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Chapter 11 Game Theory and Strategic Behavior

Topics to be Discussed

Gaming and Strategic Decisions

Dominant Strategies

The Nash Equilibrium Repeated Games

Maximin Strategy

Sequential Games : Moving irst !dvantage " GR!D#!TES $N%& '

Gaming and Strategic Decisions

(If I believe that my competitors are rational and act to maximize their ownprofits, how should I take their behavior into account when making my own profit

maximizing decisions!"

Noncooperative versus )ooperative Games

* Noncooperative Game+ Negotiation and en,orcement o, a binding contract are not possible

* Example:* )ooperative Game

+ -layers negotiate binding contracts that allo. them to plan /oint strategies

* Example: 0uyer and seller negotiating the price o, a good or service or a /ointventure by t.o ,irms "i1e1 Microso,t and !pple'

* 0inding contracts are possible

Gaming and Strategic Decisions

!n Example

2' !uction a dollar bill3' 4ighest bidder receives the dollar in return ,or the amount bid5' Second highest bidder must pay the amount he or she bid

6' 4o. much .ould you bid7

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Dominant Strategies

! and 0 are competitors and are deciding .hether or not to advertise1

* irm ! :Dominant strategy is to advertise

* irm 0 : Dominant strategy is to advertise

* $utcome : 0oth advertise

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#odified $dvertising Game

The outcome .ithout a dominant strategy ,or each ,irm is slightly di,,erent1

Dominant Strategies

$bservations2' ! has no dominant strategy1

3' 0 has a dominant strategy "advertise'1

* Should ! choose to advertise7* 8s this a Nash equilibrium7

The Nash Equilibrium Dominant Strategies* (89m doing the best 8 can no matter what you do%"

* (&ou9re doing the best you can no matter what I do%"

Nash Equilibrium* (89m doing the best 8 cangiven what you are doing"

* (&ou9re doing the best you cangiven what I am doing%"

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&roduct 'hoice &roblem

Examples ith ! Nash Equilibrium* T.o cereal companies* Mar;et ,or one producer o, crispy cereal

* Mar;et ,or one producer o, s.eet cereal

* Each ,irm only has the resources to introduce on cereal* Noncooperative

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(each )ocation Game

Scenario* T.o competitors= & and )= selling so,t drin;s* 0each 3>> yards long

* Sunbathers are spread evenly along the beach

* -rice & ? -rice )(each )ocation Game

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#aximin Strategy

)onsider

* 8, both are rational and in,ormed

+ hat is -layer 39s dominant strategy7

+ hat is the Nash equilibrium7 Maximin Strategy* Maximi@es the minimum gain that can be earned

#aximin Strategy

)onsider

* 8, -layer 3 is not rational or completely in,ormed

+ hat .ould be -layer 29s maximin strategy7

+ hat .ould be -layer 39s maximin strategy7

+ 8, 2 ;no.s 3 is using a maximin strategy= .hat outcome .ould 2 choose7

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&risoners* Dilemma

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#ixed Stragegies

-ure Strategies* Strategies in .hich player ma;e a speci,ic choice or ta;e a speci,ic action "e1g1advertise or do not advertise'

-ure strategy .ill not succeed ,or either player and there is not a Nash

equilibrium1 Mixed Strategies

* Strategies in .hich the player ma;es a random choice among t.o or more

possible actions= based on a set o, chosen probabilities1* Random choice is a Nash equilibrium because i, any other choice is made there is

an incentive ,or the other player to change1

* !pplications o, mixed strategy are very limited and o,ten unrealistic1

Pareto Efficient

An allocation is Pareto Efficient if goods cannot be reallocated to make

someone better off without making someone else worse off.

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+epeated Games

8n real li,e= ,irms play a repeated game%

ith each repetition o, the -risoners9 Dilemma= ,irms can develop reputationsabout their behavior and study the behavior o, their competitors1

8n a nonArepeated game the strategy is %o.2and %o.31

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Sequential Games !G"#$%#TES &N'()

-layers move in turn

-layers must thin; through the possible actions and rational reactions o, eachplayer

Examples

* Stac;elberg Model* Responding to a competitor9s ad campaign

Scenario* T.o ne. "s.eet= crispy' cereals

* Success,ul only i, each ,irm produces one cereal

* S.eet .ill sell better* 0oth still pro,itable .ith only one producer

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