Bayesian Nash equilibrium is a balance concept used in incomplete information games (a situation in which some game participants do not have complete information about the other participants). In this case, each player has probabilistic beliefs about the types of other players (parameters representing player preferences, information, abilities, etc.). In Bayesian Nash equilibrium, each player chooses the optimal strategy based on his beliefs and his type. As a result, no player can increase his expected gain by unilaterally changing his strategy based on a given other player’s strategy and his beliefs. A Bayesian Nash equilibrium is a state in which players’ beliefs and strategies are consistent with each other.
As discussed in POMDP, in Bayes beliefs are expressed as probability distributions
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