Game theory bayesian updating cost of updating an international flight to business class
These beliefs are represented by a probability distribution over the possible payoff functions. Harsanyi describes a Bayesian game in the following way.
Each player in the game is associated with a set of types, with each type in the set corresponding to a possible payoff function for that player.
As in games of complete information, these can arise via non-credible strategies off the equilibrium path.
In games of incomplete information there is also the additional possibility of non-credible beliefs.
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.This probability distribution is known by all players (the "common prior assumption").This modeling approach transforms games of incomplete information into games of imperfect information (in which the history of play within the game is not known to all players).An analogous concept can be defined for a Bayesian game, the difference being that every player's strategy maximizes his expected payoff given his beliefs about the state of nature.A player's beliefs about the state of nature are formed by conditioning the prior probabilities on his own type according to Bayes' rule.
In particular, the belief a player holds about another player's type might change according to his own type.