How Can Cooperative Game Theory Be Made More Relevant to Economics? : An Open Problem

Game Theory pioneers J. von Neumann and O. Morgenstern gave most of their attention to the cooperative side of the subject. But cooperative game theory has had relatively little effect on economics. In this essay, I suggest why that might be and what is needed for cooperative theory to become more relevant to economics. Cooperative game theory is the part of game theory that pertains when players can sign binding contracts determining their actions and payoffs. J. von Neumann and O. Morgenstern devoted most of their seminal book [6] to cooperative theory, with subsequent major contributions by Nash [4] and Shapley [5]. But despite its auspicious beginnings, cooperative game theory has been used far less than noncooperative theory as a predictive tool in economics. Indeed, inspection of the current leading game theory textbooks used in graduate economics programs reveals that the ratio of cooperative to noncooperative theory is remarkably low (in one such text, [1], the ratio is 0). And all Nobel Memorial Prizes awarded for game theory to date have recognized work exclusively on the noncooperative side. This imbalance may seem strange. Cooperative theory seems to offer the important advantage of giving insight into how coalitions behave, i.e., how subsets of players bargain over which actions are played. Such bargaining seems basic to many aspects of economic and political life from the European Union, to the Paris climate change agreement, to the OPEC cartel. Moreover, on the face of it, cooperative theory appears to be far less dependent on particular details about strategies—and, therefore, more robust and general—than noncooperative theory. To understand the sense in which noncooperative is more detail dependent, let us briefly go over the basic noncooperative and cooperative models. In a noncooperative game, each player i; i D 1; : : : ; n; chooses a strategy si from a strategy set Si, and the payoffs of the game are given by the mapping E. Maskin ( ) Department of Economics, Harvard University, Littauer Center, Room 312, 1805 Cambridge Street, Cambridge, MA, USA Higher School of Economics, Moscow, Russia e-mail: [email protected] © Springer International Publishing Switzerland 2016 J.F. Nash, Jr., M.Th. Rassias (eds.), Open Problems in Mathematics, DOI 10.1007/978-3-319-32162-2_9 347