Consistency and dynamic approach of indexes

Springer Science and Business Media LLC - Tập 34 - Trang 679-694 - 2009
Yan-An Hwang1, Yu-Hsien Liao2
1Department of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan
2Department of Applied Mathematics, National Pingtung University of Education, Pingtung, Taiwan

Tóm tắt

The purpose of this article is to study two indexes, the marginal index and the Banzhaf–Coleman index. For each of these two indexes, there is a corresponding reduced game that can be used to characterize it. In addition, we consider the efficient extensions of two indexes. In comparison to each characterization of two indexes, we establish a similar characterization for each extension of two indexes through an identical approach. Finally, for each of two efficient indexes, we propose a dynamic process leading to that corresponding efficient index, starting from an arbitrary efficient payoff vector.

Tài liệu tham khảo

Albizuri MJ (2001) An axiomatization of the modified Banzhaf–Coleman index. Int J Game Theory 30: 167–176 Alonso-Meijide JM, Carreras F, Fiestras-Janeiro MG, Owen G (2007) A comparative axiomatic characterization of the Banzhaf–Owen coalitional value. Dec Supp Syst 43: 701–712 Banzhaf JF (1965) Weighted voting doesn’t work: a mathematical analysis. Rutgers Law Rev 19: 317–343 Billera LJ (1972) Global stability in n-person games. Trans Am Math Soc 172: 45–56 Coleman JS (1971) Control of collectivities and the power of a collectivity to act. In: Lieberman B (eds) Social choice. Gordon and Breach, London, UK, pp 269–300 Davis M, Maschler M (1965) The Kernel of a cooperative game. Naval Res Logist Q 12: 223–259 Dubey P, Shapley LS (1979) Mathematical properties of the Banzhaf power index. Math Oper Res 4: 99–131 Haller H (1994) Collusion properties of values. Int J Game Theory 23: 261–281 Hamiache G (2001) Associated consistency and Shapley value. Int J Game Theory 30: 279–289 Harsanyi JC (1959) A bargaining model for the cooperative N-person game. In: Tucker AW, Luce RD (eds) Contributions to the theory of games IV (Annals of Mathematics Studies 40). Princeton University Press, Princeton, pp 325–355 Hart S, Mas-Colell A (1989) Potential, value, and consistency. Econometrica 57: 589–614 Hwang YA (2009) An NTU value under complement reduced game. Int J Game Theory 38: 305–324 Hwang YA, Li JH, Hsiao YH (2005) A dynamic approach to the Shapley value based on associated games. Int J Game Theory 33: 551–562 Laruelle A, Valenciano F (2001) Shapley-Shubik and Banzhaf indices revisited. Math Oper Res 26: 89–104 Lehrer E (1988) An axiomatization of the Banzhaf value. Int J Game Theory 17: 89–99 Maschler M, Owen G (1989) The consistent Shapley value for hyperplane games. Int J Game Theory 18: 389–407 Moulin H (1985) The separability axiom and equal-sharing methods. J Econ Theory 36: 120–148 Nowak AS (1997) On an axiomatization of the Banzhaf value without the additivity axiom. Int J Game Theory 26: 137–141 Owen G (1975) Multilinear extensions and the Banzhaf value. Naval Res Logist Q 22: 741–750 Owen G (1978) Characterization of the Banzhaf–Coleman index. SIAM J Appl Math 35: 315–327 Owen G (1981) Modification of the Banzhaf–Coleman index for games with a priori unions. In: Holler MJ (eds) Power, Voting and Voting Power. Physica-Verlag, Wurzburg, pp 232–238 Stearns RE (1968) Convergent transfer schemes for n-person games. Trans Am Math Soc 134: 449–459 Thomson W (2005) Consistent allocation rules. Mimeo, University of Rochester van der Brink R, van der Laan G (1998) Axiomatizations of the Normalized Banzhaf value and the Shapley value. Social Choice and Welfare 15: 567–582