Subgame Consistency in NTU Cooperative Dynamic Games

Abstract

Cooperative games suggest the possibility of enhancing the participants’ well-being in situations involving strategic interactions. Various cooperative solutions have been presented, like the Nash (1950, 1953) bargaining solution, the Shapley (1953) value, and the stable set of von Neumann and Morgenstern (1944). Frequently, the lack of sustainability of the cooperation scheme leads to break-ups of the scheme as the game evolves or even to the outright rejection of the cooperation scheme. One of the ways to uphold sustainability of a cooperation scheme is to maintain the condition of subgame consistency. In non-transferrable utility/payoff (NTU) cooperative dynamic games, the inapplicability of transfer payments makes the derivation of subgame consistent solutions extremely strenuous. In Chap. 6 subgame consistent solution in cooperative differential games with non-transferable payoffs under a constant weight scheme is provided. However, the result is confined to a specific class of games under a very restrictive set of optimality principles. Crucial problems of using constant payoff weights include the possibility of the failure of individual rationality to be fulfilled throughout the cooperative duration and the deviation from the original optimality principle as the game evolves. The use of variable payoff weights provides an effective way in achieving subgame consistency and preserving individual rationality under a wide range of optimality principles.