Deterministic calibration and Nash equilibrium

Deterministic Calibration and Nash Equilibrium

We provide a natural learning process in which the joint frequency of (time-averaged) empirical play converges into the set of convex combinations of Nash equilibria. Furthermore, the actual distribution of players’ actions is close to some (approximate) Nash equilibria on most rounds (on all but a vanishing fraction of the rounds). In this process, all players rationally choose their actions u...

Nash equilibrium

In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or...

Nash Equilibrium and Dynamics

Presented at the Opening Panel of the Conference in Honor of John Nash’s 80th Birthday at Princeton University in June 2008. Updated: October 2010. Center for the Study of Rationality, Institute of Mathematics, and Department of Economics, The Hebrew University of Jerusalem. e-mail : [email protected] web page: http://www.ma.huji.ac.il/hart I have seen “nash equilibrium” in print, as if “nash” we...

Nash Equilibrium and Mechanism Design

Nash Equilibrium and Welfare Optimality

If A is a set of social alternatives, a social choice rule (SCR) assigns a subset of A to each potential profile of individuals’ preferences over A, where the subset is interpreted as the set of ‘‘welfare optima’’. A game form (or ‘‘mechanism’’) implements the social choice rule if, for any potential profile of preferences, (i) any welfare optimum can arise as a Nash equilibrium of the game for...