International Game Theory Review

The fertile application of cooperative game techniques to cost sharing problems on networks has so far concentrated on the Stand Alone core test of fairness and/or stability, and ignored many combinatorial optimization problems where this core can be empty. I submit there is much room for an axiomatic discussion of fair division in the latter problems, where Stand Alone objections are not implementable. But the computational complexity of optimal solutions is still a very severe obstacle to this approach.

In this paper, we explain why the field of cost allocation problems with a coalition structure is a wide and promising unexplored research direction. In particular, we pose some open questions for airport games with a coalition structure.

A review of the literature on cost sharing solutions for the minimum cost spanning tree problem is proposed, with a particular focus on the folk and Kar solutions. We compare the characterizations proposed, helped by some equivalencies between sets of properties.

This paper aims to give a global vision concerning the state of the art of studies on 13 power indices and to establish which of them are more suitable for describing the real situations which are, from time to time, taken into consideration. In such contexts, different comparisons have been developed in terms of properties, axiomatic grounds and so on. This analysis points out various open problems.

This paper presents a review of literature on simple games and highlights various open problems concerning such games; in particular, weighted games and power indices.

The issue of veto may play an important role in an approval situation, mainly in political science, where several scholars dealt with this topic. In this survey we want to update the state-of-the-art, paying particular attention to the open problems that various authors pointed out in their research fields.

In this paper, we present two real-world situations in which the standard hypotheses of a bargaining problem do not hold, and discuss how to tackle these situations.

This survey deals with two-sided matching markets where one set of agents (workers/residents) has to be matched with another set of agents (firms/hospitals). We first give a short overview of a selection of classical results. Then, we review recent contributions to a complex and representative case of matching with complementarities, namely matching markets with couples. We discuss contributions from computer scientists, economists, and game theorists.

This is a brief survey describing some of the recent progress and open problems in the area of cooperative games with incomplete information. We discuss exchange economies, cooperative Bayesian games with orthogonal coalitions, and issues of cooperation in noncooperative Bayesian games.

The paper presents some issues currently under studying in the field of Cooperative Games. The related open problems are also mentioned.