In this paper we study the rationing problems in using the issue of Nash implementation in an env... more In this paper we study the rationing problems in using the issue of Nash implementation in an environment of single-crossing preferences. We show that strict monotonicity () implies strict weak no-veto power and unanimity and () is equivalent to Maskin monotonicity, which is vacuously checked in this domain. We show that any social choice correspondence that has full range can be implemented in Nash equilibria.
Please cite this article as: Doghmi, A., Ziad, A., Nash implementation in private good economies ... more Please cite this article as: Doghmi, A., Ziad, A., Nash implementation in private good economies with single-plateaued preferences and in matching problems. Mathematical Social Sciences (2014),
In this paper we give a full characterization of Nash implementability of social choice correspon... more In this paper we give a full characterization of Nash implementability of social choice correspondences (SCCs) in allotment economies on preference domains with private values and different types of indifference. We focus on single-peaked/single-plateaued preferences with worst indifferent allocations, single-troughed preferences and single-troughed preferences with best indifferent allocations. We begin by introducing a weak variant of no-veto power, called I *-weak no-veto power, which form together with unanimity and a stronger version of Maskin monotonicity a sufficient condition for Nash implementation in general environment. We apply this result to the above preference domains and we prove that any SCC that has full range is Nash implementable if and only if it satisfies Maskin monotonicity. We examine the implementability of some well-known correspondences. We give examples of SCCs that are monotonic in the unrestricted domains and also monotonic in our setup, and we provide exemples of SCCs that are not monotonic in the unrestricted domains, but monotonic and therefore Nash implementable in our context. Finally, we give examples of SCCs that are not monotonic in the restricted domains and also not monotonic in our area, and therefore not Nash implementable.
The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality,... more The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality, k-Negative Plurality, k-Borda, and Bloc, which can be considered as generalisations of well-known single-winner scoring rules. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability that a given voting rule picks out the Condorcet committee, given that such a committee exists. The second comparison is based on the likelihood of two paradoxes of committee elections: The Prior Successor Paradox and the Leaving Member Paradox which occur when a member of an elected committee leaves. In doing so, using the well-known Impartial Anonymous Culture condition, we extend the results of Kamwa and Merlin (2015) in two directions. First, our paper is concerned with the probability of the paradoxes no matter the ranking of the leaving candidate. Second, we do not only focus on the occurrence of these paradoxes when one wishes to select a committee of size k = 2 out of m = 4 candidates but we consider more values of k and m.
Dans ce papier, nous introduisons la notion de déformation des paiements dans un jeu du dilemme d... more Dans ce papier, nous introduisons la notion de déformation des paiements dans un jeu du dilemme du prisonnier. Cette notion nous permet de prendre en compte l'appréciation de chaque joueur du comportement de son adversaire. Nous déterminons les conditions sous lesquelles la coopération mutuelle constitue un équilibre. Premièrement, nos résultats montrent que contrairement à l'altruisme, la réciprocité permet de faire face au comportement opportuniste de l'égoïsme. Deuxièment, la coopération émerge avec la réciprocité, et elle peut être un équilibre de Nash dans un domaine d'information complète ou un équilibre bayésien sous certaines conditions dans un environnement d'information incomplète.
Dans ce papier, nous introduisons la notion de déformation des paiements dans un jeu du dilemme d... more Dans ce papier, nous introduisons la notion de déformation des paiements dans un jeu du dilemme du prisonnier. Cette notion nous permet de prendre en compte l'appréciation de chaque joueur du comportement de son adversaire. Nous déterminons les conditions sous lesquelles la coopération mutuelle constitue un équilibre. Premièrement, nos résultats montrent que contrairement à l'altruisme, la réciprocité permet de faire face au comportement opportuniste de l'égoïsme. Deuxièmement, la coopération émerge avec la réciprocité, et elle peut être un équilibre de Nash dans un domaine d'information complète ou un équilibre bayésien sous certaines conditions dans un environnement d'information incomplète.
