# Game Theory

Autor: faithneo • March 8, 2017 • Course Note • 727 Words (3 Pages) • 411 Views

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EC3101 – Game Theory

∙ Game Theory Basics

o Strategic interaction involves many players & many outcomes but analysis will

be limited to 2 player games with a finite number of choices

o This allows the outcomes of the games to be depicted easily in a payoff matrix o A dominant strategy is an optimal strategy for a particular player no matter

what the other player does

o If a dominant strategy for each player exists, then it is the equilibrium

outcome of the game

o Common Assumptions in Analysis

▪ All players are rational & know everyone is rational

▪ All players know the game’s structure & know everyone knows that ∙ Nash Equilibrium

o Dominant strategies do not occur very often

o An equilibrium choice of strategies for player A may be optimal for the

optimal choices for player B

o Thus, a Nash equilibrium consists of a pair of strategies where A’s choice is

optimal given B’s choice & B’s choice is optimal given A’s choice

o At a Nash equilibrium, no player has an incentive to deviate to another

strategy→Deviating will result in a less optimal outcome for the deviator o Problems: More than 1 Nash equilibrium or none at all may exist

∙ Mixed Strategies

o Thus far, analysis has been about players only choosing 1 strategy

o However, it is also possible for players to adopt a mixed strategy by assigning

probabilities to each choice & playing their choices according to those o In mixed strategies, there will always exist a Nash equilibrium

∙ Simultaneous Games

o The Prisoner’s Dilemma

- ▪ ▪For a game to be a prisoner’s dilemma, outcomes must be:

- ∙ A: Cheat, B: Cheat (C, C); A: Cheat, B: Cooperate (A, D); A: Cooperate, B: Cheat (D, A); A: Cooperate, B: Cooperate (B, B)
- ∙ Where A > B > C > D→Cheating is a strictly dominant strategy

for all players but it is socially optimal to cooperate

- ▪ ▪Unique Nash equilibrium (& dominant strategy) is for both players to

confess even though they would both be better off not doing so

- ▪ ▪This results as both players are unable to coordinate their actions &

rational analysis points to adopting the dominant strategy

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