On the "group non-bossiness" property

We extend the concept of non-bossiness to groups of agents and say that a mechanism is group non-bossy if no group of agents can change the assignment of someone else while theirs being unaffected by misreporting their preferences. First, we show that they are not equivalent properties. We, then, prove that group strategy-proofness is sufficient for group non-bossiness. While this result implies that the top trading cycles mechanism is group non-bossy, it also provides a characterization of the market structures in which the deferred acceptance algorithm is group non-bossy

On the consistency of deferred acceptance when priorities are acceptant substitutable

In the context of resource allocation on the basis of responsive priorities, Ergin (2002) identifies a necessary and sufficient condition for the deferred acceptance rule to satisfy a consistency principle. In this note, we extend this result to the domain of substitutable priorities, complementing results of Kojima and Manea (2010) and Kumano (2009).Financial support from Plan Nacional I+D+i (ECO2008–04784), the Consolider-Ingenio 2010 (CSD2006–00016) program, the Barcelona Graduate School of Economics and the Government of Catalonia (SGR2009–01142) is gratefully acknowledged

Group strategy-proofness in private good economies

Altres ajuts: SGR2014-515 ; SGR2009-0189 ; 2014-SGR-1360; Junta de Andalucia: SEJ4941, SEJ-5980; ECO2011-29355Many salient rules to allocate private goods are not only strategyproof, but also group strategy-proof, in appropriate domains of definition, hence diminishing the traditional conflict between incentives and efficiency. That is so for solutions to matching, division, cost sharing, house allocation, and auctions, in spite of the substantive disparity between these cases. In a general framework encompassing all of them, we prove that the equivalence between the two forms of strategy-proofness is due to an underlying common structure that transcends the many differences between the contexts and the mechanisms for which it holds. (JEL C78, D44, D63, D71, D82)

Nonbossy Mechanisms: Mechanism Design Robust to Secondary Goals

We study mechanism design when agents may have hidden secondary goals which will manifest as non-trivial preferences among outcomes for which their primary utility is the same. We show that in such cases, a mechanism is robust against strategic manipulation if and only if it is not only incentive-compatible, but also nonbossy -- a well-studied property in the context of matching and allocation mechanisms. We give complete characterizations of incentive-compatible and nonbossy mechanisms in various settings, including auctions with single-parameter agents and public decision settings where all agents share a common outcome. In particular, we show that in the single-item setting, a mechanism is incentive-compatible, individually rational, and nonbossy if and only if it is a sequential posted-price mechanism. In contrast, we show that in more general single-parameter environments, there exist mechanisms satisfying our characterization that significantly outperform sequential posted-price mechanisms in terms of revenue or efficiency (sometimes by an exponential factor)

Local Priority Mechanisms

We introduce a novel family of mechanisms for constrained allocation problems which we call local priority mechanisms. These mechanisms are parameterized by a function which assigns a set of agents -- the local compromisers -- to every infeasible allocation. The mechanism then greedily attempts to match agents with their top choices. Whenever it reaches an infeasible allocation, the local compromisers move to their next favorite alternative. Local priority mechanisms exist for any constraint so this provides a method of constructing new designs for any constrained allocation problem. We give axioms which characterize local priority mechanisms. Since constrained object allocation includes many canonical problems as special constraints, we apply this characterization to show that several well-known mechanisms, including deferred acceptance for school choice, top trading cycles for house allocation, and serial dictatorship can be understood as instances of local priority mechanisms. Other mechanisms, including the Boston mechanism, are not local priority mechanisms. We give necessary and sufficient conditions which characterize the local priority mechanisms that are group strategy-proof. As an application, we construct novel mechanisms for a natural variation of the house allocation problem where no existing class of mechanisms besides serial dictatorship would be applicable

Random assignment with multi-unit demands

We consider the multi-unit random assignment problem in which agents express preferences over objects and objects are allocated to agents randomly based on the preferences. The most well-established preference relation to compare random allocations of objects is stochastic dominance (SD) which also leads to corresponding notions of envy-freeness, efficiency, and weak strategyproofness. We show that there exists no rule that is anonymous, neutral, efficient and weak strategyproof. For single-unit random assignment, we show that there exists no rule that is anonymous, neutral, efficient and weak group-strategyproof. We then study a generalization of the PS (probabilistic serial) rule called multi-unit-eating PS and prove that multi-unit-eating PS satisfies envy-freeness, weak strategyproofness, and unanimity.Comment: 17 page