Cette these contient deux parties sur la theorie de l'implementation. La premiere partie trai... more Cette these contient deux parties sur la theorie de l'implementation. La premiere partie traite l'implementation en equilibre de Nash. Dans cette partie, nous avons obtenu de nouvelles conditions suffisantes a l'implementabilite en equilibre de Nash. En appliquant ces nouvelles conditions dans une economie d'echange avec preferences unimodales, nous avons prouve directement l'implementabilite de nouvelles correspondances. La deuxieme partie est consacree a l'implementation Bayesienne avec rationalite limitee. Nous avons travaille dans un domaine d'economie d'echange avec une structure informationnelle non-exclusive. Nous avons elargi les travaux d'Eliaz en proposant un nouveau concept d'equilibre, une nouvelle notion d'implementation et de nouvelles conditions pour l'implementabilite dans cet environnement
In this paper, we introduce the concept of payoff distortion in the standard prisoner's dilem... more In this paper, we introduce the concept of payoff distortion in the standard prisoner's dilemma game when strategies are driven by psychological behaviors. This concept enables to take account each player's assessment of the other player's behavior and the asymmetry of information. We determine the conditions which allow that mutual cooperation constitutes the equilibrium. we particularly focus on the reciprocity in case of complete and incomplete information about the payoffi distortion. We show that mutual cooperation is a Nash equilibrium with complete information and is a Bayesian equilibrium when each player believes that his opponent behaves with "large" reciprocity in incomplete information environment.
In this paper we study the rationing problems in using the issue of Nash implementation in an env... more In this paper we study the rationing problems in using the issue of Nash implementation in an environment of single-crossing preferences. We show that strict monotonicity () implies strict weak no-veto power and unanimity and () is equivalent to Maskin monotonicity, which is vacuously checked in this domain. We show that any social choice correspondence that has full range can be implemented in Nash equilibria.
Please cite this article as: Doghmi, A., Ziad, A., Nash implementation in private good economies ... more Please cite this article as: Doghmi, A., Ziad, A., Nash implementation in private good economies with single-plateaued preferences and in matching problems. Mathematical Social Sciences (2014),
In this article, we study the problem of Nash implementation in private good economies with singl... more In this article, we study the problem of Nash implementation in private good economies with single-peaked, single-plateaued, and single-dipped preferences in the presence of at least one minimally honest agent. We prove that all solutions of the problem of fair division satisfying unanimity can be implemented in Nash equilibria as long as there are at least three agents participating in the mechanism (game form). To justify this result, we provide a list of solutions which violate the condition of no-veto power.
In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one hand a... more In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one hand and we extend theorems 1 and 2 of Doghmi and Ziad (2008 a) to bounded rationality environments, on the other. We identify weak versions of the k-no veto power condition, in conjunction with unanimity and variants of k-monotonicity, are sufficient for implementability in k-Fault Tolerant Nash equilibria (k-FTNE). In addition, these new conditions are stable by intersection which makes it possible to check directly the k − F T N E implementability of the social choice correspondences. We apply these results to exchange economies with single-peaked preferences, to finite allocation problems, and to equilibrium theory. Firstly, we note that our conditions are satisfied by all monotonic solutions contrary to Eliaz's results (2002). Secondly, in exchange economy when preferences are single-peaked, the k-monotonicity is sufficient for the k − F T N E implementation for the correspondences and both necessary and sufficient for the functions. However, the results are negatives for the no-monotonic solutions.
In this paper, we study the Nash implementation in an allocation problem with single-dipped prefe... more In this paper, we study the Nash implementation in an allocation problem with single-dipped preferences. We show that, with at least three agents, Maskin monotonicity is necessary and sufficient for implementation. We examine the implementability of various social choice correspondences (SCCs) in this environment, and prove that some well-known SCCs are Maskin monotonic (but they do not satisfy no-veto power) and hence Nash implementable.
The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality,... more The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality, k-Negative Plurality, k-Borda, and Bloc, which can be considered as generalisations of well-known single-winner scoring rules. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability that a given voting rule picks out the Condorcet committee, given that such a committee exists. The second comparison is based on the likelihood of two paradoxes of committee elections: The Prior Successor Paradox and the Leaving Member Paradox which occur when a member of an elected committee leaves. In doing so, using the well-known Impartial Anonymous Culture condition, we extend the results of Kamwa and Merlin (2015) in two directions. First, our paper is concerned with the probability of the paradoxes no matter the ranking of the leaving candidate. Second, we do not only focus on the occurrence of these paradoxes when one wishes to select a committee of size k = 2 out of m = 4 candidates but we consider more values of k and m.
