Munich Personal RePEc Archive

Landscape in the Economy of

Conspicuous Consumptions

Situngkir, Hokky

Bandung Fe Institute

7 May 2010

Online at https://mpra.ub.uni-muenchen.de/22948/

MPRA Paper No. 22948, posted 30 May 2010 06:37 UTC

1

Landscape in the Economy of

Conspicuous Consumpt ions

Hokky Situngkir

[hs@compsoc.bandungfe.net ]

Dept . Computat ional Sociology

Bandung Fe Inst itute

Abstract

Psychological states side by side with the bounded rat ional expectat ions among social agents

contributes to the pat tern of consumpt ions in economic system. One of the psychological states are

the envy – a tendency to emulate any gaps with other agents’ propert ies. The evolut ionary game

theoret ic works on conspicuous consumpt ion are explored by growing the micro-view of economic

agency in lat t ice-based populat ions, the landscape of consumpt ions. The emerged macro-view of

mult iple equilibria is shown in computat ional simulat ive demonstrat ions altogether with the spat ial

clustered agents based upon the emerged agents’ economic profiles.

Keywords: conspicuous consumpt ion, behavioral economics, agent-based simulat ions.

2

Envy is ever joined with the comparing of a man's self;

and where there is no comparison, no envy!

F. Bacon, Sr.

Thou shalt not covet thy neighbor's wife;

thou shalt not covet thy neighbor's house, nor his field ...

nor anything that is thy neighbor's.

the 10th

rule in ten commandments

1. Introduction

There have been broad recent understandings on human economic behaviors outside economic

discourses. Economic decisions are always becoming one of the most complex things in economic

discussions. One of them is the way we choose our pat tern of consumpt ion. It has been a common

understanding that the pat tern of consumpt ion is st rongly related to the social and economic status.

A lot of things are being marketed not only for the funct ionality or degree of necessity solely, but

also related to the profile beneficiaries. M ost luxurious stuffs are placed in the market as a sort of

conspicuous consumpt ion. They are being sold and bought for the need of good reputat ion,

pecuniary st rength and good name of buyers, or social leisure of having more than others. This is

direct ly reflected in our daily urban and highly organized industrial society [19], from the type of

cellular phones, dressings, style and brand, even place of lunch and recreat ion to the luxurious home

living and daily vehicles.

While income is an important measure for social class, the pat tern of consumpt ion is the way to

show other people conspicuously the represented social class. A good and unleashed descript ion of

the relatedness of between consumpt ion is described in [18]. A lot of things are thus, bought in

order to be shown to others. Furthermore, research surveys have also confirmed how social

st rat ificat ion correlated to the cultural consumpt ion [2].

Nonetheless, those are economic phenomena since it has been direct ly related to the concavity of

the supply and demand curves for part icular products in the market , but yet , it is also related to a

deep emot ional and psychological t rait of human species, envy. This is related an interest ing field

related to behavior economics. Inequality has been understood to be one of source of unhappiness

among people (cf. [7]). Furthermore, the interest ing relat ions between inequality with the state of

well-being or happiness are related to the emot ional states of human being. As it has been noted in

[13], emot ions serves an adapt ive role in helping organisms deal with key survival issues posed by

the environment . Emot ional based decision making among economic agents might have been one of

explanat ion to the deviat ion of rat ionality in the sense of convent ional understanding (cf. [10]),

beside the realizat ions on the social boundedness on which rat ional choices must be taken ([16] &

[9]).

Recent economic discussions have int roduced a lot of interest ing discourses related to this. The

evolut ionary game theory as harmonious mixtures between biological studies, economic behavior,

and mathemat ical theories on games [17] has out lined some applicat ions into the recent problems

in economics [5]. One of interest ing points are related to the formalizat ions of the social pat tern

regarding to the game of the conspicuous consumpt ion [4]. The discourse of the evolut ionary game

theoret ic analysis on economic issues, the emot ional based economic decision making as well as the

boundedly rat ional agent based model employment in computat ional analysis are those becoming

main issues mot ivated the paper.

3

The paper is begun with the discussions related to the overview of the mathemat ical models related

to the conspicuous consumpt ions. M ost development of the model has been explored in the fashion

of analyt ically evolut ionary game theoret ic models. Discussions are cont inued to the implementat ion

of the models for wider theoret ical explorat ions by incorporat ing the acquisit ions of computat ional

simulat ions. By the end of the paper, some demonstrat ions of the toy model are presented with

some out lines to some conjectures in further development .

