Group Strategy-Proofness in Private Good Economies

… papers= Documentos de …, 2004

In this paper we develop a differentiable approach to deal with incentives in a, possibly small, subset of a general domain of preferences in economies with one public and one private good. We show that, for two agents, there is no social rule which is efficient, nondictatorial and strategy-proof. For the case of more agents the same result occurs when nondictatorship is replaced by Individual Rationality or by Envy-Freeness. Journal of Economic Literature.

Economic Theory, 2010

We show that strategy-proof allocation mechanisms for economies with public goods are dictatorial—i.e., they always select an allocation in their range that maximizes the welfare of the same single individual (the dictator). Further, strategy-proof and efficient allocation mechanisms are strongly dictatorial—i.e., they select the dictator’s preferred allocation on the entire feasible set. Thus, our results reveal the extent to which the conflict between individual incentives and other properties that may be deemed desirable (e.g., fairness, equal treatment, distributive justice) pervades resource allocation problems.

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its …nal outcome to their own bene…t by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to …nd nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically signi…cant domains where interesting rules satisfying individual strategy-proofness can be de…ned, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategyproofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide su¢ cient conditions de…ning domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules de…ned on these domains. Our results extend to intermediate versions of strategy-proofness, de…ned to exclude manipulations by small group of agents. They also provide guidelines on how to restrict the ranges of functions de…ned on domains that only satisfy our condition partially. Finally, we provide a partial answer regarding the necessity of our conditions. JEL Classi…cation Number: D71.

2002

We study the properties of mechanisms for deciding upon the provision of public goods when the feasible set is exogenously given (by financial and/or technological constraints), and individuals' preferences are represented by continuous, increasing and concave utility functions. We establish a result analog to the Gibbard-Satterthwaite Theorem: strategy-proof mechanisms are dictatorial. Further, efficient and strategy-proof mechanisms are strongly dictatorial (i.e., maximize the dictator's welfare on the entire feasible set). * Financial support from the Ministerio de Ciencia y Tecnología, grant SEC2001-0973, is gratefully acknowledged.

2020

Summary. Every agent reports his willingness to pay for one unit of good. A mechanism allocates some goods and cost shares to some agents. We generalize cross-monotonic and sequential mechanisms discussed in Juarez [2007] to provide three alternative characterizations of the group strategyproof mechanisms in an economy without indifferences. These mechanisms are also characterized in this economy by strategyproofness and non-bossiness. We extend the above mechanisms to an economy with indifferences and characterize them by strategyproof and a weak non-bossy condition. These mechanisms are also weakly group strategyproof in the new economy.

2009

2010

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its …nal outcome to their own bene…t by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to …nd nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically signi…cant domains where interesting rules satisfying individual strategy-proofness can be de…ned, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategyproofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide su¢ cient conditions de…ning domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules de…ned on these domains. Our results extend to intermediate versions of strategy-proofness, de…ned to exclude manipulations by small group of agents. They also provide guidelines on how to restrict the ranges of functions de…ned on domains that only satisfy our condition partially. Finally, we provide a partial answer regarding the necessity of our conditions.

2009

A social choice function is group strategy-proof on a domain if no group of agents can manipulate its …nal outcome to their own bene…t by declaring false preferences on that domain. Group strategy-proofness is a very attractive requirement of incentive compatibility. But in many cases it is hard or impossible to …nd nontrivial social choice functions satisfying even the weakest condition of individual strategy-proofness. However, there are a number of economically signi…cant domains where interesting rules satisfying individual strategy-proofness can be de…ned, and for some of them, all these rules turn out to also satisfy the stronger requirement of group strategyproofness. This is the case, for example, when preferences are single-peaked or single-dipped. In other cases, this equivalence does not hold. We provide su¢ cient conditions de…ning domains of preferences guaranteeing that individual and group strategy-proofness are equivalent for all rules de…ned on these domains. Our results extend to intermediate versions of strategy-proofness, de…ned to exclude manipulations by small group of agents. They also provide guidelines on how to restrict the ranges of functions de…ned on domains that only satisfy our condition partially. Finally, we provide a partial answer regarding the necessity of our conditions. JEL Classi…cation Number: D71.

Review of Economic Design, 2008

In this paper we develop a di¤erentiable approach to deal with incentives in a, possibly small, subset of a general domain of preferences in economies with one public and one private good. We show that, for two agents, there is no mechanism which is e¢ cient, strategy-proof and where consumption of both goods is positive for all agents. For the case of two or more agents the same result occurs when nondictatorship is replaced by Individual Rationality.

Social Science Research Network, 2022

We consider strategy-proof rules operating on a rich domain of preference profiles. We show that if the rule satisfies in addition tops-onlyness, anonymity, and unanimity, then the preferences in the domain have to satisfy a variant of single-peakedness (referred to as semilattice single-peakedness). We do so by deriving from the rule an endogenous partial order (a semilattice) from which the concept of a semilattice single-peaked preference can be defined. We also provide a converse of this main finding. Finally, we show how well-known restricted domains under which nontrivial strategy-proof rules are admissible are semilattice single-peaked domains. * Manuscript received January 2016; revised July 2016. 1 We would like to thank Huaxia Zeng for helpful discussions and detailed comments, Salvador Barberà for insightful comments, and Masaki Aoyagi and three referees of the journal for very helpful and constructive comments. Chatterji would like to acknowledge research support from SMU grant number C244/MSS13E001 and thank KIER, Kyoto University for its hospitality.