哈佛博弈论课件section9.ppt

Section 9: Redux Alexis Diamond adiamond@fas.harvard.edu Outline Overview of equilibrium concepts so far Example of perfect Bayesian equilibrium Example of monetary policy (see handout from last section) Theories of delegation Time-consistency Overview Nash Equilibrium Mixed-strategy Nash Equilibrium Subgame Perfect Equilibrium Bayesian Equilibrium Perfect Bayesian Equilibrium Key Terms Equilibrium path: a node to node path observed in equilibrium A strategy off the equilibrium path is never observed Any branch on which there is positive support (probability) for play forms part of the equilibrium path There may be multiple equilibrium paths if there are multiple equilibria In Nash equilibrium, the credibility of best responses judged along equilibrium path; off the path, NE may include incredible strategies In subgame perfect NE, best replies are judged in every subgame In perfect Bayesian equilibrium, best replies judged at each information set Beliefs: a probability distribution for a particular information set In mixed-strategy NE, a belief is a probability distribution over the nodes in the other player’s information set In Bayes Nash equilibrium, a belief is a probability distribution over the nodes in nature’s information set and the corresponding type of other player In perfect Bayesian equilibrium, a belief is a probability distribution over the nodes in one’s own information set. Nash Equilibrium A strategy profile S is a Nash equilibrium if and only if each player is a playing a best response to the strategies of the other players A strategy profile S is a strict Nash equilibrium if and only if each player’s strategy is the single best-response to the strategies of the other players Note that there is no strategic uncertainty Each player’s belief about another’s strategy is concentrated on actual strategy the other player uses Mixed-Strategy Nash Equilibrium A mixed-strategy Nash equilibrium is a mixed-strategy profile whereby each player is playing a be