A strong representation of a committee, formalized as a simple game, on a convex and closed set of alternatives is a game form with the members of the committee as players such that (i) the winning coalitions of the simple game are exactly those coalitions, which can get any given alternative independent of the strategies of the complement, and (ii) for any profile of continuous and convex preferences, the resulting game has a strong Nash equilibrium. In the paper, it is investigated whether committees have representations on convex and compact subsets of Rm. This is shown to be the case if there are vetoers; for committees with no vetoers the existence of strong representations depends on the structure of the alternative set as well as on that of the committee (its Nakamura-number). Thus, if A is strictly convex, compact, and has smooth boundary, then no committee can have a strong representation on A. On the other hand, if A has non-smooth boundary, representations may exist depending on the Nakamura-number (if it is at least 7).
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Paper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number
99-20.
Length: 26 pages Date of creation: Jul 1999 Date of revision: Handle: RePEc:kud:kuiedp:9920
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Find related papers by JEL classification: D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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