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Game Theory

Autor:   •  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

strategyDeviating 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 > DCheating 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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