Subgame Consistent Cooperative Solution in Random Horizon Dynamic Games

Abstract

In many game situations, the terminal time of the game is not known with certainty. Examples of this kind of problems include uncertainty in the renewal of lease, the terms of offices of elected authorities, contract renewal and continuation of agreements subjected to periodic negotiations. This Chapter presents subgame consistent solutions in discrete-time cooperative dynamic cooperative games with random horizon. The analysis is based on the work in Yeung and Petrosyan (2011). In Sect. 8.1, a discrete-time dynamic games with random duration is formulated and a dynamic programming technique for solving inter-temporal problems with random horizon is developed to serve as the foundation of solving the game problem. In Sect. 8.2, the noncooperative equilibrium is characterized with a set of random duration discrete-time Isaacs-Bellman equations. Dynamic cooperation under random horizon, group optimality and individual rationality are analyzed in Sect. 8.3. Subgame consistent solutions and their corresponding payment mechanism are presented in Sect. 8.4. An illustration in a resource extraction game with random duration lease is provided. The chapter appendices are given in Sect. 8.6. Chapter notes are provided in Sect. 8.7 and problems in Sect. 8.8.