Dinko Dimitrov

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. We characterize internally stable coalitions on the proposed domains and show how these characterizations can be used for generating a strict core element in the first case and a core element in the second case. Moreover, we prove that an element of the strict core under friends appreciation can be found in polynomial time, while finding an element of the core under enemies aversion is NP-hard.

Computational Complexity in Additive Hedonic Games

We investigate the computational complexity of several decision problems in hedonic coalition formation games and demonstrate that attaining stability in such games remains NP-hard even when they are additive. Precisely, we prove that when either core stability or strict core stability is under consideration, the existence problem of a stable coalition structure is NP-hard in the strong sense. Furthermore, the corresponding decision problems with respect to the existence of a Nash stable coalition structure and of an individually stable coalition structure turn out to be NP-complete in the strong sense.

Procedural group identification

In this paper we axiomatically characterize two recursive procedures for defining a social group. The first procedure starts with the set of all individuals who are defined by everyone in the society as group members, while the starting point of the second procedure is the set of all individuals who define themselves as members of the social group. Both procedures expand these initial sets by adding individuals who are considered to be appropriate group members by someone in the corresponding initial set, and continue inductively until there is no possibility of expansion any more.

How to Cope with Division Problems under Interval Uncertainty of Claims

The paper deals with division situations where individual claims can vary within closed intervals.Uncertainty of claims is removed by compromising in a consistent way the upper and lower bounds of the claim intervals.Deterministic division problems with compromise claims are then considered and classical division rules from the bankruptcy literature are used to generate several procedures leading to e .cient and reasonable rules for division problems under interval uncertainty of claims.

On the Axiomatic Characterization of Who is a J

Recent work by Kasher and Rubinstein (1997) considers the problem of group identification from a social choice perspective.These authors provide an axiomatic characterization of a liberal aggregator whereby the group consist of those and only those individuals each of which views oneself a member of the group.In the present paper we show that the five axioms used in Kasher and Rubinstein s characterization of the liberal aggregator are not independent and prove that only three of their original axioms are necessary and sufficient for the required characterization.

The Paretian liberal with intuitionistic fuzzy preferences : A result

Abstract.In the present paper we consider a situation in which the individual preferences and the social preference relation are intuitionistic fuzzy and study the compatibility between the Pareto principle and Sen’s minimal liberalism condition. A possible factorization of the intuitionistic fuzzy weak preference relation allows us to prove a possibility result for the case of max-min transitive social preference.

Hypercubes and compromise values for cooperative fuzzy games

For cooperative fuzzy games with a non−empty core hypercubes catching the core, the Weber set and the path solution cover are introduced. Using the bounding vectors of these hypercubes, compromise values are defined. Special attention is given to the relations between these values for convex fuzzy games.

A New Characterization of Convex Games

A cooperative game turns out to be convex if and only if all its marginal games are superadditive.

The Social Choice Approach to Group Identification

The chapter gives an overview of selected topics from the theory of group identification. As a starting point serve different axiomatic characterizations of the “libera” rule for group identification whereby the group consist of those and only those individuals each of which views oneself a member of the group. We then focus on consent rules and recursive procedures for collective determination where the opinions of other individuals in the society also count. Finally, we address recent developments in the literature with respect to gradual opinions and group identity functions.

Paths to stability in two-sided matching with uncertainty

We consider one-to-one matching problems under two modalities of uncertainty that differ in the way types are assigned to agents. Individuals have preferences over the possible types of the agents from the opposite market side and initially know the “name” but not the ”type” of the other players. Learning occurs via matching and using Bayes’ rule. We introduce the notion of a stable and consistent outcome, and show how the interaction between blocking and learning behavior shapes the existence of paths to stability in each of the uncertainty environments. Existence of stable and consistent outcomes then follows as a side result.