McQuillin, Ben (2008): The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure. Forthcoming in: Journal of Economic Theory
Download (251kB) | Preview
The Shapley value assigns, to each game that is adequately represented by its characteristic function, an outcome for each player. An elaboration on the Shapley value that assigns, to characteristic function games, a "partition function" outcome is broadly established and accepted, but elaborations to encompass games with externalities (represented by partition functions) are not. Here, I show that simultaneous consideration of the two elaborations ("generalization" and "extension") obtains a unique Shapley-type value for games in partition function form. The key requirement is that the "Extended, Generalized Shapley Value" (EGSV) should be "recursive": the EGSV of any game should be the EGSV of itself. This requirement forces us to ignore all but the payoffs to bilateral partitions. The EGSV can be conceptualized as the ex ante value of a process of successive bilateral amalgamations. Previous Shapley value extensions, if generalized, are not recursive; indeed, they iterate to the EGSV.
|Item Type:||MPRA Paper|
|Original Title:||The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure|
|Keywords:||Coalition structure; Externalities; Partition function games; Recursion; Shapley value|
|Subjects:||D - Microeconomics > D6 - Welfare Economics > D62 - Externalities
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games
|Depositing User:||Ben McQuillin|
|Date Deposited:||11. Dec 2008 09:24|
|Last Modified:||13. Mar 2015 21:21|
E.M. Bolger, A set of axioms for a value for partition function games, Int. J. Game Theory 18 (1989) 37-44.
F. Bloch, Sequential formation of coalitions in games with externalities and fixed payoff division, Games Econ. Behav. 14 (1996) 19-123.
G. de Clippel, R. Serrano, Marginal contributions and externalities in the value, Econometrica, forthcoming.
F. Gul, Bargaining foundations of Shapley value, Econometrica 57 (1989) 81-95.
S. Hart, M. Kurz, Endogenous formation of coalitions, Econometrica 51 (1983) 1047-64.
I. Macho-Stadler, D. Pérez-Castrillo, D. Wettstein, Sharing the surplus: an extension of the Shapley value for environments with externalities, J. Ec. Theory 135 (2007) 339-356.
E. Maskin, Bargaining, coalitions, and externalities, Presidential address of the Econometric Society, 2003.
R.B. Myerson, Values for games in partition function form, Int. J. Game Theory 6 (1977) 23-31.
J. Neumann, O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944.
G. Owen, Values of games with a priori unions, in: R. Henn, O. Moschlin (Eds.), Essays in Mathematical Economics and Game Theory, Springer Verlag, New York, 1977, pp. 76-88.
K.H. Pham Do, H. Norde, The Shapley value for partition function form games, Int. Game Theory Rev. 9 (2007) 353-360.
A.J. Potter, A Value for Partition Function Form Games, Working paper: Dept. of Mathematics, Hardin-simmons University, Abilene, Texas, 2000.
D. Ray, R. Vohra, A theory of endogenous coalition structures, Games Econ. Behav. 26 (1999) 286-336.
S.W. Salant, S. Switzer, R.J. Reynolds, Losses from horizontal merger: the effects of an exogenous change in the industry structure on Cournot-Nash equilibrium, Q. J. Econ. 98 (1983) 185-200.
L.S. Shapley, A value for n-person games, in: H.W. Kuhn, A.W. Tucker (Eds.), Contributions to the Theory of Games, II, Princeton University Press, Princeton, 1953, pp. 307-317.
M. Shubik, Incentives, decentralized control, the assignment of joint costs, and internal pricing, Manage. Sci. 8 (1962) 325-343.
M. Shubik, Game Theory in the Social Sciences: Concepts and Solutions, MIT Press, Cambridge, Mass., 1982.
R.M. Thrall, W.F. Lucas, n-person games in partition function form, Naval Logistics Quarterly 10 (1963) 281-293.
H.P. Young, Monotonic solutions of cooperative games, Int. J. Game Theory 14 (1985) 65-72.