'epen'e' paoff e"te' t$eis x f

an'

value' o+serveor nreali0atiot$eeiout"o#est$ea

i .i

n .i x

i

.i

................,

....,..........,......

.......)],(..[..

(......."..........

0)(....)(

,..

...,.....,,,...exp.....),...(

,......,........,..,...

,

1,

,

im

−

→−−−∞→

papakonstantinidis Pa$e K

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inay2 we ha6e to st!dy the 'win-win-win sit!ation- an ideal point of the #ar$ain the Comm!nityin%!ded as the third person2 as we as the 'Peopes A$ent) and the #ar$ainin$ Ar#itrator)

We note the n- tuple& %omm!nity roe in any #ar$ain #etween two

*pecial ca&e$ +he “3- pla7er& P:,*()#:L*

,#""A”

Consider a $ame of Prisoner"s /iemmaK=1 ny instead of two %riminas2 the (I m!st interro$ate

three criminal&1 What wo!d the payo< matri5 ook ike for this $ameU What wo!d #e the r!esU

What wo!d #e the /ominate .trate$y for ea%h payerU

.!ppose the pa7oK matri for a three-payer $ame of Prisoner"s /iemma is 3-2 then it wo!d ook

ike a %!#e2 made !p of M smaer %!#es1 Ea%h %!#e represents a di

C2 NC2 C>

C2 C2 NC>

C2 NC2 NC>

NC2 C2 C>

NC2 NC2 C>

NC2 C2 NC>

NC2 NC2 NC>

.!ppose there are some r!es1 If a three payers %onfess2 ea%h payer $ets M months in Qai1 If a three

payers ref!se to %onfess2 ea%h payer $ets months1 If ony one payer %onfesses2 heSshe waks2 and

the other two $ets = months ea%h1 inay2 if two payers %onfess2 they $et L months ea%h2 and the

third payer $ets = months1 0isted #eow are the o!t%omes with appropriate Qai times for ea%h payer1

/Pla7er 14 Pla7er 24 Pla7er 3 M /X4 X4 X

K= THE Corne *ni6ersity workin$ paper

papakonstantinidis Pa$e M

(ptionA1

(ptionA2

(ptionA3

(ptionA1

a a21 aB

(ptionA2

a21 a== aB=

(ptionA3

aB a=B a33

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C2 C2 C> M2 M2 M >

C2 NC2 C> L2 =2 L >

C2 C2 NC> L2 L2 = >

C2 NC2 NC> @2 =2 = >

NC2 C2 C> =2 L2 L >

NC2 NC2 C> =2 =2 @ >

NC2 C2 NC> =2 @2 = >

NC2 NC2 NC> 2 2 >

0et"s anaysis the o!t%omes from Payer "s perspe%ti6e: if Payer = and Payer B %onfesses2 Payer

sho!d %onfess2 =[M if Payer = %onfesses and Payer B ref!ses to %onfess2 Payer sho!d %onfess2

=[L if Payer = ref!ses to %onfess and Payer B %onfesses2 Payer sho!d %onfess2 =[L if Payer =

and Payer B ref!se to %onfess2 Payer sho!d %onfess2 [@1 Th!s2 to %onfess is a /ominate .trate$y

for Payer 2 this pro%ess works the same way for Payer = and Payer B1

The a#o6e dis%!ssion appies ony to a $ame in whi%h a payers per%ei6e a spe%i4% en$th of Qai time

as eG!ay #ad1 or e5ampe2 in an episode of Numb3rs2 '/irty (om#2) mathemati%ian Charie Epps

!sed &ame Theory and Risk Anaysis to aid (I a$ent /on Epps in interro$atin$ three %riminas1 Charie

inte$rated Risk Anaysis into the Prisoner"s /iemma1 He ar$!ed that one %rimina may ha6e more to

ose #y $oin$ to Qai than anther1 Th!s2 assi$nin$ months aone to the payo< matri5 may #e

miseadin$1 Charie performed a Risk Anaysis for ea%h %rimina and deri6ed a fa%tor for ea%h %rimina:

