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A Bayesian Nash Equilibrium (BNE) is a Nash equilibrium for a Bayesian game, which is derived from the ex-ante normal form game associated with the Bayesian framework. In a traditional (non-Bayesian) game, a strategy profile is a Nash equilibrium if every player's strategy is a best response to the other players' strategies. In this situation ...
Set up the inequality to determine whether the mixed strategy will dominate the pure strategy based on expected payoffs. u 1 / 2 Y + u 1 / 2 Z ⩼ u X. 4 + 5 > 5 Mixed strategy 1 / 2 Y and 1 / 2 Z will dominate pure strategy X for Player 2, and thus X can be eliminated from the rationalizable strategies for P2.
The free money game is an example of a "special" game with an even number of equilibria. In it, two players have to both vote "yes" rather than "no" to get a reward and the votes are simultaneous. There are two pure-strategy Nash equilibria, (yes, yes) and (no, no), and no mixed strategy equilibria, because the strategy "yes" weakly dominates "no".
A weaker degree is Bayesian-Nash incentive-compatibility (BNIC). [ 1 ] : 416 It means there is a Bayesian Nash equilibrium in which all participants reveal their true preferences. In other words, if all other players act truthfully, then it is best to be truthful.
A Nash equilibrium is a strategy profile (a strategy profile specifies a strategy for every player, e.g. in the above prisoners' dilemma game (cooperate, defect) specifies that prisoner 1 plays cooperate and prisoner 2 plays defect) in which every strategy played by every agent (agent i) is a best response to every other strategy played by all the other opponents (agents j for every j≠i) .
The two pure strategy Nash equilibria are (D, C) and (C, D). There is also a mixed strategy equilibrium where both players chicken out with probability 2/3. Now consider a third party (or some natural event) that draws one of three cards labeled: (C, C), (D, C), and (C, D), with the same probability, i.e. probability 1/3 for each card.
Informally speaking, an assessment is a perfect Bayesian equilibrium if its strategies are sensible given its beliefs and its beliefs are confirmed on the outcome path given by its strategies. The definition of sequential equilibrium further requires that there be arbitrarily small perturbations of beliefs and associated strategies with the ...
Strategy: A complete contingent plan for a player in the game. A complete contingent plan is a full specification of a player's behavior, describing each action a ...