Bargaining Sets of Majority Voting Games
Let A be a finite set of m alternatives, let N be a finite set of n players and let R N be a profile of linear preference orderings on A of the players. Let u N be a profile of utility functions for R N. We define the NTU game V uN that corresponds to simple majority voting, and investigate its Aumann-Davis-Maschler and Mas-Colell bargaining sets. The first bargaining set is nonempty for m � 3 and it may be empty for m � 4. However, in a simple probabilistic model, for fixed m, the probability that the Aumann-Davis-Maschler bargaining set is nonempty tends to one if n tends to infinity. The Mas-Colell bargaining set is nonempty for m � 5 and it may be empty for m � 6. Furthermore, it may be empty even if we insist that n be odd, provided that m is sufficiently large. Nevertheless, we show that the Mas-Colell bargaining set of any simple majority voting game derived from the k-th replication of R N is nonempty, provided that k � n + 2.
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- Vohra, Rajiv, 1991. "An existence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 19-34.
- Mas-Colell, Andreu, 1989. "An equivalence theorem for a bargaining set," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 129-139, April.
- Bezalel Peleg & Peter Sudholter, 2004.
"On the Non-Emptiness of the Mas-Colell Bargaining Set,"
Discussion Paper Series
dp360, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
- Peleg, Bezalel & Sudholter, Peter, 2005. "On the non-emptiness of the Mas-Colell bargaining set," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 1060-1068, December.
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