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, 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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- repec:ebl:ecbull:v:3:y:2008:i:71:p:1-10 is not listed on IDEAS
- 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.
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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, vol. 136(1), pages 767-775, September.
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- René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
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- Radzik, Tadeusz, 2013. "Is the solidarity value close to the equal split value?," Mathematical Social Sciences, Elsevier, vol. 65(3), pages 195-202.
- Chameni Nembua, Célestin & 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. "“Procedural” values for cooperative games," International Journal of Game Theory, Springer, vol. 42(1), pages 305-324, February.
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