Maximal Domain for Strategy-Proof Rules in Allotment Economies

We consider the problem of allocating an amount of a perfectly divisible good among a group of n agents. We study how large a preference domain can be to allow for the existence of strategy-proof, symmetric, and efficient allocation rules when the amount of the good is a variable. This question is qualified by an additional requirement that a domain should include a minimally rich domain. We first characterize the uniform rule (Bennasy, 1982) as the unique strategy-proof, symmetric, and efficient rule on a minimally rich domain when the amount of the good is fixed. Then, exploiting this characterization, we establish the following: There is a unique maximal domain that includes a minimally rich domain and allows for the existence of strategy-proof, symmetric, and efficient rules when the amount of good is a variable. It is the single-plateaued domain.

Reallocation of an infinetely divisible good

We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and endowment variations on the outcome. The central properties which are studied in this context are population monotonicity, bilateral consistency, (endowment) monotonicity and (endowment) strategy-proofness. Furthermore, the uniform reallocation rule is Pareto optimal and satisfies several equity conditions, e.g., equal-treatment and envy-freeness. We study the trade-off between properties concerning variation and properties concerning equity. Furthermore, we provide several characterizations of the uniform reallocation rule based on these properties.mathematical economics and econometrics ;

Not obviously manipulable allotment rules

In the problem of allocating a single non-disposable commodity among agents whose preferences are single-peaked, we study a weakening of strategy-proofness called not obvious manipulability (NOM). If agents are cognitively limited, then NOM is sufficient to describe their strategic behavior. We characterize a large family of own-peak-only rules that satisfy efficiency, NOM, and a minimal fairness condition. We call these rules "simple". In economies with excess demand, simple rules fully satiate agents whose peak amount is less than or equal to equal division and assign, to each remaining agent, an amount between equal division and his peak. In economies with excess supply, simple rules are defined symmetrically. We also show that the single-plateaued domain is maximal for the characterizing properties of simple rules. Therefore, even though replacing strategy-proofness with NOM greatly expands the family of admissible rules, the maximal domain of preferences involved remains basically unaltered

The Strategy-Proof Provision of Public Goods under Congestion and Crowding Preferences

We examine the strategy-proof provision of excludable public goods when agents care not only about the level of provision of a public good, but also the number of consumers. We show that on such domains strategy- proof and efficient social choice functions satisfying an outsider independence condition must be rigid in that they must always assign a fixed number of consumers, regardless of individual desires to participate. The fixed number depends on the attitudes of agents regarding group size - being small when congestion effects dominate (individuals prefer to have fewer other consumers) and large when cost sharing effects dominate (agents prefer to have more consumers). A hierarchical rule selects which consumers participate and a variation of a generalized median rule to selects the level of the public good. Under heterogeneity in agents' views on the optimal number of consumers, strategy-proof, efficient, and outsider independent social choice functions are much more limited and in an important case must be dictatorial.Public Goods, Congestion, Club Goods, Strategy-Proof

The Division Problem under Constraints

The work of G. Bergantiños is partially supported by research grants ECO2008-03484-C02-01 and ECO2011-23460 from the Spanish Ministry of Science and Innovation and FEDER. J. Massó acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075) and through grant ECO2008-0475-FEDER (Grupo Consolidado-C), and from the Generalitat de Catalunya, through the prize "ICREA Academia" for excellence in research and grant SGR2009-419. The work of A. Neme is partially supported by the Universidad Nacional de San Luis, through grant 319502, and by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), through grant PIP 112-200801-00655.The division problem under constraints consists of allocating a given amount of an homogeneous and perfectly divisible good among a subset of agents with single-peaked preferences on an exogenously given interval of feasible allotments. We characterize axiomatically the family of extended uniform rules proposed to solve the division problem under constraints. Rules in this family extend the uniform rule used to solve the classical division problem without constraints. We show that the family of all extended uniform rules coincides with the set of rules satisfying efficiency, strategy-proofness, equal treatment of equals, bound monotonicity, consistency, and independence of irrelevant coalitions