Generalized Equilibrium Results for Games with Incomplete Information

Milgrom and Weber (Milgrom, P. R., Weber, R. J. 1985. Distributional strategies for games with incomplete information. Math. Oper. Res.10 619–632.) gave an existence result for a Nash equilibrium in a game with incomplete information, using their notion of a distributional strategy. Here we obtain a substantial improvement of their existence result in terms of the more traditional concept of a behavioral strategy. This improvement is reached very naturally as an application of a theory of weak convergence for transition probabilities, which is recapitulated extensively in this paper. Also, a new result on the weak convergence of product transition probabilities is included.