nach oben

Theory and Decision

Erschienen in:

03.02.2017

Axiomatization and implementation of a class of solidarity values for TU-games

verfasst von: Sylvain Béal, Eric Rémila, Philippe Solal

Erschienen in: Theory and Decision | Ausgabe 1/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

A new class of values combining marginalistic and egalitarian principles is introduced for cooperative TU-games. It includes some modes of solidarity among the players by taking the collective contribution of some coalitions to the grand coalition into account. Relationships with other class of values such as the Egalitarian Shapley values and the Procedural values are discussed. We propose a strategic implementation of our class of values in subgame perfect Nash equilibrium. Two axiomatic characterizations are provided: one of the whole class of values, and one of each of its extreme points.

Vorheriger Artikel Does inducing choice procedures make individuals better off? An experimental study

Nächster Artikel A note on budget constraints and outside options in common agency

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

The modified version of the null player axiom invoked in Nowak and Radzik (1994) does not rely on a parameter.

Desirability appears in the literature under different names, such as local monotonicity (e.g. Malawski 2013; Brink et al. 2013) or Fair treatment (e.g. Radzik and Driessen 2013).

Monotonicity is also known as Positivity (e.g. Kalai and Samet 1987) and Weak monotonicity (e.g. Malawski 2013). We refrain from using the latter name because Weak monotonicity is used in Brink et al. (2013) for a weak version of Strong monotonicity as introduced by Young (1985).

Banzhaf, J. F. (1965). Weighted voting doesn’t work: A mathematical analysis. Rutgers Law Review, 19, 317–343.

Béal, S., Rémila, E., & Solal, P. (2015). Preserving or removing special players: What keeps your payoff unchanged in TU-games? Mathematical Social Sciences, 73, 23–31.CrossRef

Casajus, A., & Huettner, F. (2013). Null players, solidarity, and the egalitarian Shapley values. Journal of Mathematical Economics, 49, 58–61.CrossRef

Casajus, A., & Huettner, F. (2014a). On a class of solidarity values. European Journal of Operational Research, 236, 583–591.CrossRef

Casajus, A., & Huettner, F. (2014b). Weakly monotonic solutions for cooperative games. Journal of Economic Theory, 154, 162–172.CrossRef

Chameni Nembua, C. (2012). Linear efficient and symmetric values for TU-games: Sharing the joint gain of cooperation. Games and Economic Behavior, 74, 431–433.CrossRef

Demange, G. (1984). Implementing efficient egalitarian outcomes. Econometrica, 52, 1167–1177.CrossRef

Driessen, T. S. H., & Funaki, Y. (1991). Coincidence of and collinearity between game theoretic solutions. OR Spektrum, 13, 15–30.CrossRef

Driessen, T. S. H., & Radzik, T. (2003). Extensions of Hart and Mas-Colell’s consistency to efficient, linear, and symmetric values for TU-games. In: L.A., P., D.W.K., Y. (Eds.), ICM Millennium Lectures on Games. volume dedicated to the International Congress of Mathematicians, Game Theory and Applications Satellite Conference, August 14-17, 2002, Quindao, China, pp. 147–166. Springer, Heidelberg, Germany.

García, D., & Vanden, J. M. (2009). Information acquisition and mutual funds. Journal of Economic Theory, 144, 1965–1995.CrossRef

Joosten, R. (1996). Dynamics, equilibria and values, dissertation no. 96-37, Faculty of Economics and Business, Maastricht University.

Ju, Y., Borm, P., & Ruys, P. (2007). The consensus value: a new solution concept for cooperative games. Social Choice and Welfare, 28, 685–703.CrossRef

Ju, Y., & Wettstein, D. (2009). Implementing cooperative solution concepts: a generalized bidding approach. Economic Theory, 39, 307–330.CrossRef

Kalai, E., & Samet, D. (1987). On weighted Shapley values. International Journal of Game Theory, 16, 205–222.CrossRef

Kamijo, Y., & Kongo, T. (2012). Whose deletion does not affect your payoff? the difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value. European Journal of Operational Research, 216, 638–646.CrossRef

Malawski, M. (2007). A note on equal treatment and symmetry of values, Report, Institute of Computer Science PAS.

