Monotonicity and Egalitarianism (revision of CentER DP 2019-007)

This paper identifies the maximal domain of transferable utility games on which aggregate monotonicity (no player is worse o when the worth of the grand coalition increases) and egalitarian core selection (no other core allocation can be obtained by a transfer from a richer to a poorer player) are compatible. On this domain, which includes the class of large core games, we show that these two axioms characterize a unique solution which even satisfies coalitional monotonicity (no member is worse off when the worth of one coalition increases) and strong egalitarian core selection (no other core allocation can be obtained by transfers from richer to poorer players)

On minimax and Pareto optimal security payoffs in multicriteria games

[EN] In this paper, we characterize minimax and Pareto-optimal security payoff vectors for general multicriteria zero-sum matrix games, using properties similar to the ones that have been used in the single criterion case. Our results show that these two solution concepts are rather similar, since they can be characterized with nearly the same sets of properties. Their main difference is the form of consistency that each solution concept satisfies. We also prove that both solution concepts can transform into each other, in their corresponding domains. (C) 2017 Elsevier Inc. All rights reserved.We would like to thank Dr. Francisco R. Fernandez for his useful comments on earlier versions of this paper. The authors also want to acknowledge the financial support from grants FQM-5849 (Junta de Andalucia\FEDER) and MTM2016-74983-C02-01, MTM2013-46962-C02-01 (MICINN, Spain).Puerto Albandoz, J.; Perea Rojas Marcos, F. (2018). On minimax and Pareto optimal security payoffs in multicriteria games. Journal of Mathematical Analysis and Applications. 457(2):1634-1648. https://doi.org/10.1016/j.jmaa.2017.01.002S16341648457

The incentive core in co-investment problems

We study resource-monotonicity properties of core allocations in coinvestment problems: those where a set of agents pool their endowments of a certain resource or input in order to obtain a joint surplus or output that must be allocated among the agents. We analyze whether agents have incentives to raise their initial contribution (resource-monotonicity). We focus not only on looking for potential incentives to agents who raise their contributions, but also in not harming the payoffs to the rest of agents (strong monotonicity property). A necessary and suficient condition to fulfill this property is stated and proved. We also provide a subclass of coinvestment problems for which any core allocation satisfies the aforementioned strong resource-monotonicity property. Moreover, we introduce the subset of core allocations satisfying this condition, namely the incentive core

Monotonicity of the core-center of the airport game

Abstract One of the main goals of this paper is to improve the understanding of the way in which the core of a specific cooperative game, the airport gam

Racionalitat i monotonia en jocs cooperatius: possibilitats i impossibilitats

Treballs Finals del Doble Grau d'Administració i Direcció d'Empreses i de Matemàtiques, Facultat d'Economia i Empresa i Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Curs: 2021-2022 , Tutor: Josep Vives i Santa-Eulàlia i Pere CallejaLes solucions puntuals dels jocs cooperatius recomanen com repartir allò que els agents poden obtenir si cooperen. En aquest treball, fem una anàlisi sobre quines de les solucions més importants satisfan certes propietats de racionalitat i/o monotonia. En particular, estudiem el comportament de solucions ben conegudes com són el valor de Shapley, el prenucleolus i el prenucleolus per-càpita respecte de la propietat de selecció del core i de propietats de monotonia com la monotonia coalicional. La propietat de selecció del core imposa que sempre que sigui possible, la recomanació feta per una solució no ha de donar incentius als agents individuals ni a cap coalició a anar per lliure, és a dir, a trencar la cooperació. Es per aquest motiu que la considerem una propietat de racionalitat. En canvi, la propietat de monotonia coalicional requereix que sempre que una coalició es faci més forta (mentre que el valor de les altres coalicions no varia), cap membre de la coalició surti perdent. Veiem com la imposició d’aquestes propietats impossibilitaran trobar una solució que compleixi les dues. Llavors, relaxem la propietat de monotonia per introduir la propietat de monotonia agregada. Aquesta propietat demana que si la coalició de tots els jugadors es fa més forta (i el valor de la resta de coalicions es manté igual), cap agent surti perdent. En aquest cas, no només el prenucleolus per-càpita satisfà la combinació de selecció del core i monotonia agregada, sinó que tot un conjunt de solucions ho fa, del qual n’estudiem la geometria. Finalment, definim una nova propietat de monotonia coalicional, la monotonia coalicional dèbil, amb la qual deixem la porta oberta a un estudi futur quant a si és o no compatible amb la selecció del core

The aggregate-monotonic core

We introduce the aggregate-monotonic core as the set of allocations of a transferable utility cooperative game attainable by single-valued solutions that satisfy core-selection and aggregate-monotonicity. We provide a necessary and sufficient condition for the coincidence of the core and the aggregate-monotonic core. Finally, we introduce upper and lower aggregate-monotonicity for set-valued solutions, and characterize the aggregate-monotonic core using core-selection and upper and lower aggregatemonotonicity

The aggregate-monotonic core

We introduce the aggregate-monotonic core as the set of allocations of a transferable utility cooperative game attainable by single-valued solutions that satisfy core-selection and aggregate-monotonicity. We provide a necessary and sufficient condition for the coincidence of the core and the aggregate-monotonic core. Finally, we introduce upper and lower aggregate-monotonicity for set-valued solutions, and characterize the aggregate-monotonic core using core-selection and upper and lower aggregatemonotonicity