Implementing with veto players: a simple non cooperative game

The paper adapts a non cooperative game presented by Dagan, Serrano and Volij (1997) for bankruptcy problems to the context of TU veto balanced games. We investigate the relationship between the Nash outcomes of a noncooperative game and solution concepts of cooperative games such as the nucleolus, kernel and the egalitarian core.

Egalitarianism in convex fuzzy games

cooperative games;algorithm

Egalitarianism in Convex Fuzzy Games

In this paper the egalitarian solution for convex cooperative fuzzy games is introduced.The classical Dutta-Ray algorithm for finding the constrained egalitarian solution for convex crisp games is adjusted to provide the egalitarian solution of a convex fuzzy game.This adjusted algorithm is also a finite algorithm, because the convexity of a fuzzy game implies in each step the existence of a maximal element which corresponds to a crisp coalition.For arbitrary fuzzy games the equal division core is introduced.It turns out that both the equal division core and the egalitariansolution of a convex fuzzy game coincide with the corresponding equal division core and the constrained egalitarian solution, respectively, of the related crisp game.game theory

Monotonicity Problems of Interval Solutions and the Dutta-Ray Solution for Convex Interval Games

This paper examines several monotonicity properties of value-type interval solutions on the class of convex interval games and focuses on the Dutta-Ray (DR) solution for such games. Well known properties for the classical DR solution are extended to the interval setting. In particular, it is proved that the interval DR solution of a convex interval game belongs to the interval core of that game and Lorenz dominates each other interval core element. Consistency properties of the interval DR solution in the sense of Davis-Maschler and of Hart-Mas-Colell are verified. An axiomatic characterization of the interval DR solution on the class of convex interval games with the help of bilateral Hart-Mas-Colell consistency and the constrained egalitarianism for two-person interval games is given.cooperative interval games;convex games;the constrained egalitarian solution;the equal division core;consistency

A Dual Model of Cooperative Value

An expanded model of value in cooperative games is presented in which value has either a linear or a proportional mode, and NTU value has either an input or an output basis. In TU games, the modes correspond to the Shapley (1953) and proportional (Feldman (1999) and Ortmann (2000)) values. In NTU games, the Nash (1950) bargaining solution and the Owen- Maschler (1989, 1992) value have a linear mode and an input basis. The egalitarian value (Kalai and Samet (1985)) has a linear mode and an output basis. The output-basis NTU proportional value (Feldman (1999)) and the input-basis variant, identified here, complete the model. The TU proportional value is shown to have a random marginal contribution representation and to be in the core of a positive convex game. The output-basis NTU variant is shown to be the unique efficient Hart and Mas-Colell consistent NTU value based on equal proportional gain in two-player TU games. Both NTU proportional values are shown to be equilibrium payoffs in variations of the bargaining game of Hart and Mas-Colell (1996). In these variations, players' probabilities of participation at any point in the game are a function of their expected payoff at that time. Limit results determine conditions under which players with zero individual worth receive zero value. Further results show the distinctive nature of proportional allocations to players with small individual worths. In an example with a continuum of players bargaining with a monopolist, the monopolist obtains the entire surplus.cooperative game, value, mode, basis, bilateral cooperation, endogenous bargaining power, potential, equal proportional gain, consistency, noncooperative bargaining, zero players, monopoly

The Equal Split-Off Set for Cooperative Games

In this paper the equal split-o. set is introduced as a new solution concept for cooperative games.This solution is based on egalitarian considerations and it turns out that for superadditive games the equal split-o. set is a subset of the equal division core.Moreover, the proposed solution is single valued on the class of convex games and it coincides with the Dutta-Ray constrained egalitarian solution.

A Technical Note on Lorenz Dominance in Cooperative Games

AMS classification: 91A12Cooperative games;Lorenz dominance;egalitarianism;con- strained egalitarian solution;equal split-off set

The Rights-Egalitarian Solution for NTU Sharing Problems

The purpose of this paper is to extend the Rights Egalitarian solution (Herrero, Maschler & Villar, 1999) to the context of non-transferable utility sharing problems. Such an extension is not unique. Depending on the kind of properties we want to preserve we obtain two different generalizations. One is the "proportional solution", that corresponds to the Kalai-Smorodinsky solution for surplus sharing problems and the solution in Herrero (1998) for rationing problems. The other is the "Nash solution” that corresponds to the standard Nash bargaining solution for surplus sharing problems and the Nash rationing solution (Mariotti & Villar (2005) for the case of rationing problems.Sharing problems, rights egalitarian solution, NTU problems.

Stability and fairness in models with a multiple membership

This article studies a model of coalition formation for the joint production (and finance) of public projects, in which agents may belong to multiple coalitions. We show that, if projects are divisible, there always exists a stable (secession-proof) structure, i.e., a structure in which no coalition would reject a proposed arrangement. When projects are in- divisible, stable allocations may fail to exist and, for those cases, we resort to the least core in order to estimate the degree of instability. We also examine the compatibility of stability and fairness on metric environments with indivisible projects. To do so, we explore, among other things, the performance of several well-known solutions (such as the Shapley value, the nucleolus, or the Dutta-Ray value) in these environments.stability, fairness, membership, coalition formation