Econom/c Theory 9 Springer-Verlag 1994 Convergence and approximation results for non-cooperative Bayesian games: learning theorems*

Summary. Let T denote a cont inuous time horizon and {Gt:teT} be a net (generalized sequence) of Bayesian games. We show that: (i) if {xt: te T} is a net of Bayesian Nash Equi l ibr ium (BNE) strategies for G t, we can extract a subsequence which converges to a l imit full information BNE strategy for a one shot l imit full information Bayesian game. (ii) If {xt:t~T} is a net of approx imate or et-BNE strategies for the game G t we can still extract a subsequence which converges to the one shot l imit full information equi l ibr ium BNE strategy. (iii) Given a l imit full information BNE strategy of a one shot l imit full information Bayesian game, we can find a net of et-BNE strategies {xt:t~T} in {Gt:teT} which converges to the limit full information BNE strategy of the one shot game. 1