Assoc. Prof. Yeşim Kuştepeli1 GAME THEORY AND APPLICATIONS DOMINANT STRATEGY

Assoc. Prof. Yeşim Kuştepeli2 Static Game with Pure strategies strictly dominates strictly higher payoffDominant strategy: Strategy S1 strictly dominates S2 for a player if given any collection of strategies that could be played by the other players, playing S1 results in a strictly higher payoff for that player than playing S2. strictly dominatedS2 is said to be strictly dominated by S1. strictly dominant strategyequilibriumThe strategy profile {S1, S2, ….} is a strictly dominant strategy equilibrium if for every player i, Si is a strictly dominant strategy.

Assoc. Prof. Yeşim Kuştepeli3 weakly dominates lower payoff strictly higher payoffWeakly Dominant strategy: Strategy S1 weakly dominates S2 for a player if given any collection of strategies that could be played by the other players, playing S1 never results in a lower payoff for that player than playing S2 and in at least one instance S1 gives the player a strictly higher payoff than does S2. weakly dominatedS2 is said to be weakly dominated by S1. weakly dominant strategyequilibriumThe strategy profile {S1, S2, ….} is a weakly dominant strategy equilibrium if for every player i, Si is a weakly dominant strategy.

Assoc. Prof. Yeşim Kuştepeli4 iterated strictly dominant strategyIterated Dominant strategy: Strategy S1 is an iterated strictly dominant strategy for a player if and only if it is the only strategy in the intersection of the following sequence of rested sets of strategies: 1) Si,1 consists of all of player i’s strategies that are not strictly dominated 2) for n>1 Si,n consists of strategies in Si,n-1 that are not strictly dominated when we restrict the other players to the strategies in Sj,n-1. iterated strictly dominant strategyequilibriumThe strategy profile {S1, S2, ….Sn} is an iterated strictly dominant strategy equilibrium if for every player i, Si is a iterated strictly dominant strategy.

Assoc. Prof. Yeşim Kuştepeli5 A Nash equilibrium is a strategy profile {S1*, S2*, ….Sn*} such that each strategy Si* is an element of set of possible strategies and maximixes the function fi(x)= vi(Si*, …..Si-1*, x, Si+1*, …..Sn*) among the elements of the possible strategy set. At a Nash equilibirum, each player’s equilibrium strategy is a best-response to the belief that the other players will adopt their Nash equilibirum strategies.

Assoc. Prof. Yeşim Kuştepeli6 Russia USA disarmrearm disarm(10,10)(-10,50) rearm(50,-10)(0,0)

Assoc. Prof. Yeşim Kuştepeli7 Pl.2 Pl.1 narrowwide narrow(14,14)(0,16) wide(16,0)(0,0)

Assoc. Prof. Yeşim Kuştepeli8 Pl.2 Pl.1 Don’t drill narrowwide Don’t drill (0,0)(0,44)(0,31) narrow(44,0)(14,14)(-1,16) wide(31,0)(16,-1)(1,1)