On Societies Choosing Social Outcomes, and their Memberships : Strategy-proofness

April 2017, Volume 48, Issue 4, pp 857-875The work of G. Bergantiños is partially supported by research Grants ECO2014-52616-R from the Spanish Ministry of Science and Competitiveness, GRC 2015/014 from "Xunta de Galicia", and 19320/PI/14 from " Fundaci ón Séneca de la Región de Murcia". J. Massó acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563) and Grant ECO2014-53051, and from the Generalitat de Catalunya, through Grant SGR2014-515. The paper was partly written while J. Massó was visiting the Department of Economics at Stanford University; he wishes to acknowledge its hospitality as well as financial support from the Ministerio de Educación, Cultura y Deporte through project PR2015-00408. The work of A. Neme is partially supported by the Universidad Nacional de San Luis, through Grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), through Grant PIP 112-200801-00655.We consider a society whose members have to choose not only an outcome from a given set of outcomes but also the subset of agents that will remain members of the society. We assume that each agent is indifferent between any two alternatives (pairs of final societies and outcomes) provided that the agent does not belong to any of the two final societies, regardless of the chosen outcome. Under this preference domain restriction we characterize the class of all strategy-proof, unanimous and outsider independent rules as the family of all serial dictator rules

The Division Problem under Constraints

The work of G. Bergantiños is partially supported by research grants ECO2008-03484-C02-01 and ECO2011-23460 from the Spanish Ministry of Science and Innovation and FEDER. J. Massó acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075) and through grant ECO2008-0475-FEDER (Grupo Consolidado-C), and from the Generalitat de Catalunya, through the prize "ICREA Academia" for excellence in research and grant SGR2009-419. The work of A. Neme is partially supported by the Universidad Nacional de San Luis, through grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), through grant PIP 112-200801-00655.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

The division problem with maximal capacity constraints

We thank an anonymous referee whose comments and suggestions helped us to write a better paper. The work of G. Bergantiños is partially supported by research grant ECO2008-03484-C02-01 from the Spanish Ministry of Science and Innovation and FEDER. Support for the research of J. Massó was received through the prize "ICREA Acadèmia" for excellence in research, funded by the Generalitat de Catalunya. He also acknowledges the support of MOVE (where he is an affiliated researcher), of the Barcelona Graduate School of Economics (where he is an affiliated professor), and of the Government of Catalonia, through grant SGR2009-419. His work is also supported by the Spanish Ministry of Science and Innovation through grants ECO2008-04756 (Grupo Consolidado-C) and CONSOLIDER-INGENIO 2010 (CDS2006-00016). The work of A. Neme is partially supported by the Universidad Nacional de San Luis through grant 319502 and by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) through grant PICT-02114.The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. Most of the literature has implicitly assumed that all divisions are feasible. In this paper we consider the division problem when each agent has a maximal capacity due to an objective and verifiable feasibility constraint which imposes an upper bound on his share. Then each agent has a feasible interval of shares where his preferences are single-peaked. A rule has to propose to each agent a feasible share.We focus mainly on strategy-proof, efficient and consistent rules and provide alternative characterizations of the extension of the uniform rule that deals explicitly with agents' maximal capacity constraint

The chi-compromise value for non-transferable utility games

We thank Carles Rafels, Howard Petith, and a referee for their helpful comments. Financial support from the Spanish Ministry of Education and Culture (through grants PB98-0870 and PB98-0613-C02-01), from the Xunta de Galicia (through grant PGIDT00PXI30001PN), and from the Departament d'Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya through grant 2000SGR-0054) is gratefully acknowledged. The paper was partially written while Jordi Massó was visiting the Universidad Nacional de San Luis (Argentina). He acknowledges the hospitality of its Instituto de Matemática Aplicada and the nancial support through a sabbatical fellowship from the Spanish Ministry of Education and Culture.We introduce a compromise value for non-transferable utility games: the Chi-compromise value. It is closely related to the Compromise value introduced by Borm, Keiding, McLean, Oortwijn, and Tijs (1992), to the MC-value introduced by Otten, Borm, Peleg, and Tijs (1998), and to the Ω-value introduced by Bergantiños, Casas- Méndez, and Vázquez-Brage (2000). The main difference being that the maximal aspiration a player may have in the game is his maximal (among all coalitions) marginal contribution. We show that it is well defined on the class of totally essential and non-level games. We propose an extensive-form game whose subgame perfect Nash equilibrium payoffs coincide with the Chi-compromise valu

The division problem with voluntary participation

We thank Bettina Klaus, an Associate Editor and a referee for helpful comments. We are specially grateful to William Thomson for his many comments and suggestions. The work of G. Bergantiños is partially supported by research grant ECO2008-03484-C02-01 from the Spanish Ministry of Science and Innovation and FEDER. Support for the research of J. Massó was received through the prize ICREA Acadèmia for excellence in research, funded by the Generalitat de Catalunya. He also acknowledges the support of MOVE, where he is an affiliated researcher, and the Barcelona Graduate School of Economics (through its Research Recognition Programme), where he is an a¢ liated professor. His work is also supported by the Spanish Ministry of Science and Innovation, through grants ECO2008-04756 (Grupo Consolidado-C) and CONSOLIDER-INGENIO 2010 (CDS2006-00016), and by the Generalitat de Catalunya, through grant SGR2009-419. The work of A. Neme is partially supported by the Universidad Nacional de San Luis, through grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), through grant PIP 112-200801-00655.The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents shares. We study a subclass of e¢ cient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents voluntary participation

Stable Partitions in Many Division Problems : The Proportional and the Sequential Dictator Solutions

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

An undominated Nash equilibrium for voting by committees with exit

We consider the problem of a society whose members choose, with a voting by committees, a subset of new members from a given set of candidates. After knowing the elected candidates, former members may decide either stay or exit the society. We analyze the voting behavior of members who take into account the effect of their votes not only on the elected candidates, but also on the final composition of the society. For additive and monotonic preferences with dichotomous bads we construct a strategy profile that is an undominated pure strategy Nash equilibrium of the induced voting game

Single agents and the set of many-to-one stable matchings

We thank José Alcade, Carmen Beviá, Flip Klijn, David Pérez-Castrillo, Howard Petith, Alvin Roth, Tayfun Sönmez, and an associate editor for helpful comments. We are especially grateful to an anonymous referee whose suggestions and comments helped to improve the paper considerably. Financial support through a grant from the Programa de Cooperación Científica Iberoamericana is acknowledged. The work of Jordi Massó is also partially supported by Research Grants PB96-1192 from the Dirección General de Investigación Científica y Técnica, Spanish Ministry of Education, and SGR98-62 from the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. The paper was partially written while Alejandro Neme was visiting the UAB under a sabbatical fellowship from the Spanish Ministry of Education.Some properties of the set of many-to-one stable matchings for firms that have responsive preferences and quotas are not necessarily true when firms' preferences are substitutable. In particular, we provide examples in which firms have substitutable preferences but firms and workers may be "single" in one stable matching and matched in another one. We identify a set of axioms on firms' preferences guaranteeing that the set of unmatched agents is the same under every stable matching. We also propose a weaker condition than responsiveness, called separability with quotas or q-separability, that together with substitutability implies this set of axioms

The Division problem with voluntary participation

The division problem consists of allocating a given amount of an homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this paper we consider the division problem when agents' participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents' shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents' voluntary participation