Cooperative Game Theory and the Theory of the State

In Welfare Economics and the Theory of the State, Baumol (1952) argued that phenomena of the sort that came to be known as “market failures” (Bator 1958) marked out the domain of action of a liberal state in a predominantly market economy. More recently, as the influence of game theory on economics has become more important, economists have often made the contrast of cooperative and noncooperative solutions a basis for such a judgment, characterizing “market failures” as inefficient noncooperative outcomes and arguing that state action could be justified as realizing a cooperative solution. However, the development of cooperative game theory has made it difficult to formalize this informal argument. This paper revisits the issue, adapting ideas from effectivity theory in cooperative game theory for special cases in which limited money transfers are allowed. Representing the game in extensive form, money transfers are among the basic proper subgames of the underlying game. Because backward induction eliminates the transfers, transfers never occur in the noncooperative (subgame perfect Nash) equilibrium of the game. However, transfers may dominate non-transfer solutions and define the core of the cooperative game, in one or both of two senses. Examples are given in which cooperative solutions without transfers do not improve on the noncooperative equilibrium, but solutions in the effectivity cores with transfers provide plausible market and public policy solutions. For large-N games, following a tactic in The Theory of Games and Economic Behavior, the paper posits a fictitious N+1st player whose outcome set is null and whose only strategies are transfers. Since the N+1st player – “the state” – can be a member of any coalitions, some transfers may be available to any coalition. This model is used to characterize a Pigovian tax and to argue that the stability of the tax may depend on how the revenue from the tax is redistributed, suggesting a rationale for a proposal due to the Climate Leadership Council, a free-market conservative group.