Nash Consistent Representation of Constitutions: A Reaction to the Gibbard Paradox

B. Peleg, H.J.M. Peters*, A.J.A. Storcken

*Corresponding author for this work

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Abstract

The concept of an effectivity function is adopted as a formal model of a constitution. A game form models the actions available and permissible to individuals in a society. As a representation of the constitution such a game form should endow each group in society with the same power as it has under the constitution. Another desirable property is Nash consistency of the game form: whatever the individual preferences, the resulting game should be minimally stable in the sense of possessing a Nash equilibrium. A first main result of the paper is a characterization of all effectivity functions that have a Nash consistent representation for the case without special structure on the set of alternatives (social states). Next, a similar result is derived for the case where the set of alternatives is a topological space and the effectivity function is topological. As a special case, veto functions are considered. Further results concern Pareto optimality of Nash equilibrium outcomes.
Original languageEnglish
Pages (from-to)267-287
JournalMathematical Social Sciences
Volume43
DOIs
Publication statusPublished - 1 Jan 2002

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