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.