Good and bad objects: the symmetric difference rule

We consider the problem of ranking sets of objects, the members of which are mutually compatible. Assuming that each object is either good or bad, we axiomatically characterize a cardinality-based rule which arises naturally in this dichotomous setting.

Minimum Cost Spanning Tree Games and Spillover Stability

This paper discusses minimum cost spanning tree games and argues that the standard approach of using a transferable utility game to come up with a fair allocation of the total costs has some flaws. A new model of spillover games is presented, in which each agent's decision whether or not to cooperate is properly taken into account.minimum cost spanning tree problems, transferable utility games, spillovers

Simple Priorities and Core Stability in Hedonic Games

In this paper we study hedonic games where each player views every other player either as a friend or as an enemy. Two simple priority criteria for comparison of coalitions are suggested, and the corresponding preference restrictions based on appreciation of friends and aversion to enemies are considered. It turns out that the first domain restriction guarantees non-emptiness of the strong core and the second domain restriction ensures non-emptiness of the weak core of the corresponding hedonic games. Moreover, an element of the strong core under friends appreciation can be found in polynomial time, while finding an element of the weak core under enemies aversion is NP-hard. We examine also the relationship between our domain restrictions and some sufficient conditions for non-emptiness of the core already known in the literature.Additive separability, Coalition formation, Core stability, Hedonic games, NP-completeness, Priority

Egalitarianism in Nontransferable Utility Games

This paper studies egalitarianism in the context of nontransferable utility games by introducing and analyzing the egalitarian value. This new solution concept is based on an egalitarian negotiation procedure in which egalitarian opportunities of coalitions are explicitly taken into account. We formulate conditions under which it leads to a core element and discuss the egalitarian value for the well-known Roth-Shafer examples. Moreover, we characterize the new value on the class of bankruptcy games and bargaining games

Fall back proper equilibrium

Proper equilibrium plays a prominent role in the literature on non-cooperative games. The underlying thought experiment in which the players play a passive role is, however, unsatisfying, as it gives no justification for its fundamental idea that severe mistakes are made with a significantly smaller probability than innocuous ones. In this paper, we introduce a more active role for the players, leading to the refinement of fall back proper equilibrium

Decomposition of Network Communication Games

Using network control structures this paper introduces network communication games as a generalization of vertex games and edge games corresponding to communication situations and studies their decomposition into unanimity games. We obtain a relation between the dividends of the network communication game and the underlying transferable utility game, which depends on the structure of the undirected graph. This relation extends the computational results for tree communication networks to general undirected graphs and is used to derive new characterizations of the Myerson value and the position value. Moreover, network communication games also allow to consider both the vertices and the edges of the graph as players, leading to a new network value

A Strategic Approach to Bankruptcy Problems Based on the TAL Family of Rules

This paper analyzes bankruptcy problems from a strategic perspective using the parameterized TAL family of bankruptcy rules. We construct a strategic game where every player selects a parameter, and the rule from the TAL family that corresponds to the mean of the chosen parameters is used to divide the estate. We prove the existence of Nash equilibria for this strategic game. In particular, we provide the set of all Nash equilibria for two players, and for more players, we prove existence by constructing a Nash equilibrium of a particular form based on the notion of a pivotal player