The purpose of this paper is to establish the intrinsic relations between the cores of exact games on σ-algebras and the extensions of exact games to function spaces. Given a probability space, exact functionals are defined on L∞ as an extension of exact games. To derive a probabilistic representation for exact functionals, we endow them with two probabilistic conditions: law invariance and the...

In order to describe partial cooperation structures, this paper introduces complete coalition structures as sets of feasible coalitions. A complete coalition structure has a property that, for any coalition, if each pair of players in the coalition belongs to some feasible coalition contained in the coalition then the coalition itself is also feasible. The union stable structures, which constit...

While most of the literature starting with Shapley and Scarf (1974) have considered a static exchange economy with indivisibilities, this paper studies the dynamics of such an economy. We find that both the dynamics generated by competitive equilibrium and the one generated by weakly dominance relation, converge to a set of allocations we define as strictly stable, which we can show to exist. M...

I characterize games for which there is an order on strategies such that the game has strategic complementarities. I prove that, with some qualifications, games with a unique equilibrium have complementarities if and only if Cournot bestresponse dynamics has no cycles; and that all games with multiple equilibria have complementarities. As applications of my results, I show: 1. That generic 2X2 ...

An appropriate (interim) notion of the core for an economy with incomplete information depends on the amount of information that coalitions can share. The coarse and fine core, as originally defined by Wilson (1978), correspond to two polar cases, involving no information sharing and arbitrary information sharing, respectively. We propose a new core notion, the credible core, which incorporates...

We propose positive and normative foundations for the average prekernel of NTU games, and compare them with the existing ones for the prekernel. In our non-cooperative analysis, the average prekernel is understood as the equilibrium payoffs of a game where each player faces the possibility of bargaining at random against any other player. In the cooperative analysis, we characterize the average...

Evolutionary arguments in non-cooperative game theory are becoming more and more important to justify or refine equilibrium concepts. In cooperative game theory they are rare but growing in number. This paper discusses various approaches, in particular their usefulness and relevance for real world voting games. As the existing approaches turn out to fail to provide any empirically relevant insi...

Thomson (Consistent solutions to the problem of fair division when preferences are single-peaked, J. Econ. Theory 63 (1994), 219 245) proved that the uniform rule of the fair division problem, where preferences are single-peaked, is the unique rule which is bilaterally consistent, continuous, Pareto optimal, and envy-free, in a setting of an infinite number of potential agents. We show that the...

A class of cooperative games is introduced which arises from situations in which a set of agents is hierarchically structured and where potential individual economic abilities interfere with the behavioristic rules induced by the organization structure. These games form a cone generated by a specific class of unanimity games, namely those based on coalitions called peer groups. Different econom...

A (TU) cooperative game is extendable (Kikuta and Shapley, 1986) if every core allocation of each sub-game can be extended to a core allocation of the game. It is strongly extendable if any minimal vector in the upper core of any of its sub-games can be extended to a core allocation. We prove that strong extendability is equivalent to largeness of the core (Sharkey, 1982). Further, we character...