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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We review the use of Young measures in analyzing relaxed and generalized formulations for typical problems of optimization including variational principles, optimal control problems, models in materials science, optimal design problems and nonlocal optimization problems.

By an effective extension of the conjugate function concept a general framework for duality-stability relations in nonconvex optimization problems can be studied. The results obtained show strong correspondences with the duality theory for convex minimization problems. In specializations to mathematical programming problems the canonical Lagrangian of the model appears as the extended Lagrangian considered in exterior penalty function methods.

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