Subgame Consistency in Randomly-Furcating Cooperative Stochastic Dynamic Games

Abstract

This Chapter considers subgame consistent cooperative solutions in randomly furcating stochastic discrete-time dynamic games. In particular, in this type of games the evolution of the state is stochastic and future payoff structures are not known with certainty. The presence of random elements in future payoff structures and stock dynamics are prevalent in many practical game situations like regional economic cooperation, corporate joint ventures and transboundary environmental management. The analysis is based on Yeung and Petrosyan (2013a). It first develops a class of randomly furcating stochastic dynamic games in which future payoff structures of the game furcates or branches out randomly and the discrete-time game dynamics evolves stochastically. Nash equilibria of this class of games are characterized for non-cooperative outcomes and subgame-consistent solutions are derived for cooperative paradigms. A discrete-time analytically tractable payoff distribution procedure contingent upon specific random realizations of the state and payoff structure is derived. Worth mentioning is that in computer modeling and operations research discrete-time analysis often proved to be more applicable and compatible with actual data than continuous-time analysis. The Chapter is organized as follows. The game formulation and non-cooperative equilibria are given in Sect. 9.1. Group optimality and individual rationality under dynamic cooperation are discussed in Sect. 9.2. Subgame consistent solutions and payment mechanism leading to the realization of these solutions are obtained in Sect. 9.3. Section 9.4 presents an illustration in cooperative resource extraction. Extensions of the model are provided in Sect. 9.5. Chapter appendices, chapter notes and problems are presented in Sect. 9.6, Sect. 9.7, and Sect. 9.8 respectively.