In this work, we extend the concept of Fault Tolerant Implementation of Eliaz (2002) to the conce... more In this work, we extend the concept of Fault Tolerant Implementation of Eliaz (2002) to the concept of Fault Tolerant Implementation in incomplete information environments. In particular, we work in a domain where information is non-exclusive by choosing a model of pure exchange economy. As in Eliaz (2002), we suppose the existence of at most k faulty players who do not act in an optimal way, either because they do not understand the rules of the game or they make mistakes. We develop a new concept of equilibrium, called k-Fault Tolerant Bayesian Equilibrium (k − F T BE) and a new concept of implementation, called fault tolerant Bayesian implementation. In model of pure exchange economy, we show that weak k-Bayesian monotonicity is a necessary condition for the implementation of social choice correspondences in k − F T BE. We also introduce the no-exclusiveness information condition (k − N EI), and we show that k-Bayesian monotonicity and k − N EI are sufficient conditions for implementation when there are at least three players and the number of the faulty players is less then 1 2 n − 1.
In this paper, we generalize Theorem 1 of Dutta and Sen (2009) by replacing no veto power conditi... more In this paper, we generalize Theorem 1 of Dutta and Sen (2009) by replacing no veto power condition by a variety of its weak versions and unanimity. By applying our results to exchange economies with single peaked preferences, we implement all solutions of the problem of fair division, either the non monotonic solutions or the monotonic solutions which violate the no veto power condition.
In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one ha... more In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one hand and we extend theorems 1 and 2 of Doghmi and Ziad (2008a) to bounded rationality environments, on the other. We identify weak versions of the k-no veto power condition, in conjunction with unanimity and variants of k-monotonicity, are sufficient for implementability in k- Fault Tolerant
We reexamine Maskin's Theorem by proposing slight modifications on Maskin's conditions of monoton... more We reexamine Maskin's Theorem by proposing slight modifications on Maskin's conditions of monotonicity and no veto power. We show that any social choice correspondence (SCC) that satisfies strict monotonicity, strict no veto power and unanimity can be implemented in Nash equilibria.
In this paper we study the rationing problems in using the issue of Nash implementation in an env... more In this paper we study the rationing problems in using the issue of Nash implementation in an environment of single-crossing preferences. We show that strict monotonicity () implies strict weak no-veto power and unanimity and () is equivalent to Maskin monotonicity, which is vacuously checked in this domain. We show that any social choice correspondence that has full range can be implemented in Nash equilibria.
Please cite this article as: Doghmi, A., Ziad, A., Nash implementation in private good economies ... more Please cite this article as: Doghmi, A., Ziad, A., Nash implementation in private good economies with single-plateaued preferences and in matching problems. Mathematical Social Sciences (2014),
In this paper we give a full characterization of Nash implementability of social choice correspon... more In this paper we give a full characterization of Nash implementability of social choice correspondences (SCCs) in allotment economies on preference domains with private values and different types of indifference. We focus on single-peaked/single-plateaued preferences with worst indifferent allocations, single-troughed preferences and single-troughed preferences with best indifferent allocations. We begin by introducing a weak variant of no-veto power, called I *-weak no-veto power, which form together with unanimity and a stronger version of Maskin monotonicity a sufficient condition for Nash implementation in general environment. We apply this result to the above preference domains and we prove that any SCC that has full range is Nash implementable if and only if it satisfies Maskin monotonicity. We examine the implementability of some well-known correspondences. We give examples of SCCs that are monotonic in the unrestricted domains and also monotonic in our setup, and we provide exemples of SCCs that are not monotonic in the unrestricted domains, but monotonic and therefore Nash implementable in our context. Finally, we give examples of SCCs that are not monotonic in the restricted domains and also not monotonic in our area, and therefore not Nash implementable.
The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality,... more The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality, k-Negative Plurality, k-Borda, and Bloc, which can be considered as generalisations of well-known single-winner scoring rules. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability that a given voting rule picks out the Condorcet committee, given that such a committee exists. The second comparison is based on the likelihood of two paradoxes of committee elections: The Prior Successor Paradox and the Leaving Member Paradox which occur when a member of an elected committee leaves. In doing so, using the well-known Impartial Anonymous Culture condition, we extend the results of Kamwa and Merlin (2015) in two directions. First, our paper is concerned with the probability of the paradoxes no matter the ranking of the leaving candidate. Second, we do not only focus on the occurrence of these paradoxes when one wishes to select a committee of size k = 2 out of m = 4 candidates but we consider more values of k and m.