2. Overview of the M odel

The presentat ion of the paper shows lat t ice-based populat ions as landscapes reflect ing the

allocat ions of ordinary and conspicuous expenses by economic agents. As described in [8], the lat t ice

based populat ions, or more generally the neighborhood st ructure usually “ tends to favor the long-

term co-existence of st rategies which would not co-exist in well-mixed populat ions” . This is the

dynamics as once int roduced in [1, 6] and thus implemented in cultural disseminat ion model [12],

and also used as model to discover some dynamical characterist ics in corrupt ion [14]. The plat form

is part icular kinds of agent based model [11] in which we ut ilize as computat ional experiments

media. Another similar previous work related to advert ising could also worth for ment ion [15].

Imagine a landscape where people are represented on lat t ices and grids. Each agent is given the

same amount of money, and it is on their decision to allocate an (0,1]x = amount of the money for

ordinary necessit ies. While the savings and investments are neglected, the 1 x− fract ion of the

money is thus allocated for luxurious expenditures. The later expense is thus becoming the source of

envy among economic agents, things that influence their apprehension on their surroundings and

thus give impact to their decision making. Thus, the expected pay off on each round of the game

thus depends on each agent ’s ordinary consumpt ion ( u ) and her allocat ion of for the conspicuous

consumpt ion (U ),

U cuϕ = + (1)

where 0c ≥ denotes the constant marginal rate subst itut ion. The ordinary consumpt ion can be

stated as a concave ut ility funct ion,

lncu c x= , (2)

and as 0x → we have ϕ → −∞ reflect ing the importance of the ordinary consumpt ion, while the

ut ility funct ion due to ordinary expenses would be ( ,0]cu ∈ −∞ - a fact that no one will completely

neglects the ordinary consumpt ion expect for the limit ing case of 0c = .

The main of the focus in the game is thus the conspicuous consumpt ion: how much is the fract ion

needed to sat isfy the social effect of envy when other surrounding people have more (or less)

fract ion for the conspicuous expenses. An evolut ionary modeling of this has been analyt ically

analyzed by the calculat ing the gradient dynamics in the fashion of cumulat ive dist ribut ion of

funct ion [4].

Our approach in the paper is related to the implementat ion of the models showing the economic

behavior as pointed out in [19] as consumpt ions of the excellent goods that is socially related to the

evidence of wealth. In this game, if an economic agent compare her allocated expenses for excellent

goods is bigger than other, she would be in the psychological state of envy – a thing that mot ivates

her to allocate bigger consumpt ion if they interact again in the future. This envy however must be

constrained due to her allocat ion of ordinary consumpt ion which is a necessity and cannot be

4

nullif ied. Here, when an agent allocates a fract ion of x to the ordinary consumpt ion (thus allocate a

fract ion of (1 )x− for conspicuous one) and find out that other agent that interacts with her pay the

fract ion of y x< for the same respect ive expenditures (thus (1 )y− for excellent goods), then she

will have disut ility in the proport ion of

( , ) min{0, ( )}r x y y x= − (3)

In the analyt ical model as proposed by [4], the payoff can be writ ten,

1

0 0 0

( , ) ( , ) ( ) ( ) ( ) ( )

x x

U x D r x y dD y y x dD y D y dy= = − = −∫ ∫ ∫ (4)

where ( )D y is the cumulat ive dist ribut ion funct ion of other’s decision on the fract ion to the

ordinary consumpt ion and give us a consequence to the total payoff of an agent ,

0

( , ) ln ( )

x

x D c x D y dyϕ = − ∫ . (5)

It is easy to see that that in the limit ing case

0

( ) 0

x

D y dy =∫ , a corresponding agent that allocates

sufficient ly small amount of x for ordinary consumpt ion gets the maximum payoff related to her

envy to others. The gradient dynamics, on which agents adjust the value of x is.

( )x

cD x

x x

ϕϕ ∂ = −∂

@ (6)

Figure 1. The landscape of allocat ion for ordinary consumpt ion

after the rule of envy is implemented for T=250 rounds

3. Experiments with spatially-bounded agents

A numerical simulat ions is conducted in [5] in order to see the possible stable equilibria of the

problems by a discret izat ion of equat ion (5) in such a way,

5

1 1

1ln ln

N N

i i

i i

c x F x c x FN

ϕ= =

= − ∆ = −∑ ∑ (7)

With the gradient as analyt ically shown in eq. (6),

n n

n

cF

xϕ = − (8)

where i

F denotes the cumulat ive dist ribut ion funct ion obtained from the numerical integrat ion of

the probability measure i

f in the i -th interval among

1

N

i i

k

F f x=

= ∆∑ (9)

as i

f is the average density of M number consumers with st rategies divided in x∆ equal N

number of intervals, as to 1

xN

∆ = . Consequent ly, we have 0

( ) 0F x = and ( ) 1N

F x = , a sort of

rank among whole agents – from which the name rank dependent consumpt ion came from.

