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We define and study games with upper bounds. In one of these games there are upper bounds on the possible payoffs for some coalitions. These restrictions require adjustments in the definitions of solution concepts. In the current paper we study the effect of the restrictions on the core and define and study the so-called truncated core. [ABSTRACT FROM AUTHOR]

Many public goods that are provided by coalitions have a group-size effect. Namely, people prefer to consume a public good in a larger coalition. This paper studies local public goods games with anonymous and separable group-size effect. The core is nonempty when coalition feasible sets are monotonic and players' preferences over public goods satisfy a condition called cardinal connectedness. Moreover, a core allocation consists of connected coalitions. [ABSTRACT FROM AUTHOR]

In the framework of the solution theory for cooperative transferable utility games, Hamiache axiomatized the well-known Shapley value as the unique one-point solution verifying the inessential game property, continuity, and associated consistency. The purpose of this paper is to extend Hamiache’s axiomatization to the class of efficient, symmetric, and linear values, of which the Shapley value is the most important representative. For this enlarged class of values, explicit relationships to the Shapley value are exploited in order to axiomatize such values with reference to a slightly adapted inessential game property, continuity, and a similar associated consistency. The latter axiom requires that the solutions of the initial game and its associated game (with the same player set, but a different characteristic function) coincide. [ABSTRACT FROM AUTHOR]

The paper follows Kalai and Samet’s (Econometrica 53:307–327, 1985) construction to define a possible extension of the equal allocation of nonseparable costs (EANSC) to games without transferable utilities. We offer a characterization of the EANSC based on the axiom of independence of irrelevant monotonic transformation [Chang and Hwang (Int J Game Theory 32:253–271, 2003) introduced this axiom, and they named it independence of irrelevant expansions. The referee points out that the terminology is inappropriate. So, we change the name.] introduced by Chang and Hwang (Int J Game Theory 32:253–271, 2003) as well as on several familiar axioms. Specifically, we show that the EANSC is the only solution to satisfy Pareto optimality, translation covariance, anonymity, TU-bilateral consistency (or TU-converse consistency), aggregate monotonicity, and independence of irrelevant monotonic transformation. [ABSTRACT FROM AUTHOR]

A family of core extensions for cooperative TU-games is introduced. These solution concepts are non-empty when applied to non-balanced games yet coincide with the core whenever the core is non-empty. The extensions suggest how an exogenous regulator can sustain a stable and efficient outcome, financing a subsidy via individual taxes. Economic and geometric properties of the solution concepts are studied. When taxes are proportional, the proportional prenucleolus is proposed as a single-valued selection device. An application of these concepts to the decentralization of a public goods economy is discussed. [ABSTRACT FROM AUTHOR]

This paper reinterprets the γ-core (Chander and Tulkens in Int Tax Pub Financ 2:279–293, 1995; in Int J Game Theory 26:379–401, 1997) and justifies it as well as its prediction that the efficient coalition structure is stable in terms of the coalition formation theory. The problem of coalition formation is formulated as an infinitely repeated game in which the players must choose whether to cooperate or not. It is shown that a certain equilibrium of this game corresponds to the γ-core assumption that when a coalition forms the remaining players form singletons, and that the grand coalition is an equilibrium coalition structure. [ABSTRACT FROM AUTHOR]

We examine a variety of stability and equilibrium definitions that have been used to study the formation of social networks among a group of players. In particular we compare variations on three types of definitions: those based on a pairwise stability notion, those based on the Nash equilibria of a link formation game, and those based on equilibria of a link formation game where transfers are possible. [ABSTRACT FROM AUTHOR]

Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided. [ABSTRACT FROM AUTHOR]