Dans ce papier, nous introduisons la notion de déformation des paiements dans un jeu du dilemme d... more Dans ce papier, nous introduisons la notion de déformation des paiements dans un jeu du dilemme du prisonnier. Cette notion nous permet de prendre en compte l'appréciation de chaque joueur du comportement de son adversaire. Nous déterminons les conditions sous lesquelles la coopération mutuelle constitue un équilibre. Premièrement, nos résultats montrent que contrairement à l'altruisme, la réciprocité permet de faire face au comportement opportuniste de l'égoïsme. Deuxièment, la coopération émerge avec la réciprocité, et elle peut être un équilibre de Nash dans un domaine d'information complète ou un équilibre bayésien sous certaines conditions dans un environnement d'information incomplète.
Dans ce papier, nous introduisons la notion de déformation des paiements dans un jeu du dilemme d... more Dans ce papier, nous introduisons la notion de déformation des paiements dans un jeu du dilemme du prisonnier. Cette notion nous permet de prendre en compte l'appréciation de chaque joueur du comportement de son adversaire. Nous déterminons les conditions sous lesquelles la coopération mutuelle constitue un équilibre. Premièrement, nos résultats montrent que contrairement à l'altruisme, la réciprocité permet de faire face au comportement opportuniste de l'égoïsme. Deuxièmement, la coopération émerge avec la réciprocité, et elle peut être un équilibre de Nash dans un domaine d'information complète ou un équilibre bayésien sous certaines conditions dans un environnement d'information incomplète.
Cette these contient deux parties sur la theorie de l'implementation. La premiere partie trai... more Cette these contient deux parties sur la theorie de l'implementation. La premiere partie traite l'implementation en equilibre de Nash. Dans cette partie, nous avons obtenu de nouvelles conditions suffisantes a l'implementabilite en equilibre de Nash. En appliquant ces nouvelles conditions dans une economie d'echange avec preferences unimodales, nous avons prouve directement l'implementabilite de nouvelles correspondances. La deuxieme partie est consacree a l'implementation Bayesienne avec rationalite limitee. Nous avons travaille dans un domaine d'economie d'echange avec une structure informationnelle non-exclusive. Nous avons elargi les travaux d'Eliaz en proposant un nouveau concept d'equilibre, une nouvelle notion d'implementation et de nouvelles conditions pour l'implementabilite dans cet environnement
In this paper, we introduce the concept of payoff distortion in the standard prisoner's dilem... more In this paper, we introduce the concept of payoff distortion in the standard prisoner's dilemma game when strategies are driven by psychological behaviors. This concept enables to take account each player's assessment of the other player's behavior and the asymmetry of information. We determine the conditions which allow that mutual cooperation constitutes the equilibrium. we particularly focus on the reciprocity in case of complete and incomplete information about the payoffi distortion. We show that mutual cooperation is a Nash equilibrium with complete information and is a Bayesian equilibrium when each player believes that his opponent behaves with "large" reciprocity in incomplete information environment.
In this paper we study the rationing problems in using the issue of Nash implementation in an env... more In this paper we study the rationing problems in using the issue of Nash implementation in an environment of single-crossing preferences. We show that strict monotonicity () implies strict weak no-veto power and unanimity and () is equivalent to Maskin monotonicity, which is vacuously checked in this domain. We show that any social choice correspondence that has full range can be implemented in Nash equilibria.
Please cite this article as: Doghmi, A., Ziad, A., Nash implementation in private good economies ... more Please cite this article as: Doghmi, A., Ziad, A., Nash implementation in private good economies with single-plateaued preferences and in matching problems. Mathematical Social Sciences (2014),
In this article, we study the problem of Nash implementation in private good economies with singl... more In this article, we study the problem of Nash implementation in private good economies with single-peaked, single-plateaued, and single-dipped preferences in the presence of at least one minimally honest agent. We prove that all solutions of the problem of fair division satisfying unanimity can be implemented in Nash equilibria as long as there are at least three agents participating in the mechanism (game form). To justify this result, we provide a list of solutions which violate the condition of no-veto power.
