game theory3 博弈论 英文.pptxVIP

Introduction to Game TheoryLecture 3 ReviewStrict Weak Best Response Mixed Strategy NE SummaryNE - ReviewNash Equilibrium is a concept of a steady state in given situationNo one can unilaterally improve their payoff, therefore no one has incentive to deviate from equilibrium actionNash Equilibrium is an action profile in which every player’s action is best response to every other player’s action/ 43 ReviewStrict Weak Best Response Mixed Strategy NE SummaryNE - ReviewNo player wishes to change her behavior, knowing the other players’ behavior = there are no regretsEquilibrium behavior is based on general knowledge and experience with similar players and situations; not on particular circumstances/ 43 ReviewStrict Weak Best Response Mixed Strategy NE SummaryNE - Review We can find Nash equilibria by: Elimination of strictly dominated strategies “Circle Method”Elimination method is sometimes imprecise, NE (Circle Method, Best responses) is stronger./ 43 ReviewStrict Weak Best Response Mixed Strategy NE SummaryPreviewStrict vs weak dominanceBest response functions (why circles work)Mixed strategies Nash equilibrium/ 43 ReviewStrict WeakBest Response Mixed Strategy NE SummaryStrict vs. Weak Dominance/ 43 ReviewStrict WeakBest Response Mixed Strategy NE SummaryStrict Dominance Definition: player i’s action ai strictly dominates her action bi if ui(ai,a?i)ui(bi,a?i) for every list a?i of the other players’ actions, where ui is a payoff function that represents player i’s preferences Definition: If any action strictly dominates the action bi, we say that bi is strictly dominated/ 43 ReviewStrict WeakBest Response Mixed Strategy NE SummaryWeak Dominance Definition: player i’s action ai weakly dominates her action bi if ui(ai,a?i)≥ui(bi,a?i) for every list a?i of the other players’ actions, where ui is a payoff fun