Center for Economic Research, Department of Economics, University of Minnesota
This paper studies the asymptotic behavior of Bayesian learning processes for general
finite-player, finite-strategy normal form games. Initially, each player is presumed to know
his own payoff function but not the payoff functions of the other players. Strategies are
initially determined as a Bayesian Nash equilibrium of the incomplete information game
in which each player's private characteristic is his payoff function. These strategies are
then observed by all players, causing a revision of beliefs. The new beliefs determine a new
Bayesian Nash equilibrium and so on. Assuming that the common prior distribution of
payoff functions satisfies independence across players, it is proved that the conditional distributions
on strategies converge to the set of Nash equilibria with probability one. Under
a further assumption that the prior distributions are sufficiently uniform, convergence to
the set of Nash equilibria is proved for every profile of payoff functions, that is, for every
normal form game.
Jordan, J.S., (1990), "Bayesian Learning in Normal Form Games", Discussion Paper No. 257, Center for Economic Research, Department of Economics, University of Minnesota.
Jordan, James S..
Bayesian Learning in Normal Form Games.
Center for Economic Research, Department of Economics, University of Minnesota.
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