BUSCADOR RECOLECTA

In this work, we consider games with coalitional structure. We afford two new parallel axiomatic characterizations for the well-known Owen and Banzhaf–Owen coalitional values. Two properties are common to both characterizations: a property of balanced contributions and a property of neutrality. The results prove that the main difference between these two coalitional values is that the former is efficient, while the latter verifies a property of 2-efficiency.

In this paper, we define a modification of the Shapley value for the model of TU games with a priori unions. We provide two characterizations of this value and a new characterization of the Banzhaf-Owen coalitional value.

In this paper we consider coalition configurations (Albizuri et al. in Games Econ Behav 57:1–17, 2006), that is, families of coalitions not necessarily disjoint whose union is the grand coalition, and give a generalization of the Shapley value (Contributions to the theory of games II, Princeton University Press, Princeton, pp 307–317, 1953) and the Owen value (Essays in mathematical economics and game theory, Springer, Berlin, pp 76–88, 1977) when coalition configurations form. This will be an alternative definition to the one given by Albizuri et al., Ministerio de Ciencia e Innovación | Ref. ECO2011-23460, Ministerio de Economía y Competitividad | Ref. ECO2012-33618, Universidad del País Vasco | Ref. UFI11/5, Universidad del País Vasco | Ref. GIU13/31, Xunta de Galicia | Ref. 10PXIB362299PR

In coalitional games in which the players are partitioned into groups, we study the incentives of the members of a group to leave it and become singletons. In this context, we model a non-cooperative mechanism in which each player has to decide whether to stay in her group or to exit and act as a singleton. We show that players, acting myopically, always reach a Nash equilibrium., Ministerio de Ciencia e Innovación | Ref. ECO2011-23460, Xunta de Galicia | Ref. 10PXIB362299PR

n agents located along a river generate residues that then require cleaning to return the river to its natural state, which entails some cost. We propose several rules to distribute the total pollutant-cleaning cost among all the agents. We provide axiomatic characterizations using properties based on water taxes. Moreover, we prove that one of the rules coincides with the weighted Shapley value of a game associated with the problem., Ministerio de Ciencia e Innovación | Ref. ECO2008-03484-C02-01, Ministerio de Ciencia e Innovación | Ref. ECO2011-23460

The division problem under constraints consists of allocating a given amount of an homogeneous and perfectly divisible good among a subset of agents with single-peaked preferences on an exogenously given interval of feasible allotments. We characterize axiomatically the family of extended uniform rules proposed to solve the division problem under constraints. Rules in this family extend the uniform rule used to solve the classical division problem without constraints. We show that the family of all extended uniform rules coincides with the set of rules satisfying efficiency, strategy-proofness, equal treatment of equals, bound monotonicity, consistency, and independence of irrelevant coalitions.

We study how to partition a set of agents in a stable way when each coalition in the partition has to share a unit of a perfectly divisible good, and each agent has symmetric single-peaked preferences on the unit interval of his potential shares. A rule on the set of preference profiles consists of a partition function and a solution. Given a preference profile, a partition is selected and as many units of the good as the number of coalitions in the partition are allocated, where each unit is shared among all agents belonging to the same coalition according to the solution. A rule is stable at a preference profile if no agent strictly prefers to leave his coalition to join another coalition and all members of the receiving coalition want to admit him. We show that the proportional solution and all sequential dictator solutions admit stable partition functions. We also show that stability is a strong requirement that becomes easily incompatible with other desirable properties like efficiency, strategy-proofness, anonymity, and non-envyness.