Center for Economic Research, Department of Economics, University of Minnesota
Any social choice correspondence satisfying monotonicity and no veto
power with at least three participants is Nash implementable. This theorem
by Haskin, of which an extended version was proved by Williams, requires a
rather large strategy space. Each participant announces every participant's
preferences and an alternative. This paper presents a significantly smaller
strategy space when the number of participants is large. Each participant
announces his own preferences, his neighbor's preferences, an alternative, and
an integer between zero and the number of participants less one. With this
specification of the strategy spaces, the Haskin-Williams Theorem remains
valid without imposing any restrictions on the size of the alternative set or
the environment set. That is, a complete proof for the original Haskin
theorem is provided.
Saijo, T., (1985), "Strategy Space Reduction in the Maskin - Williams Theorem: Sufficient Conditions for Nash Implementation", Discussion Paper No. 213, Center for Economic Research, Department of Economics, University of Minnesota.
Strategy Space Reduction in the Maskin - Williams Theorem: Sufficient Conditions for Nash Implementation.
Center for Economic Research, Department of Economics, University of Minnesota.
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