Bayesian Nash Equilibrium
In a non-Bayesian game, a strategy profile is a Nash equilibrium if every strategy in that profile is a best response to every other strategy in the profile; i.e., there is no strategy that a player could play that would yield a higher payoff, given all the strategies played by the other players. In a Bayesian game (where players are modeled as risk-neutral), rational players are seeking to maximize their expected payoff, given their beliefs about the other players (in the general case, where players may be risk averse or risk-loving, the assumption is that players are expected utility-maximizing).
A Bayesian Nash equilibrium is defined as a strategy profile and beliefs specified for each player about the types of the other players that maximizes the expected payoff for each player given their beliefs about the other players' types and given the strategies played by the other players.
This solution concept yields an abundance of equilibria in dynamic games, when no further restrictions are placed on players' beliefs. This makes Bayesian Nash equilibrium an incomplete tool with which to analyse dynamic games of incomplete information.
Read more about this topic: Bayesian Game
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—Ogden Nash (1902–1971)
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—Ralph Waldo Emerson (1803–1882)