Payer K12 Payer = 12 Payer B =L1>1 If a three %riminas $o to Qai for the same en$th of

time2 Payer B has more to ose than the others1 0isted #eow are the o!t%omes with appropriate Qai

times m!tipied #y risk fa%tors for ea%h payer1

/Pla7er 14 Pla7er 24 Pla7er 3 M /X4 X4 X

C2 C2 C> LB1=2 1=2 =1= >

C2 NC2 C> K12 KM1M2 M1 >

C2 C2 NC> K12 M12 BL1M >

C2 NC2 NC> @2 KM1M2 BL1M >

NC2 C2 C> 1M2 M12 M1 >

NC2 NC2 C> 1M2 KM1M2 @ >

NC2 C2 NC> 1M2 @2 BL1M >


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NC2 NC2 NC> B1L2 1L2 @1L >

ominate *trateg7$

Payer : C Y Payer =: C z Payer B: C

Payer : C Y Payer =: NC z Payer B: C

Payer : NC Y Payer =: C z Payer B: C

Payer : NC Y Payer =: NC z Payer B: C

Pla7er 3L& ominate *trateg7 M <

Payer : C Y Payer B: C z Payer =: C

Payer : C Y Payer B: NC z Payer =: C

Payer : NC Y Payer B: C z Payer =: C

Payer : NC Y Payer B: NC z Payer =: C


Payer B: C Y Payer =: C z Payer : C

Payer B: C Y Payer =: NC z Payer : C

Payer B: NC Y Payer =: C z Payer : C

Payer B: NC Y Payer =: NC z Payer : C


The /ominate .trate$y for ea%h payer is sti to %onfess In Numb3rs2 the (I a$ent p!t a three

%riminas into the same room1 Then2 the mathemati%ian presented ea%h %rimina"s risk fa%tor1 Payer remained indi1 E6en tho!$h ea%h payer"s /ominate .trate$y is to %onfess2 it

sho!d #e %onsidered that some payers may #e more moti6ated to %onfess than others1 And if timin$

matters2 the %rimina with the most to ose may %onfess #efore the others1

But

papakonstantinidis Pa$e @

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n s s sS ××= ...21the set of strate$y pro4es and ))(),......(()( 1 x f x f x f n= is payo< f!n%tion2 i1 e a strate$ypro4e2 #y its pro#a#iity

A%%ordin$ to a#o6e anay8ed NE $

A strate$y pro4e S x ∈* is a )ash #G!ii#ri!m NE if no !niatera de6iation in strate$y #y anysin$e payer is pro4ta#e for that payer2 that is:

),(),(:, ***

: iiiiiiii x x f x x f S xi −− ≥∈∀

irst of a2 in the s!$$ested “in-in-in” eG!ii#ri!m) Comm!nity is the third in6isi#e> party of any #ar$ain #etween two It has a distin$!ished presen%e It aso %aims its 'own) share #y thepro#a#iity

*s!ay2 the $ame is payed #y ha6in$ a the payers sim!taneo!sy pi%k their indi6id!a strate$ies1 Itwi #e !sef! to ima$ine that a payers pi%k their strate$ies at the same time: payer pi%ks some

11 S s ∈ payer = pi%ks some 22 S s ∈ We %an des%ri#e the set of strate$ies %hosen #y the n payersas the ordered tuplen −

This &et of choice& re&ult& in some strate$y pro4e S s∈ whi%h we %a the outcome of the $ame1

Ea%h payer has a set of preferen%es o6er these o!t%omes S s∈ 1 We ass!me that ea%h pla7erL&

preference& over lotterie& o6er S %an #e represented #y some 6on Ne!mann-Dor$enstern !tiity

f!n%tion RS u i →:

At the %on%!sion of the $ame2 then2 ea%h payer I i∈ re%ei6es a pa7oK

iiiii s su su −= ,

The payo< ea%h payer re%ei6es depends not ony on the strate$y she pi%ked #!t aso on the strate$ieswhi%h a the other payers pi%ked1 In other words the payo< to any one payer depends on the entirestrate$y pro4e payed1

SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

In the %ase of

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SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

If the Comm!nity ser6i%es" #ar$ainin$ strate$y is continuou&l7 improving2 then2 in the idea %ase2 i1e in the e6e of the optim!m state #ar$ainin$ ser6i%es2 i1e

02 =ε

In this %ase2 the payo< ea%h payer and the Comm!nity re%ei6es depends not ony on the strate$y theone payer et A> pi%ked #!t aso on the strate$ies whi%h a the other payers (-'C)2 where 'C" theComm!nity> pi%ked1

We"6e ass!med that ea%h pla7erL& preference& over lotterie& o6er S %an #e represented #y

some 6on Ne!mann-Dor$enstern !tiity f!n%tion RS u i →: In other words the payo< to any onepayer depends on the entire strate$y pro4e payed2 #y its %orrespondin$ pro#a#iity payer"spreferen%es o6er otteries>

n

"

B

A

) B A

xU

U

xU

!$ere

U U U

)100(

,

,

−−=

==

As the '

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)1.(..............................)](.....)([ 111im ε =−−∞→

nni. x

x f x f a

=

)2....(),,(),,(:,,, 21*

1

*

1

**

1:11 ε =−∈∀ +−+−+− i"iii"iii"ii x x x f x x x f S x x xi

"asei'eal ...

021 == ε ε

+he a#o6e math reations2 te !s how thet$

i x payer #eha6es2 to win It tes !s2 the payo< that

ea%h payer in%!din$ the Comm!nity> re%ei6es2 depends not ony on strate$y that one payer pi%ked2

#!t aso on the strate$ies whi%h a the other payers in%!din$ the Comm!nity> pi%ked

(!t2 now we %onsider2If2

its#a-enot $as!$i"$)SW Wea-nessStrate&i")o##unitt$eto

'ue s plaer ot$er t$eof strate&ies+est t$eion"onsi'erat inta-in&

!it$out s strate&'e"isiono!n$ista-es plaer &enerall xt$e

t$en

x x x f x x x f S x x xi

t$

i

i"iii"iii"ii

.........),("......."...

),(....................

)..(........,)......(...

)2....(0),,(),,(:,,, 21*

1

*

1

**

1:11 ≠=−∈∀ +−+−+− ε

This means that a .TATE reati6ey weak and ins!O%ient p!#i% ser6i%es" strate$y on '#ar$ainin$se%tor) e$ non-aw-a#idin$ state2 ta5 rates insta#iity stat!s2 et%1> is m!%h easier to prod!%eins!O%ient o!t%omes:

This res!ts in a part of the dea the #est informed #e%a!se of the fai!re of the state to o to take ad6anta$e of this '#ias) for the satisfa%tion of their indi6id!a needs atthe hi$hest e6e2 witho!t %a%!atin$ the %orrespondin$ de$radation of the other payer"s e5pe%tations- &ee )SW

Nowadays it is now 6ery %ommon in pra%ti%e2

We s!pport that2 thet$

i x payer mu&t take his her> own de%ision ha6in$ perfe%t information Yor e6en

no perfe%t information 9ar&an7i4 5ohn : YM=1


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)2....(),,(),,(:,,,

)1(........................................)](......)([

21

*

1

*

1

**

1:11

111im

ε

ε

=−∈∀

=−−

+−+−+−

∞→

i"iii"iii"ii

nni. x


x f x f a

Now2 there are %om#inations2 e5pressed the fo!r > aternati6e 6ersions:

1ε

2ε

0,0 0,0≠0,0 ≠ 0,0 ≠≠

are e5a%ty the payo

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)2.......(0),,(),,(:,,,

)1(..................................................0)](......)([

21

*

1

*

1

**

1:11

11im

≠=−∈∀

=−−

+−+−+−

∞→

ε i"iii"iii"ii

nni. x


x f x f a

rom the a#o6e theoreti%a de4nitions2 pa7oK re;e%ts the desira#iity of an outcome to a payer2 forwhate6er reason1 When the o!t%ome is random2 payo shows that the 4na res!t o!t%ome> for the t$i payer %oin%ides with his e5pe%tedpayo

