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
Famous quotes containing the words nash and/or equilibrium:
“Your hair may be brushed, but your mind’s untidy,
You’ve had about seven hours’ sleep since Friday,
No wonder you feel that lost sensation;
You’re sunk from a riot of relaxation.”
—Ogden Nash (1902–1971)
“When a person hasn’t in him that which is higher and stronger than all external influences, it is enough for him to catch a good cold in order to lose his equilibrium and begin to see an owl in every bird, to hear a dog’s bark in every sound.”
—Anton Pavlovich Chekhov (1860–1904)