Game Theory
EC3101 – Game Theory ∙ Game Theory Basicso Strategic interaction involves many players & many outcomes but analysis will be limited to 2 player games with a finite number of choiceso 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 doeso If a dominant strategy for each player exists, then it is the equilibrium outcome of the gameo 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 ofteno An equilibrium choice of strategies for player A may be optimal for the optimal choices for player Bo 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 choiceo 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 Strategieso Thus far, analysis has been about players only choosing 1 strategyo 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 Gameso 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