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B1

0

0

2

1

=

≠

ε

ε

)2.......(0),,(),,(:,,,

)1...(........................................0)](......)([

21

*

1

*

1

**

1:11

111im

==−∈∀

≠=−−

+−+−+−

∞→

ε

ε

i"iii"iii"ii

nni. x


x f x f a

Reation > shows that the 4na res!t for the t$i payer does not %oin%ides with the e5pe%ted ret!rns

rom eG!ation => that the Comm!nity has spent eG!a reso!r%es to a%hie6e eG!a res!t of terms of the Comm!nity e5pendit!re for the sta#iity of #ar$ainin$ 'poi%y) .o from > and => that atho!$h

the odds of the t$i payer %oin%ide with his e5pe%tations2 #!t this was a oss in other areas of poi%y2 iemore %osts than it reay deser6ed this res!t

1

0

0

2

1

≠

≠

ε

ε

)2.......(0),,(),,(:,,,

)1...(........................................0)](......)([

21

*

1

*

1

**

1:11

111im

≠=−∈∀

≠=−−

+−+−+−

∞→

ε

ε

i"iii"iii"ii

nni. x


x f x f a

Th

e worst res!t2 %omin$ from the worst %om#ination

Neither #ar$ainers are satis4ed nor Comm!nity spends eno!$h reso!r%es2 to impro6e the poi%y of thesta#iity of '#ar$ains) This sit!ation is !s!ay2 in nowadays

'A$ent of *tate Pop!ation)

0et now %onsider the prime

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Here )(γ pU %an #e 6iewed as the pro4t that the *tate the Comm!nity2 with its .er6i%es> makes in

'sein$) the safety and its ser6i%es2 to the Citi8ens in ne$otiations with another or with G!aity #*+to the CITIEN with2 a 'e6e of a%%epted state Spoiti%a #ar$ainin$ ser6i%es) γ

)())(,()( γ γ γ γ t * & U a −=

0et:

)(........................ s f uei profile strate&i"of fun"tionaisu Paoff iii =

We ha6e to ma5imi8e the o#Qe%ti6e- f!n%tion2 i1 e the payo< f!n%tion2 whi%h is the 'in%enti6e) or themoti6ation for startin$ the #ar$ain with another person

In this frame2 Comm!nity- the 'C) payer2 m!st parti%ipate with its 'own) e5pe%tations2 its )own)payo< f!n%tion and its own strate$i% pro4e

.o we ha6e2

},..2,..1{........0

)....,(..max..:...max 21

n x x

( x p

x x xU fun"tionUtilit

ii

ii

n

∈∀≥

≤∑

PA:#+( #DD,

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3,2,1)....,,(),,(:,

},...2,1{,.....0

,,...

).....(.max:....max

.,..........

,

*

3

*

21

**

1

*

1

21

=≥∈∀

=∀≥

==≤

===+−

∑

i x x x f x x x f S xi

T$en

ni x

strate&ies xies pro+a+ilit p ( x p

x x xU Fun"tionUtilit

ei Effi"ien" Paretot$eion"onsi'erat inta-in&

Generall

iiii"iiiii

i

iiii

n

In the %ase that 'Comm!nity) pays roe2 of the third payer ony> in the '$ame) :

fun"tion paoff x f u

profile strate& x

x x x f x x x f x x x f x x x f S xi

(O%EL NTINI%IS PAPA2ONSTAWIN WIN WIN

iii

i

"i) iii) iii) iiiiii

..)(

..

),,(),,.(),..,(),,(:,

.....

21

*

111

*

1

**

1

*

1

==

=

≥≥≥∈∀

−−

+−+−=+−

),,(),,.(),..,(),,(:,

....

