Subgame‐consistent cooperative solutions in randomly furcating stochastic dynamic games

In the analysis of cooperative stochastic dynamic games a stringent condition–subgame consistency–is required for a dynamically stable solution. A cooperative solution is subgame consistent if an extension of the solution policy to a subgame starting at a later time with a feasible state brought about by prior optimal behavior would remain optimal. This paper considers subgame consistent cooperative solutions in randomly furcating stochastic discrete‐time dynamic games. Analytically tractable payoff distribution procedures contingent upon specific random realizations of the state and payoff structures are derived. In computer modeling and operations research discrete‐time analysis often proved to be more applicable and compatible with actual data than continuous‐time analysis. This is the first time that a subgame consistent solution for randomly‐furcating stochastic dynamic games has been obtained. It widens the application of cooperative dynamic game theory to discrete‐time problems where the evolution of the state and future payoff structures are not known with certainty.