Semivalues: weighting coefficients and allocations on unanimity games

This is a post-peer-review, pre-copyedit version of an article published in Optimization letters. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11590-017-1224-8.Each semivalue, as a solution concept defined on cooperative games with a finite set of players, is univocally determined by weighting coefficients that apply to players’ marginal contributions. Taking into account that a semivalue induces semivalues on lower cardinalities, we prove that its weighting coefficients can be reconstructed from the last weighting coefficients of its induced semivalues. Moreover, we provide the conditions of a sequence of numbers in order to be the family of the last coefficients of any induced semivalues. As a consequence of this fact, we give two characterizations of each semivalue defined on cooperative games with a finite set of players: one, among all semivalues; another, among all solution concepts on cooperative games.Peer ReviewedPostprint (author's final draft

A note on multinomial probabilistic values

This is a post-peer-review, pre-copyedit version of an article published in "TOP". The final authenticated version is available online at: https://doi.org/10.1007/s11750-017-0464-1Multinomial values were previously introduced by one of the authors in reliability and extended later to all cooperative games. Here, we present for this subfamily of probabilistic values three new results, previously stated only for binomial semivalues in the literature. They concern the dimension of the subspace spanned by the multinomial values and two characterizations: one, individual, for each multinomial value; another, collective, for the whole subfamily they form. Finally, an application to simple games is providedPeer ReviewedPostprint (author's final draft

On the axiomatic characterization of the coalitional multinomial probabilistic values

The coalitional multinomial probabilistic values extend the notion of multinomial probabilistic value to games with a coalition structure, in such a way that they generalize the symmetric coalitional binomial semivalues and link and combine the Shapley value and the multinomial probabilistic values. By considering the property of balanced contributions within unions, a new axiomatic characterization is stated for each one of these coalitional values, provided that it is defined by a positive tendency profile, by means of a set of logically independent properties that univocally determine the value. Two applications are also shown: (a) to the Madrid Assembly in Legislature 2015–2019 and (b) to the Parliament of Andalucía in Legislature 2018–2022.This research project was partially supported by funds from the Spanish Ministry of Science and Innovation under grant PID2019-104987GB-I00.Peer ReviewedPostprint (published version

Some properties for probabilistic and multinomial (probabilistic) values on cooperative games

This is an Accepted Manuscript of an article published by Taylor & Francis in Optimization on 18-02-2016, available online: http://www.tandfonline.com/10.1080/02331934.2016.1147035.We investigate the conditions for the coefficients of probabilistic and multinomial values of cooperative games necessary and/or sufficient in order to satisfy some properties, including marginal contributions, balanced contributions, desirability relation and null player exclusion property. Moreover, a similar analysis is conducted for transfer property of probabilistic power indices on the domain of simple games.Peer ReviewedPostprint (author's final draft

Forming and Dissolving Partnerships in Cooperative Game Situations

A group of players in a cooperative game are partners (e.g., as in the form of a union or a joint ownership) if the prospects for cooperation are restricted such that cooperation with players outside the partnership requires the accept of all the partners. The formation of such partnerships through binding agreements may change the game implying that players could have incentives to manipulate a game by forming or dissolving partnerships. The present paper seeks to explore the existence of allocation rules that are immune to this type of manipulation. An allocation rule that distributes the worth of the grand coalition among players, is called partnership formation-proof if it ensures that it is never jointly profitable for any group of players to form a partnership and partnership dissolution-proof if no group can ever profit from dissolving a partnership. The paper provides results on the existence of such allocation rules for general classes of games as well as more specific results concerning well known allocation rules.cooperative games; partnerships; partnership formation-proof; partnership dissolution-proof

Articles indexats publicats per investigadors del Campus de Terrassa: 2012

Aquest infrome recull els 221 treballs publicats per 216 investigadors/es del Campus de Terrassa en revistes indexades al Journal Citation Report durant el 2012Preprin

Articles indexats publicats per investigadors del Campus de Terrassa: 2013

Aquest informe recull els 228 treballs publicats per 177 investigadors/es del Campus de Terrassa en revistes indexades al Journal Citation Report durant el 2013Preprin