21

*

111

*

1

**

1

*

1 "i) iii) iii) iiiiii x x x f x x x f x x x f x x x f S xi

( E1UILIBRIU (O%EL NTINI%IS PAPA2ONSTAWIN WIN WIN

≥≥≥∈∀

−−

+−+−=+−

fun"tion paoff x f uan' profile strate& x iiii ....)(....... ===

'XX11It is a %ontri#!tion in .o%ia .%ien%e Theory: (y introd!%in$ the third poe Comm!nity> in any#ar$ain #etween two payers in a $ame thro!$h the sensiti8ation pro%ess> this mode %ontri#!tes in

#eha6iora .%ien%es1 It forms the patform of a '.o%ia Tr!st) %reation2 eadin$ to .o%ia Cohesion at0o%a 0e6e2 at east>KLXXX) I.A>

KL in - in - in Papakonstantinidis mode has #een %hara%teri8ed as a new Theory in .o%ia.%ien%es in many %o!ntries1 It has #een transated in H!n$arian an$!a$e1 It has #een a%%epted inIndia2 Phiippines2 (an$adesh2 .o!th Afri%a /!r#an> as we as in Word r$ani8ation2 as for e5ampe#y the Internationa .o%ioo$i%a Asso%iation I1.1A> as it prod!%es a new '#ar$ainin$ phiosophy) As ithas #een written2 as a %omment: 'it is interestin$ to note any feed#a%k to s!%h a mode2 that is openand ;e5i#e to reforms2 ha6in$ as prin%ipe the third 'win) that is disseminated to a fa%tors of o%aso%ia Y I.A2 R& =L

papakonstantinidis Pa$e M

8/17/2019 2016 the NEW+ 04 28

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*,!),D,:

Ta#e : .ee%ti6e 6iew of the internationa iterat!re #y $ro!ped dis%ipines>

#conomic& *ociolog7 :uraldevelopment?:ural

touri&m managementand development

'noledgemanagement and

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M2 -L=1Nash2 F1 1>1 Non%ooperati6e$ames1 AnnasofDathemati%s22 =ML-=1Nash2 F1 1@>1EG!ii#ri!mpoints in n-person $ames1Pro%eedin$s of the NationaA%ademy of

.%ien%es1Nash2 F1 1B>1 Two-person%ooperati6e$ames1E%onometri%a2=2 =M-@Ne!man 6on> Dor$ensternK> '&ame Theory andE%onomi%(eha6ior) Y The Prin%eton*ni6ersityPress *1 .Harsanyi2 F1LK2No6em#er>1&ames within%ompeteinformation2payed #y(ayesianpayers1Contri#!tionNo#e >Dana$ement.%ien%e2 B>1,!hn2 H1 W12

• Coeman FMM> '.o%iaCapita in theCreation ofH!man Capita)

Ameri%an Fo!rna of.o%ioo$y .!ppement -.=@ Chi%a$o*ni6ersity

• We#er2 Da51MS1'The Nations.tate andE%onomi% Poi%yrei#!r$Address>) inWe#er: Poiti%aWritin$s.

ed1Strans1 P10assman and R1.peirs1Cam#rid$e:Cam#rid$e*ni6ersityPress1

• Arnstein2 .herry R1L> 7A 0adder of Citi8enParti%ipation27 Fo!rna of the

Ameri%a Pannin$Asso%iation- FAIP2Vo1 B2 No1 2

• riedmann F andWea6er C K>'Territory and!n%tion: TheE6o!tion ofRe$iona Pannin$*ni6ersity ofCaifornia Press)*1C101A Press *1.>(erkey and 0osAn$ees Caifornia

• Papakonstantinidis

01A =@@B> 'R!ra To!rism: 'Win-Win-Win)Fo!rna ofHospitaity and To!rism Vo!me 2iss!e =2 S=@@B pp-K@2 IN/IA I..N@K=-KKMKwww1Qohat1%om

• ,okossis Charis anda1 =@@=>'.!staina#e R!ra To!rism) Papa8issisEd2 &ree%e trns2 p1pB==-B=

•

(r!$$er E ML3Endo$eno!s/e6eopment: a%on%ept #etween!topia and reaity)

