Subgame Consistent Solution for Random-Horizon Cooperative Dynamic Games

In cooperative dynamic games a stringent condition — that of subgame consistency — is required for a dynamically stable cooperative solution. In particular, a cooperative solution is subgame consistent if an extension of the solution policy to a subgame starting at a later time with a state brought about by prior optimal behavior would remain optimal. This paper extends subgame consistent solutions to dynamic (discrete-time) cooperative games with random horizon. In the analysis new forms of the Bellman equation and the Isaacs-Bellman equation in discrete-time are derived. Subgame consistent cooperative solutions are obtained for this class of dynamic games. Analytically tractable payoff distribution mechanisms which lead to the realization of these solutions are developed. This is the first time that subgame consistent solutions for cooperative dynamic games with random horizon are presented.