Linear efficient and symmetric values for TU-games: sharing the joint gain of cooperation

Chameni Nembua, Célestin (2010): Linear efficient and symmetric values for TU-games: sharing the joint gain of cooperation.

Abstract

Two 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: TU-games; single valued solution; Shapley value, marginal contribution; null player axiom.
• Subjects: D - Microeconomics > D4 - Market Structure, Pricing, and Design > D46 - Value Theory; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games

References

[1] Brink, R. Van Den, Null or Nullifying players: The difference between Shapley value and the equal division solutions. Journal of Economic Theory (2007) 136: 767-775.

[2] Brink, R. Van Den and Yukihiko Funaki, Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games. Theory and Decision (2008) Vol 67, N°3; pp 303-340.

[3] Chameni Nembua, Célestin and Nicolas Gabriel Andjiga: Linear, efficient and symmetric values forTU-games. Economics Bulletin, :(2008) Vol. 3, No. 71 pp. 1-10.

[4] Hermandez-Lamoneda, Luis, Ruben Juarez, and Francisco Sanchez-Sanchez : Solution Without dummy axiom for TU cooperative games.Economics Bulletin (2008),Vol.3, No.1 pp 1-9.

[5] Nowak A.S. and Radzik T. A solidarity Value for n-person Transferable Utility games.Int Jour of Game Theory (1994), 23: 43-48.

[6] Shapley L.S , A value for n-person games. In: Kuhn H, Tucker AW (eds)Contributions to the theory of games, (1953) vol. II. Princeton University Press, Princeton,NJ.

[7] Yuan Ju, P. Born and P. Ruys ,The Concensus Value: a new solution concept for cooperative games. Soc. Choice Welfare (2007), 28 685-703.