• Di&cher"anfred "/200 ,nowed$e2%ompe5ity2 and

inno6ationsystems Fo!rnaof &eo$raphi%a.ystems =@@L>Edition:.prin$er-Vera$(erin andHeide#er$&m#H Co1 ,&

• Papakonstantinidis 01A =@@>',nowed$eCreation andthe win-win-winmode).%ienti4%

Re6iew ofAppiedE%onomi%s TEIPI Ed2 Fan=@@

.pais2 &12Papakonstantinidis2 01andPapakonstantinidis2 .1=@@> 3An inno6ati6e

#ar$ainin$ so!tionanaysis for 6erti%a%ooperati6epromotionmana$ementde%isions"2 InnovativeMarketing2 Vo1 2 No1B2 pp1KY=1

.pais2 &1andPapakonstantinidis2 01=@> 3An appi%ationof the win-win-winPapakonstantinidismode as aninno6ati6e #ar$ainin$

so!tion anaysis in%ooperati6e saespromotion%ampai$ns"2ro!ee"ings o# t$e%t$ Annual &urome"'on#eren!e o# t$e&urome" A!a"em o#usiness2 pp1K=YK1

• .pais2 &1 =@=> 3Aninte$rated #ar$ainin$so!tion anaysis for6erti%a %ooperati6esaes promotion%ampai$ns #ased on

the win-win-winPapakonstantinidismode"2 Journal o# A**lie" usiness+esear!$2 Vo1 =M2 No1B2 pp1BYBMB1

• Papakonstantinidis=@=> The win-win-winPapakonstantinidismode -A #eha6ioraanaysis in dynami%asystems The NonInstr!mentaRationaity Parado5Case-st!dy: Heeni%

• Pa6o6I6an P1=K> Conditioned

Re;e5es:AnIn6esti$ation of thePhysioo$i%aA%ti6ity of theCere#raCorte5) Transated #y &1 V1Anrep=K>5ford*ni6ersity

Press0N/N

•


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( ) )..........(0'**........

max**

3EROof nei+or$oo' inor U BU +e#ust t$is for

U U U U U U

) B A

) B AG B A

===∩∩

.....

)...(..

......

..,...

..

.....

..

......

,......

),(,(

2

fro# paoff

'eS T$us

+'enoteWe

for Besi'es

foS xS"

&ivenan For

xS !$ere

of set finitea

N set a!it$

pS N G

i

. " .

i

ii

∈

−

∆

=

=

=

+he +rinomial i&tributionConsider a seG!en%e of n independent trias of an e5periment1 The #inomia distri#!tion arises if ea%htria %an res!t in 2 o!t%omes2 s!%%ess or fai!re2 with 45ed pro#a#iity of s!%%ess p at ea%h tria1 If X

%o!nts the n!m#er of s!%%esses2 then );..( pn Bino#ial X ≈

Now s!ppose that at ea%h tria there are B possi#iities2 say 's!%%ess)2 'fai!re)2 or 'neither) of the two2 with %orrespondin$ pro#a#iities θ θ −− p p 1,...,.. whi%h are the same for a trias1If we write neit$er for an' failure for su""ess for ..,..1..,....,..0,....,..1 − then theo!t%ome of n trias %an #e des%ri#ed as a seG!en%e of n n!m#ers:

)1...0,..1...........).....( 2,..1 −= valuesta-esiea"$!$ereiii .nω

#6io!sy2 θ θ −−=−===== pi P i P pi P . . . 1)1(,...)0(,......)1(

e8nition /1 0et X #e the n!m#er of trias where 1 o%%!rs2 and Y #e the n!m#er of trias where and0 o%%!rs1 The Qoint distri#!tion of the pair / X, Y is %aed the trinomia distri#!tion1

e8nition /2 .!ppose we repeat an e5periment n independent times2 with ea%h e5perimentendin$ in one of three m!t!ay e5%!si6e and e5ha!sti6e ways s!%%ess2 4rst kind of fai!re2 se%ondkind of fai!re

,f we et X denote the n!m#er of times the e5periment res!ts in a s!%%ess2 et Y denote then!m#er of times the e5perimen

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