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.

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