On some decisive players for linear efficient and symmetric values in cooperative games with transferable utility

Nembua Célestin, Chameni and Wendji Clovis, Miamo (2017): On some decisive players for linear efficient and symmetric values in cooperative games with transferable utility.

Abstract

The main goal of the paper is to shed light on economic allocations issues, in particular by focusing on individuals who receive nothing (that is an amount of zero allocation or payoff). It is worth noting that such individuals may be considered, in some contexts, as poor or socially excluded. To this end, our study relies on the notion of cooperative games with transferable utility and the Linear Efficient and Symmetric values (called LES values) are considered as allocation rules. Null players in Shapley sense are extensively studied ; two broader classes of null players are introduced. The analysis is facilitated by the help of a parametric representation of LES values. It is clearly shown that the control of what a LES value assigns as payoffs to null players gives significant information about the characterization of the value. Several axiomatic characterizations of subclasses of LES values are provided using our approach.

• Item Type: MPRA Paper
• Language: English
• Keywords: TU-game, Linear Efficient and Symmetric value, Null players, Average null players, Shapley value, Solidarity value.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; D - Microeconomics > D3 - Distribution > D31 - Personal Income, Wealth, and Their Distributions; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations

References

Chameni Nembua C and Andjiga N G (2008), Linear, efficient and symmetric values for TU-games. Economics Bulletin, Vol. 3, No. 71 pp. 1-10.

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.

Chameni Nembua C and Miamo Wendji C (2016), Ordinal equivalence of values, Pigou-Dalton transfers and inequality in TU-games. Games and Economic Behavior 99,117-133.

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

Hernandez-Lamoneda L, Juarez R and Sanchez-Sanchez F (2008), Solution without dummy axiom for TU cooperative games. Economic Bulletin 3 (1), 19.

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

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

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

Radzik T and Driessen T S (2016), Modeling values for TU-games using generalized versions of consistency, stardardness and the null player property, Math Meth Oper Res, 83 179-205.

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

Shapley L S (1953), A value for n-person games. In : Kuhn HW, Tucker AW (eds) Contributions to the Theory of Games II, Annals of Mathematics Studies, Princeton University Press, Princeton, 307-317.

Van den Brink R (2007), Null or nullifying players : The difference between the Shapley value and equal division solution. Journal of Economic Theory 136 : 767-775.

Yang C H (1997), A Family of Values for n-person Cooperative Transferable Utility Games. MS. Thesis. University at Buffalo.

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