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GAME THEORY AND APPLICATIONS

GAME THEORY AND APPLICATIONS. DOMINANT STRATEGY. Static Game with Pure strategies

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GAME THEORY AND APPLICATIONS

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  1. GAME THEORY AND APPLICATIONS DOMINANT STRATEGY Prof. Dr. Yeşim Kuştepeli

  2. Static Game with Pure strategies • Dominant 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. • S2 is said to be strictly dominated by S1. • The strategy profile {S1, S2, ….} is a strictly dominant strategyequilibrium if for every player i, Si is a strictly dominant strategy. Prof. Dr. Yeşim Kuştepeli

  3. Weakly 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. • S2 is said to be weakly dominated by S1. • The strategy profile {S1, S2, ….} is a weakly dominant strategyequilibrium if for every player i, Si is a weakly dominant strategy. Prof. Dr. Yeşim Kuştepeli

  4. Iterated 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. • The strategy profile {S1, S2, ….Sn} is an iterated strictly dominant strategyequilibrium if for every player i, Si is a iterated strictly dominant strategy. Prof. Dr. Yeşim Kuştepeli

  5. 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. Prof. Dr. Yeşim Kuştepeli

  6. Prof. Dr. Yeşim Kuştepeli

  7. Prof. Dr. Yeşim Kuştepeli

  8. Prof. Dr. Yeşim Kuştepeli

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