Cooperative Multicriteria Games with Public and Private Criteria: An Investigation of Core Concepts

A new class of cooperative multicriteria games is introduced which takes into account two different types of criteria: private criteria, which correspond to divisible and excludable goods, and public criteria, which in an allocation take the same value for each coalition member. The different criteria are not condensed by means of a utility function, but left in their own right. Moreover, the games considered are not single-valued, but each coalition can realize a set of vectors - representing the outcomes of each of the criteria - depending on several alternatives. Two core concepts are defined: the core and the dominance outcome core. The relation between the two concepts is studied and the core is axiomatized by means of consistency properties.

Kalai-Smorodinsky Bargaining Solution Equilibria

Multicriteria games describe strategic interactions in which players, having more than one criterion to take into account, don't have an a-priori opinion on the rel- ative importance of all these criteria. Roemer (2005) introduces an organizational interpretation of the concept of equilibrium: each player can be viewed as running a bargaining game among criteria. In this paper, we analyze the bargaining problem within each player by considering the Kalai-Smorodinsky bargaining solution. We provide existence results for the so called Kalai-Smorodinsky bargaining solution equilibria for a general class of disagreement points which properly includes the one considered in Roemer (2005). Moreover we look at the refinement power of this equilibrium concept and show that it is an effective selection device even when combined with classical refinement concepts based on stability with respect to perturbations such as the the extension to multicriteria games of the Selten's (1975) trembling hand perfect equilibrium concept.

On Multicriteria Games with Uncountable Sets of Equilibria

The famous Harsanyi's (1973) Theorem states that generically a finite game has an odd number of Nash equilibria in mixed strategies. In this paper, we show that for finite multicriteria games (games with vector-valued payoffs) this kind of result does not hold. In particular, we show, by examples, that it is possible to find balls in the space of games such that every game in this set has uncountably many equilibria so that uncountable sets of equilibria are not nongeneric in multicriteria games. Moreover, we point out that, surprisingly, all the equilibria of the games cor- responding to the center of these balls are essential, that is, they are stable with respect to every possible perturbation on the data of the game. However, if we consider the scalarization stable equilibrium concept (introduced in De Marco and Morgan (2007) and which is based on the scalarization technique for multicriteria games), then we show that it provides an effective selection device for the equilibria of the games corresponding to the centers of the balls. This means that the scalarization stable equilibrium concept can provide a sharper selection device with respect to the other classical refinement concepts in multicriteria games.

Bipolarization of posets and natural interpolation

The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of $[0,1]^n$. We take this basic fact as a starting point to define the Choquet integral in a very general way, using the geometric realization of lattices and their natural triangulation, as in the work of Koshevoy. A second aim of the paper is to define a general mechanism for the bipolarization of ordered structures. Bisets (or signed sets), as well as bisubmodular functions, bicapacities, bicooperative games, as well as the Choquet integral defined for them can be seen as particular instances of this scheme. Lastly, an application to multicriteria aggregation with multiple reference levels illustrates all the results presented in the paper.Interpolation; Choquet integral; Lattice; Bipolar structure

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

Game theory approach to competitive economic dynamics

This thesis deals both with non-cooperative and cooperative games in order to apply the mathematical theory to competitive dynamics arising from economics, particularly quantity competition in oligopolies and pollution reduction models in IEA (International Environmental Agreements)

Cooperative Multicriteria Games with Public and Private Criteria:An Investigation of Core Concepts

A new class of cooperative multicriteria games is introduced which takes into account two different types of criteria: private criteria, which correspond to divisible and excludable goods, and public criteria, which in an allocation take the same value for each coalition member. The different criteria are not condensed by means of a utility function, but left in their own right. Moreover, the games considered are not single-valued, but each coalition can realize a set of vectors - representing the outcomes of each of the criteria - depending on several alternatives. Two core concepts are defined: the core and the dominance outcome core. The relation between the two concepts is studied and the core is axiomatized by means of consistency properties.

Game theory approach to competitive economic dynamics

This thesis deals both with non-cooperative and cooperative games in order to apply the mathematical theory to competitive dynamics arising from economics, particularly quantity competition in oligopolies and pollution reduction models in IEA (International Environmental Agreements)