The Matroska theorem

A “most general model of a dynamic game” (where the players make simultaneous moves step-by-step) will be constructed. This game can be viewed as a formalization of an entire series of applied problems in new political economy, as well as other areas of theoretical economics. Our model generalizes the classical formulation of the dynamic programming problem for an infinite horizon, Markov games, ordinary games of several players, and, finally, the standard model of an infinite repeating game. The proof of the theorem is based on “nested” theorems on existence of stationary points: the principle of contracting mappings on the inside, and Kakutani’s theorem on the outside. Because of this construction, we dubbed it the “Matroska theorem”.