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Representation of constitutions under incomplete information

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  • Bezalel Peleg
  • Shmuel Zamir

Abstract

We model constitutions by effectivity functions. We assume that the constitution is common knowledge among the members of the society. However, the preferences of the citizen are private information. We investigate whether there exist decision schemes (i. e., functions that map profiles of (dichotomous) preferences on the set of outcomes to lotteries on the set of social states), with the following properties: i) The distribution of power induced by the decision scheme is identical to the effectivity function under consideration; and ii) the (incomplete information) game associated with the decision scheme has a Bayesian Nash equilibrium in pure strategies. If the effectivity function is monotonic and superadditive, then we find a class of decision schemes with the foregoing properties. When applied to n-person games in strategic form, a decision scheme d is a mapping from profiles of (dichotomous) preferences on the set of pure strategy vectors to probability distributions over outcomes (or equivalently, over pure strategy vectors). We prove that for any feasible and individually rational payoff vector of a strategic game, there exists a decision scheme that yields that payoff vector as a (pure) Nash equilibrium payoff in the game induced by the strategic game and the decision scheme. This can be viewed as a kind of purification result.

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp634.

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Length: 25 pages
Date of creation: Jan 2013
Date of revision:
Handle: RePEc:huj:dispap:dp634

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  1. Hans Keiding & Bezalel Peleg, 2006. "Binary effectivity rules," Review of Economic Design, Springer, vol. 10(3), pages 167-181, December.
  2. Peleg, Bezalel & Peters, Hans & Storcken, Ton, 2002. "Nash consistent representation of constitutions: a reaction to the Gibbard paradox," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 267-287, March.
  3. Gibbard, Allan, 1974. "A Pareto-consistent libertarian claim," Journal of Economic Theory, Elsevier, vol. 7(4), pages 388-410, April.
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