In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one hand a... more In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one hand and we extend theorems 1 and 2 of Doghmi and Ziad (2008 a) to bounded rationality environments, on the other. We identify weak versions of the k-no veto power condition, in conjunction with unanimity and variants of k-monotonicity, are sufficient for implementability in k-Fault Tolerant Nash equilibria (k-FTNE). In addition, these new conditions are stable by intersection which makes it possible to check directly the k − F T N E implementability of the social choice correspondences. We apply these results to exchange economies with single-peaked preferences, to finite allocation problems, and to equilibrium theory. Firstly, we note that our conditions are satisfied by all monotonic solutions contrary to Eliaz's results (2002). Secondly, in exchange economy when preferences are single-peaked, the k-monotonicity is sufficient for the k − F T N E implementation for the correspondences and both necessary and sufficient for the functions. However, the results are negatives for the no-monotonic solutions.
In this paper, we study the Nash implementation in an allocation problem with single-dipped prefe... more In this paper, we study the Nash implementation in an allocation problem with single-dipped preferences. We show that, with at least three agents, Maskin monotonicity is necessary and sufficient for implementation. We examine the implementability of various social choice correspondences (SCCs) in this environment, and prove that some well-known SCCs are Maskin monotonic (but they do not satisfy no-veto power) and hence Nash implementable.
The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality,... more The goal of this paper is to propose a comparison of four multi-winner voting rules, k-Plurality, k-Negative Plurality, k-Borda, and Bloc, which can be considered as generalisations of well-known single-winner scoring rules. The first comparison is based on the Condorcet committee efficiency which is defined as the conditional probability that a given voting rule picks out the Condorcet committee, given that such a committee exists. The second comparison is based on the likelihood of two paradoxes of committee elections: The Prior Successor Paradox and the Leaving Member Paradox which occur when a member of an elected committee leaves. In doing so, using the well-known Impartial Anonymous Culture condition, we extend the results of Kamwa and Merlin (2015) in two directions. First, our paper is concerned with the probability of the paradoxes no matter the ranking of the leaving candidate. Second, we do not only focus on the occurrence of these paradoxes when one wishes to select a committee of size k = 2 out of m = 4 candidates but we consider more values of k and m.
In this work, we extend the concept of Fault Tolerant Implementation of Eliaz (2002) to the conce... more In this work, we extend the concept of Fault Tolerant Implementation of Eliaz (2002) to the concept of Fault Tolerant Implementation in incomplete information environments. In particular, we work in a domain where information is non-exclusive by choosing a model of pure exchange economy. As in Eliaz (2002), we suppose the existence of at most k faulty players who do not act in an optimal way, either because they do not understand the rules of the game or they make mistakes. We develop a new concept of equilibrium, called k-Fault Tolerant Bayesian Equilibrium (k − F T BE) and a new concept of implementation, called fault tolerant Bayesian implementation. In model of pure exchange economy, we show that weak k-Bayesian monotonicity is a necessary condition for the implementation of social choice correspondences in k − F T BE. We also introduce the no-exclusiveness information condition (k − N EI), and we show that k-Bayesian monotonicity and k − N EI are sufficient conditions for implementation when there are at least three players and the number of the faulty players is less then 1 2 n − 1.
In this paper, we generalize Theorem 1 of Dutta and Sen (2009) by replacing no veto power conditi... more In this paper, we generalize Theorem 1 of Dutta and Sen (2009) by replacing no veto power condition by a variety of its weak versions and unanimity. By applying our results to exchange economies with single peaked preferences, we implement all solutions of the problem of fair division, either the non monotonic solutions or the monotonic solutions which violate the no veto power condition.
In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one ha... more In this paper, we reexamine Eliaz's results (2002) of fault tolerant implementation on one hand and we extend theorems 1 and 2 of Doghmi and Ziad (2008a) to bounded rationality environments, on the other. We identify weak versions of the k-no veto power condition, in conjunction with unanimity and variants of k-monotonicity, are sufficient for implementability in k- Fault Tolerant
We reexamine Maskin's Theorem by proposing slight modifications on Maskin's conditions of monoton... more We reexamine Maskin's Theorem by proposing slight modifications on Maskin's conditions of monotonicity and no veto power. We show that any social choice correspondence (SCC) that satisfies strict monotonicity, strict no veto power and unanimity can be implemented in Nash equilibria.
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