Linear efficient and symmetric values for TU-games: sharing the joint gain of cooperation
AbstractTwo well-known single valued solutions for TU-games are the Shapley value and Solidarity value, which verify three properties: Linearity, Symmetry and Efficiency, and the null player axiom. On the other hand, the interpretation of the two values is usually related on the marginal contribution of a player that joins a coalition. The paper generalizes the approach. First, the marginal contribution concept is extended to any valued solution that satisfies the three properties. Second, the null player axiom is also generalized and it is shown that any single valued solution satisfying the three properties is uniquely characterized by a null player axiom. In particular, the paper provides new interpretations, in the sense of marginal contribution, for other well-known single values such as Egalitarian value and Consensus value and also offers the opportunity for recasting in extensive form some well-established results.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 31249.
Date of creation: 2010
Date of revision: 2010
TU-games; single valued solution; Shapley value; marginal contribution; null player axiom.;
Other versions of this item:
- Chameni Nembua, C., 2012. "Linear efficient and symmetric values for TU-games: Sharing the joint gain of cooperation," Games and Economic Behavior, Elsevier, Elsevier, vol. 74(1), pages 431-433.
- D46 - Microeconomics - - Market Structure and Pricing - - - Value Theory
- D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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- van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, Elsevier, vol. 136(1), pages 767-775, September.
- Francisco Sanchez-Sanchez & Ruben Juarez & Luis Hernandez-Lamoneda, 2008. "Solutions without dummy axiom for TU cooperative games," Economics Bulletin, AccessEcon, vol. 3(1), pages 1-9.
- CÃ©lestin Chameni Nembua & Nicolas Gabriel Andjiga, 2008. "Linear, efficient and symmetric values for TU-games," Economics Bulletin, AccessEcon, vol. 3(71), pages 1-10.
- Nowak, Andrzej S & Radzik, Tadeusz, 1994. "A Solidarity Value for n-Person Transferable Utility Games," International Journal of Game Theory, Springer, Springer, vol. 23(1), pages 43-48.
- repec:ebl:ecbull:v:3:y:2008:i:71:p:1-10 is not listed on IDEAS
- repec:ebl:ecbull:v:3:y:2008:i:1:p:1-9 is not listed on IDEAS
- Ju, Y. & Borm, P.E.M. & Ruys, P.H.M., 2004.
"The Consensus Value: A New Solution Concept for Cooperative Games,"
Discussion Paper, Tilburg University, Center for Economic Research
2004-50, Tilburg University, Center for Economic Research.
- Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer, Springer, vol. 28(4), pages 685-703, June.
- Ju, Y. & Borm, P.E.M. & Ruys, P.H.M., 2007. "The consensus value: A new solution concept for cooperative games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-195202, Tilburg University.
- RenÃ© Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, Springer, vol. 67(3), pages 303-340, September.
- Chameni Nembua, CÃ©lestin & Demsou, Themoi, 2013. "Ordinal equivalence of values and Pigou-Dalton transfers in TU-games," MPRA Paper 44895, University Library of Munich, Germany, revised 09 Mar 2013.
- Marcin Malawski, 2013. "â€œProceduralâ€ values for cooperative games," International Journal of Game Theory, Springer, Springer, vol. 42(1), pages 305-324, February.
- Casajus, AndrÃ© & HÃ¼ttner, Frank, 2012.
"Null players, solidarity, and the egalitarian Shapley values,"
113, University of Leipzig, Faculty of Economics and Management Science.
- Casajus, AndrÃ© & Huettner, Frank, 2013. "Null players, solidarity, and the egalitarian Shapley values," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 58-61.
- Casajus, AndrÃ© & Huettner, Frank, 2014. "On a class of solidarity values," European Journal of Operational Research, Elsevier, Elsevier, vol. 236(2), pages 583-591.
- Lee, Joosung & Driessen, Theo S.H., 2012. "Sequentially two-leveled egalitarianism for TU games: Characterization and application," European Journal of Operational Research, Elsevier, Elsevier, vol. 220(3), pages 736-743.
- Radzik, Tadeusz, 2013. "Is the solidarity value close to the equal split value?," Mathematical Social Sciences, Elsevier, Elsevier, vol. 65(3), pages 195-202.
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