When the focus of our at tent ion is the mult iple equilibria, this approach has given interest ing

results. Yet , another perspect ive can also be offered related to the economic agent ’s boundedness

related to the conspicuous consumpt ion. In reality, the people are “ t rapped” in social surroundings

in which envy and vanity is sourced upon cognit ively. People do not have to compare his

expenditures with those he would only “ meet” on television, but people that are socially related to

them.

Figure 2. Different average equilibra at different values of c.

Thus,

cells or

view is mor

the ri

neighb

total n

the se

as,

( ,i jϕ

where

neighb

On an

( ,x i j t

where

consu

payoff

her nei

s, we t ransform

or square

is more lik

right grid

hborhood

l neighbors,

set of st rat

, , ) lni j t c=

re N

xυ

is

hbors, inde

any

, , 1)i j t + =

re (N N

x iυ υ

' ‹“ ›« fi

sumpt ion.

ayoff is larger

r neighbors’

nsform the

are lat t ices

like a torus

grids with t

d (with conn

ors, [ ]Nυ =t rategies x

[ln ( , ,c x i j t=

is the decis

ndexed as N

+ =

( ,x i

(x i' ‹“ ›« fi

( , , )N N

i j tυ υ

' ‹“ ›« fi

n. Thus, an

er than the

ors’ decision

the discret iz

s located at

torus: the low

the left

connect ions

8= ). In e

(0, ]x ∈ ∞

] 1, )

N

j tλ

= + −∑

cision of n

{1,2Nυ =

), , , (i j t iϕ ϕ

( , , )N N

x i j tυ υ

' ‹“ ›« fi

, )N

j tυ

' ‹“ ›« fi is th

an agent wo

the average

ons for ordi

Fig

t izat ion as

d at a two

lowest two

ft one. T

ns betwee

each t ime

, ]∈ ∞ and as an

) ( , ,N

t x i jυ

+ − ∑

neighbors

1,2,...,8} , t

( , , )i j tϕ ϕ< ' ‹“ ›« fi

, ) , N

t othυ

' ‹“ ›« fi

the averag

t would sta

age payoff of

rdinary con

Figure 3. Ag

as suggeste

two-dimensio

st two-dimensio

The myop

een nearest

me step t T

an adaptat

, , ) ( N Nj t x i + −

ors for ordi

, that has ma

) ( ,N N

t i j tυ υ

ϕ ϕ< ' ‹“ ›« fi

otherwise

rage of the

stay with t

ayoff of her nei

ary consumpt ion

Agents’ equili

sted in eq.

sional virtu

sional grids ar

myopic agen

arest and ne

1, 2,...,t T=tat ion of eq.

( , )N Ni j tυ υ

rdinary con

as made the

, , )N N

Nj t

υ υυ

' ‹“ ›« fi

se

the averag

the same

eighbors a

ion otherw

ents’ equilibrium po

q. (7) into r

rtual world

ids are past

ents evaluat

next -nearest

...,t T , every

eq. (1), (3)

, )

consumpt ion

he respect i

' ‹“ ›« fi

verage deci

same fract ion

ors and chang

rwise.

rium points for c=

representat

world of ,i j L=asted toget

luate their

rest neighb

ry agent ev

(3) and (4),

(10)

ion and λct ive agent

(11)

ecision of

ion of ordi

nge her de

c=0.1

ntat ion of

, 1,...,j L=

ether with t

eir payoffs

hbors, thus

evaluates

), we can wr

10)

λ denotes

nt envious,

11)

of neighbors

ordinary con

decision into

of agents p

while the

th the highe

ayoffs in the

hus each ag

s her payoff

n write the

tes the num

s, ( )x t y t<

bors for or

onsumpt ion

into the ave

6

placed in

the global

ghest , and

e M oore

agent has

ayoff from

he pay off

number of

) ( )N

y tυ

< .

