Elena Inarra

Egalitarian solutions in the core

Abstract. In this paper we define the Lorenz stable set, a subset of the core consisting of the allocations that are not Lorenz dominated by any other allocation of the core. We introduce the leximin stable allocation, which is derived from the application of the Rawlsian criterion on the core. We also define and axiomatize the egalitarian core, a set of core allocations for which no transfer from a rich player to a poor player is possible without violating the core restrictions. We find an inclusive relation of the leximin stable allocation and of the Lorenz stable set into the egalitarian core.

The Shapley value and average convex games

In this paper we reformulate the necessary and sufficient conditions for the Shapley value to lie in the core of the game. Two new classes of games, which strictly include convex games, are introduced: average convex games and partially average convex games. Partially average convex games, which need not be superadditive, include average convex games. The Shapley value of a game for both classes is in the core. Some Cobb Douglas production games with increasing returns to scale turn out to be average convex games. The paper concludes with a comparison between the new classes of games introduced and some previous extensions of the convexity notion.

A Simple Algorithm for the Nucleolus of Airport Profit Games

In this paper we present a procedure for calculating the nucleolus for airport profit games which are a generalization of the airport cost games.

Bankruptcy of Fishing Resources: The Northern European Anglerfish Fishery

Since 1983 the Northern European anglerfish fishery, exploited by fleets of seven countries, has been regulated using a policy of Total Allowable Catch (TAC). In this paper, the strategy followed by the European Union (EU) in distributing the established TAC among the seven countries is explored. It is inferred that the EU has utilized a weighted proportional rule, taking the average catches for the period 1973-78 as the reference point. On the other hand, given that the fishery situation for the years 1993, 1994, and 1995 can be characterized as a bankruptcy problem, this paper also explores, as possible means of enriching the Common European Fishery policy, alternatives to this rule. This work proposes the application of two additional rules derived from game theory, the nucleolus and the Shapley value, and studies their properties. The analysis suggests that it may be worth considering not only the proportional distribution, but also the alternative rules.

EGALITARIAN SETS FOR TU-GAMES

The paper introduces and studies egalitarian sets in the context of TU-games. Those solutions follow the idea that a payoff is egalitarian if it is bilaterally egalitarian.

Population monotonic allocation schemes on externality games

Abstract. This paper introduces a new class of cooperative games called externality games. In these games each player contributes with their specific endowment and also with their presence to the total worth of the coalition she belongs to. We prove that for these games there exists a unique efficient, anonymous and population monotonic rule: the proportional rule. A subclass of externality games is also analyzed. Games in this subclass are not necessarily convex although we show that the Shapley value is in the core of these games, but it is not a population monotonic rule.

Absorbing sets in roommate problems

We analyze absorbing sets as a solution for roommate problems with strict preferences. This solution provides the set of stable matchings when it is non-empty and some matchings with interesting properties otherwise. In particular, all matchings in an absorbing set have the greatest number of agents with no incentive to change partners. These “satisfied” agents are paired in the same stable manner. In the case of multiple absorbing sets we find that any two such sets differ only in how satisfied agents are matched with each other.

Absorbing and generalized stable sets

Within the framework of an abstract system we establish the existing relationship between the following two solutions: The absorbing sets solution and the generalized stable sets solution.

Artificial distinction and real discrimination

In this paper we consider the hawk-dove game played by a finite population formed by two types of individual who fail to recognize their own type but do observe the type of their opponent. In this game we find two evolutionarily stable strategies and show that in each of them one type of individuals suffers more aggression than the other. When a continuum of individuals is considered there are no evolutionarily stable strategies but neutrally stable strategies.

A new solution concept for the roommate problem: Q-stable matchings

The aim of this paper is to propose a new solution concept for the roommate problem with strict preferences. We introduce maximum irreversible matchings and consider almost stable matchings (Abraham et al., 2006) and maximum stable matchings (Tan 1990, 1991b). These solution concepts are all core consistent. We find that almost stable matchings are incompatible with the other two concepts. Hence, to solve the roommate problem we propose matchings that lie at the intersection of the maximum irreversible matchings and maximum stable matchings, which we call Q-stable matchings. We construct an efficient algorithm for computing one element of this set for any roommate problem. We also show that the outcome of our algorithm always belongs to an absorbing set (Inarra et al., 2013).