Subgame Consistent Cooperative Solution in Dynamic Games

Abstract

In many game situations, the evolutionary process is in discrete time rather than in continuous time. An extension of the analysis to a discrete-time dynamic framework is provided in this chapter. In particular, it presents an analysis on subgame consistent solutions which entail group optimality and individual rationality for cooperative (deterministic and stochastic) dynamic games. It integrates the works of Yeung and Petrosyan (2010) and Chapters 12 and 13 of Yeung and Petrosyan (2012a). We first present in Sect. 7.1 a general formulation of cooperative dynamic games in discrete time with the noncooperative outcomes, and the notions of group optimality and individual rationality. Subgame consistent cooperative solutions with corresponding payoff distribution procedures are derived in Sect. 7.2. An illustration of cooperative resource extraction in discrete time is given in Sect. 7.3. A general formulation of coopeartive stochastic dynamic games in discrete time is given in Sect. 7.4. Subgame consistent cooperative solutions with corresponding payoff distribution procedures are derived in Sect. 7.5. An illustration of cooperative resource extraction under uncertainty in discrete time is given in Sect. 7.6. A heuristic approach to obtaining subgame consistent solutions for cooperative dynamic games is provided in Sect. 7.7. Section 7.8 contains Appendices of the Chapter. Chapter Notes are given in Sect. 7.9 and problems in Sect. 7.10. In addition, to make the discrete-time analysis in this Chapter fully in line with the continuous-time analyses presented in earlier chapters a terminal condition is added to each player’s payoff in Yeung and Petrosyan (2010, 2012a).