Subgame Perfect Cooperation in an Extensive Game

Abstract

Abstract: This paper brings together two of the most important solution concepts of game theory –subgame-perfect Nash equilibrium of a non-cooperative game and the core of a cooperativegame. Our approach rests on two fundamental ideas: (1) Given an extensive game, the formationof a coalition leads to a new game where all the members of the coalition become one player. (2) At the origin of any subgame, the only possible coalitions consist of players who have decision nodes in the subgame. We introduce a concept of subgame perfect cooperative equilibrium, which we label the gamma-core of an extensive game. We provide a necessary and sufficient condition for the existence of the gamma-core of an extensive game of perfect information. As a motivating example, we formulate the problem of global warming as a dynamic game with simultaneous moves and show that if the payoff functions are quadratic, then the gamma-core of the game is nonempty.