Nash implementable domains for the Borda count

We characterize the preference domains on which the Borda count satisfies Maskin monotonicity. The basic concept is the notion of a "cyclic permutation domain" which arises by fixing one particular ordering of alternatives and including all its cyclic permutations. The cyclic permutation domains are exactly the maximal domains on which the Borda count is strategy-proof (when combined with every tie breaking rule). It turns out that the Borda count is monotonic on a larger class of domains. We show that the maximal domains on which the Borda count satisfies Maskin monotonicity are the "cyclically nested permutation domains." These are the preference domains which can be obtained from the cyclic permutation domains in an appropriate recursive way.Maskin monotonicity; Borda count; restricted preference domains

Nash implementable domains for the Borda count

We characterize the preference domains on which the Borda count satisfies Maskin monotonicity. The basic concept is the notion of a "cyclic permutation domain" which arises by fixing one particular ordering of alternatives and including all its cyclic permutations. The cyclic permutation domains are exactly the maximal domains on which the Borda count is strategy-proof (when combined with every tie breaking rule). It turns out that the Borda count is monotonic on a larger class of domains. We show that the maximal domains on which the Borda count satisfies Maskin monotonicity are the "cyclically nested permutation domains." These are the preference domains which can be obtained from the cyclic permutation domains in an appropriate recursive way

The scholarship assignment problem

There are n graduate students and n faculty members. Each student will be assigned a scholarship by the joint faculty. The socially optimal outcome is that the best student should get the most prestigious scholarship, the second-best student should get the second most prestigious scholarship, and so on. The socially optimal outcome is common knowledge among all faculty members. Each professor wants one particular student to get the most prestigious scholarship and wants the remaining scholarships to be assigned according to the socially optimal outcome. We consider the problem of finding a mechanism such that in equilibrium, all scholarships are assigned according to the socially optimal outcome.Publicad

Maskin-Monotonic Scoring Rules

Cataloged from PDF version of article.We characterize which scoring rules are Maskin-monotonic for each social choice problem as a function of the number of agents and the number of alternatives. We show that a scoring rule is Maskin-monotonic if and only if it satisfies a certain unanimity condition. Since scoring rules are neutral, Maskin-monotonicity turns out to be equivalent to Nash-implementability within the class of scoring rules. We propose a class of mechanisms such that each Nash-implementable scoring rule can be implemented via a mechanism in that class. Moreover, we investigate the class of generalized scoring rules and show that with a restriction on score vectors, our results for the standard case are still valid

Nash Implementation Using Undominated Strategies

This paper provides a characterization of fully implementable outcomes using undominated Nash equilibrium, i.e. a Nash equilibrium in which no one uses a weakly dominated strategy. The analysis is conducted in general domains in which agents have complete information. Our main result is that with at least three agents any social choice function or correspondence obeying the usual no veto power condition is implementable unless some players are completely indifferent over all possible outcomes. This result is contrasted with the more restrictive implementation findings with either (unrefined) Nash equilibrium or subgame perfect equilibrium

Implementation Theory

This surveys the branch of implementation theory initiated by Maskin (1977). Results for both complete and incomplete information environments are covered

Nash Implementation Using Undominated Strategies

We study the problem of implementing social choice correspondences using the concept of undominated Nash equilibrium, i.e. Nash equilibrium in which no one uses a weakly dominated strategy. We show that this mild refinement of Nash equilibrium has a dramatic impact on the set of implementable correspondences. Our main result is that if there are at least three agents in the society, then any correspondence which satisfies the usual no veto power condition is implementable unless some agents are completely indifferent over all possible outcomes. Many common welfare criteria, such as the Pareto correspondence, and several familiar voting rules, such as majority and plurality rules, satisfy our conditions. This possibility result stands in sharp contrast to the more restrictive findings with implementation in either Nash equilibrium or subgame perfect equilibrium. We present several examples to illustrate the difference between undominated Nash implementation and implementation with alternative solution concepts

Implementation in dominant strategy equilibrium

Ankara : Department of Economics and the Institute of Economics and Social Sciences of Bilkent University, 1995.Thesis (Master's) -- Bilkent University, 1995.Includes bibliographical references leaves 77-79.A social choice rule is any proposed solution to the problem of collective decision making and it embeds the normative features that can be attached to the mentioned problem. Implementation of social choice rules in dominant strategy equilibrium is the decentralization of the decision power among the agents such that the outcome that is a priori recommended by the social choice rule can be obtained as a dominant strategy equilibrium outcome of the game form which is endowed with the preferences of the individuals. This work has two features. First, it is a survey on the literature on implementation in dominant strategy and its link with the economic theory. Second, it constructs some new relationships among the key terms of the literature. In this framework, it states and proves a slightly generalized version of the Gibbard-Satterthwaite impossibility theorem. Moreover, it states and proves that the cardinality of a singlepeaked domain converges to zero as the number of alternatives increase to infinity.Kıbrıs, ÖzgürM.S