ordinary

ion if her

average of

n

al

nd

e

s

m

off

of

y

er

of

4. Computational Experiments

From

among

condu

simulat

consu

strate

averag

subst i

consu

One of

social

interv

for cequilib

higher a

Intere

end of

higher

agents),

becom

. Computational Experiments

From the mod

ng agents

nducted in

ulat ive proc

sumpt ion a

st rategies for mor

rage allocat

st itut ion ( csumpt ion s

of interest

ial classes.

rvals in wh

0.1c = is s

ilibrium po

er and low

rest ingly, t

of rounds

er allocat io

nts), while

come a uniqu

. Computational Experiments

model, we ca

ts due to th

n square lat t

rocess is s

and thus aft

for more. The

ocat ion of or

c ). It is cle

should be

Figure 4. T

est ing thing

s. It is wort

hich agents

is shown in

point near

ower profile

y, this can a

nds of simulat

cat ion for or

ile most of

unique prop

. Computational Experiments

can do co

their alloca

lat t ices o

s shown in

s after rou

he not -cha

ordinary c

clear that

be allocated.

The emergen

ing that we

orth to note

ents stop ch

in figure 3.

ar the value

rofile agents. T

also be vis

ulat ion, it i

ordinary co

of agents ar

operty that

computat i

llocat ions of

of 30L = in figure

rounds of sim

hanging stat

ary consumpt

at the high

ated.

rgence of so

shows

we can lear

ote that th

changing t

3. However,

lue of the a

ts. Thus, the

visualized a

it is obvious

consumpt i

ts are in the

at we coul

tat ional exp

of ordinary

30 for Te 1: the in

simulat ion

states refle

pt ion as sh

gher the va

f social class

s the high, l

arn from o

the averag

g their allocat

ever, it is inte

he average a

the equilibr

d as the clu

us that the

pt ion (i.e.:

the state of

uld have g

xperiments

ary and con

250T = ro

init ial rand

on stay at e

flect the equ

shown in f

value of c

cial class: the allocat i

gh, low profile agents.

our simulat

rage value

locat ion for

nterest ing to

e as some l

ilibria is show

clustered ag

there are som

.e.: lower prof

of medium

gained from

nts that wo

conspicuous

rounds of

random cond

at equilibria

equilibrium

n figure 2 for

c , the mor

the allocat ion for o

file agents.

ulat ion is t

e as shown

for ordinary

g to see that

e less agen

own to be

agents spat

some clust

rofile agen

ium class of

from the com

would reve

us consump

of games

condit ion of

ria when age

um and can

2 for variou

more fract io

r ordinary c

s the emerge

wn in figur

ary consum

that most of

ents are kee

e in a kind

spat ially as

lustered age

ents), lowe

of ordinary

computat

eveal the u

umpt ions. O

s with var

of allocat

agents do n

can be seen

ious value

fract ion of incom

dinary consumpt i

ergence of

ure 2 cam

umpt ion. O

most of agents

keeping th

nd of interv

as shown in

agents to b

ower one (i.e.

ary consum

tat ional age

Cluster

Clusters

unique equ

. Our simul

ariable c =ocat ion to or

o not chan

een on the co

ue of margi

ncome to or

nsumpt ion

of spat ially

came from a

One of the

ts are findi

their statu

rval.

in figure 4

be in the

i.e.: higher

sumpt ion. T

agent-based

usters of lower

usters of highe

7

equilibria

ulat ion is

.1c = . The

ordinary

ange their

e constant

marginal rate

to ordinary

lly located

a sort of

he results

nding their

status as the

4. At the

e state of

er profile

n. This has

ed model

ower profile

gher profile

ia

is

e

ary

eir

t

e

y

ed

of

eir

e

e

of

le

as

del

ile

from t

of eco

consu

and low

From

lucky

are se

accum

consu

locat io

in suc

our sim

accum

throug

the model

economic c

sumpt ion in

lower prof

From our simu

cky enough t

set or at le

umulated p

sumpt ions.

ocat ions filled

uch ways e

simulat ion

umulated p

ughout the

among agents

del as int ro

c classes b

in the stat

rofile agents amo

Figure 5.

