93 Views

Download Presentation
## GAME THEORY AND APPLICATIONS

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

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