Mechanism Design

A social choice function: A function that determines a social choice according to players’ preferences over the different possible alternatives. A mechanism: a game in incomplete information, in which player strategies are based on their private preferences. A mechanism implements a social choice function f if the equilibrium strategies yield an outcome that coincides with f . Dominant strategies: An equilibrium concept where the strategy of each player maximizes her utility, no matter what strategies the other players choose. Bayesian-Nash equilibrium: An equilibrium concept that requires the strategy of each player to maximize the expected utility of the player, where the expectation is taken over the types of the other players. VCG mechanisms: A family of mechanisms that implement in dominant strategies the social choice function that maximizes the social welfare.