Malawski, M. (2013). “Procedural” values for cooperative games. International Journal of Game Theory, 42, 305–324.CrossRef

Moulin, H. (1984). The conditional auction mechanism for sharing a surplus. Review of Economic Studies, 51, 157–170.CrossRef

Moulin, H., & Jackson, M. O. (1992). Implementing a public project and distributing its cost. Journal of Economic Theory, 57, 125–140.CrossRef

Nowak, A. S., & Radzik, T. (1994). A solidarity value for \(n\)-person transferable utility games. International Journal of Game Theory, 23, 43–48.CrossRef

Pérez-Castrillo, D., & Wettstein, D. (2001). Bidding for the surplus: a non-cooperative approach to the Shapley value. Journal of Economic Theory, 100, 274–294.CrossRef

Pérez-Castrillo, D., & Wettstein, D. (2002). Choosing wisely: a multi-bidding approach. American Economic Review, 92, 1577–1587.CrossRef

Radzik, T., & Driessen, T. (2013). On a family of values for TU-games generalizing the Shapley value. Mathematical Social Sciences, 65, 105–111.CrossRef

Radzik, T., & Driessen, T. (2016). Modeling values for TU-games using generalized versions of consistency, standardness and the null player property. Mathematical Methods of Operations Research, 83, 179–205.CrossRef

Ruiz, L. M., Valenciano, F., & Zarzuelo, J. M. (1996). The least square prenucleolus and the least square nucleolus. Two values for TU games based on the excess vector. International Journal of Game Theory, 25, 113–134.CrossRef

Ruiz, L. M., Valenciano, F., & Zarzuelo, J. M. (1998). The family of least square values for transferable utility games. Games and Economic Behavior, 24, 109–130.CrossRef

Shapley, L. S. (1953). A value for \(n\)-person games. In H. W. Kuhn & A. W. Tucker (Eds.), Contribution to the Theory of Games vol II, Annals of Mathematics Studies 28. Princeton: Princeton University Press.

Sprumont, Y. (1990). Population monotonic allocation schemes for cooperative games with transferable utility. Games and Economic Behavior, 2, 378–394.CrossRef

Stone, D. A. (1993). The struggle for the soul of health insurance. Journal of Health Politics, Policy and Law, 18, 287–317.CrossRef

van den Brink, R. (2007). Null players or nullifying players: the difference between the Shapley value and equal division solutions. Journal of Economic Theory, 136, 767–775.CrossRef

van den Brink, R., & Funaki, Y. (2015). Implementation and axiomatization of discounted Shapley values. Social Choice and Welfare, 45, 329–344.

van den Brink, R., Funaki, Y., & Ju, Y. (2013). Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values. Social Choice and Welfare, 40, 693–714.CrossRef

Young, H. P. (1985). Monotonic solutions of cooperative games. International Journal of Game Theory, 14, 65–72.CrossRef

Titel: Axiomatization and implementation of a class of solidarity values for TU-games
verfasst von: Sylvain Béal
Eric Rémila
Philippe Solal
Publikationsdatum: 03.02.2017
Verlag: Springer US
Erschienen in: Theory and Decision / Ausgabe 1/2017
Print ISSN: 0040-5833
Elektronische ISSN: 1573-7187
DOI: https://doi.org/10.1007/s11238-017-9586-z

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 1/2017

A note on budget constraints and outside options in common agency

Comparing uncertainty aversion towards different sources

Meaningful learning in weighted voting games: an experiment

Does inducing choice procedures make individuals better off? An experimental study

Coordination when there are restricted and unrestricted options

Stake effects on ambiguity attitudes for gains and losses

Premium Partner