Game Theory

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