Nontransferable utility cooperative dynamic games

Abstract

Cooperation in an inter-temporal framework under nontransferable utility/payoffs (NTU) presents a highly challenging and extremely intriguing task to game theorists. This chapter provides a coherent analysis on NTU cooperative dynamic games. The formulations of NTU cooperative dynamic games in continuous time and in discrete time are provided. The issues of individual rationality, Pareto optimality, and an individual player's payoff under cooperation are presented. Monitoring and threat strategies preventing the breakup of the cooperative scheme are presented. Maintaining the agreed-upon optimality principle in effect throughout the game horizon plays an important role in the sustainability of cooperative schemes. The notion of time (subgame optimal trajectory) consistency in NTU differential games is expounded. Subgame consistent solutions in NTU cooperative differential games and subgame consistent solutions via variable payoff weights in NTU cooperative dynamic games are provided.