Subgame Consistency Under Furcating Payoffs, Stochastic Dynamics and Random Horizon

Abstract

This Chapter investigates the class of randomly furcating stochastic dynamic games with uncertain game horizon. In particular, in this class of games, there exist uncertainties in the state dynamics, future payoff structures and game horizon. The non-cooperative Nash equilibrium is characterized and subgame-consistent cooperative solutions is derived. A discrete-time analytically tractable payoff distribution procedures contingent upon specific random realizations of the state and payoff structure are derived. This approach widens the application of cooperative dynamic game theory to discrete-time random horizon problems where the evolution of the state and future environments are not known with certainty. In addition, a corresponding form of Bellman equations for solving inter-temporal problems with randomly furcating payoffs and random horizon is developed to serve as the foundation of solving the game problem. To characterize a noncooperative game equilibrium, a set of random duration discrete-time Hamilton-Jacobi-Bellman equations is presented. Subgame consistent solution and corresponding Payoff Distribution Procedures are provided. The analysis is developed along the work of Yeung and Petrosyan (2014c).