mulat ion, w

h that they

at least they

payoff rel

s. Obvious

lled with suc

ys emerging

ons. Those

payoffs t

the spat ial l

Fig

ng agents thro

high pay off

low pay off

t roduced in

based du

state of mu

ents among

. The landscape

are filled with agents wh

, we could

ey have alr

ey have ne

relat ively

usly, the e

uch lucky ag

ing the spat

se agents ar

there wo

al landscape

Figure 6. Th

throughout the c

ay off

pay off

in eq. (5) a

due to th

mult iple equ

g the sea of a

e landscape of pay

led with agents wh

ld also obs

already clos

neighbors w

y higher th

emergent

cky agents. Ro

at ially clust

ts are cluste

would be

pe related

The equilibri

ut the computat i

) and (6). Fr

their profile

equilibria:

a of averag

payoff after

ed with agents whose higher accumula

observe som

lose enoug

ors with such

than the

nt spat ial p

Rounds by

lustered ag

stered one

e such gra

ed to the op

equilibrium points as

mputat ional simulat i

). From the

rofile in thei

a: there are

rage profile

ter T=250 ro

se higher accumula

some inter

ugh to the

uch allocat i

e others. F

l pat terns

by rounds i

agents whos

e another

gradat ion.

opt imum a

ints as the at t ract

nal simulat ion.

he big pictu

their allocat

are “ islands”

le persons.

rounds: the darker the

se higher accumulated pay

erest ing as

e equilibri

ocat ions of or

. Figure 5

s are show

s in our sim

hose relat ivel

er and to t

n. This refl

m and best fract

the at t ractors based

on. The inter

cture, there

ocat ion to

nds” repres

s.

the darker the

se higher accumulated payoffs

aspects sp

ria when t

ordinary c

5 shows t

own here.

simulat ions

at ively high

the cluste

eflects the

st fract ion of or

based on en

he interval of the equili

re has bee

to ordinary

esent ing th

the darker the red cells

s.

spat ially. Som

n the random

ary consumpt

ows this in o

e. In the fig

ns they acc

igher payoffs

stered agen

he diffusion

n of ordinary

n envy

f the equilibria is sh

been an eme

ary and lu

the higher

cells

. Some age

ndom init ial

pt ion. Thos

our landsca

figure, dark

accumulate

ayoffs at the

ents whos

ions of st rat

nary consum

ria is shown.

8

mergence

luxurious

er profile

agents are

ializat ions

hose have

ndscape of

arker red

ate payoffs

he end of

ose lower

st rategies

sumpt ion.

wn.

e

s

ile

e

s

ve

f

ed

ayoffs

f

r

s

9

However, the process of the diffusions along the rounds of our computat ional simulat ions can be

seen vaguely in the phase map corresponding to the mapping of ( ) ( 1)x t x t→ + . This is shown in

the figure 6.The random init ializat ion has been at t racted to the intervals of equilibria. This is a sort of

at t ractor of envy. Whatever the init ial st rategies, they will always be at t racted to the intervals as

shown in figure 3, and the equilibrium st rategy decided by agents are thus related direct ly to their

respect ive spat ial posit ions i.e.: in what kind of neighborhood she is placed upon. Thus we have

demonstrated that the evolut ionary processes do not only depend upon the st rategies that are

being used in the games but also the respect ive posit ions of the strategic occupants.

5. Concluding Remarks

We have shown the discussions incorporat ing the computat ional agent based models of the game

on allocat ing ordinary and conspicuous consumpt ions among economic agents. While the task came

from one of the proxy of the evolut ionary (economics) game theory, the presentat ion is based on an

implemented fashion of computat ional simulat ions. The lat ter has been enriched the works on the

boundedness of agents due to the myopic evaluat ions of agents on their neighborhood and some

spat ially emerged facts while macro-view equilibria have been reached over rounds of simulat ions.

An interest ing result is shown related to the varying, yet clustered populat ions and an at t ractor of

envy on the landscape of allocat ions between ordinary and conspicuous consumpt ion. While the size

of the allocat ion for conspicuous consumpt ion is related to the economic profile of agents, it is also

visually shown in 2-dimensional lat t ices the emergence of higher, lower, as well as medium classes

of economic profiles.

While in general the model depicts how emot ional state – in this case, envy – could become a source

of the concavity of the demand funct ion, the promising future works could be conjectured to see

how evolut ionary game theory can be explored for other factors and variables used by agents, e.g.

the development of economic discourse based on psychological behaviors, evolut ionary paradigms

on mult iple equilibria, as well as computer simulat ions as toy models. The further works on this

research inquiries would also be conjectured to the recognit ion of psychological aspects e.g.

happiness or well-being-ness, to the emerging macro-pat tern of economic decisions. This is left for

future work.

Acknowledgement

Author thanks Surya Research Internat ional for the provision of financial support in which period the

paper is writ ten. All fault remains author’s.

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