Nash consistent representation of constitutions: a reaction to the Gibbard paradox

Abstract

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Representations of Political Power Structures by Strategically Stable Game Forms: A Survey

“…It is clear that if x ε ∩{B(h): h ε N}, then x satisfies (14) for R N. . Hence, we have proved one direction of the following important theorem, due to Peleg, Peters, and Storcken [20]. Theorem 8.…”

On existence of ex post Nash consistent representation for effectivity functions

“…In the case n = 2 this condition is equivalent to at least one of the two players being a so-called singleton player: a singleton player is a player for whom all minimal sets for which this player is effective, are singletons. We also show that, if only one of the players has more than one type, then ex post Nash consistency imposes no additional restrictions compared to Nash consistency (as in Peleg et al 2002). In the final part of the paper we provide a short discussion on effectivity functions that have no ex post Nash consistent representation, but for which a representation exists if we restrict the number of types-a special case being the mentioned one where only one player has more than one type.…”

“…Specifically, if T = {T } with |T i | = 1 for every i ∈ N , then an ex post consistent game form is Nash consistent (cf. Peleg et al 2002). We say that effectivity function E has an ex post consistent representation for a collection T of information structures if there exists a game form such that is a representation of E and is ex post consistent for T .…”

“…Later, we will extend and modify this game form to obtain our main results. Alternative representing game forms can be found in many places, notably Peleg (1998), Peleg et al (2002), Peleg and Peters (2010), and Boros et al (2010).…”

“…An important further question is whether we can find rules (in accordance with the constitution) such that there is a situation in which the society is stable, that is, in some state of equilibrium. Peleg et al (2002) answered this question by characterizing effectivity functions that have a Nash consistent representation, i.e., a game form representing the effectivity function and having a Nash equilibrium for any profile of preferences of the individuals. See Peleg and Peters (2010) for an extensive treatment of this topic and related issues.…”