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A dynamic model of barter exchange
, 2014
"... We consider the problem of efficient operation of a barter exchange platform for indivisible goods. We introduce a dynamic model of barter exchange where in each period one agent arrives with a single item she wants to exchange for a different item. We study a homogeneous and stochastic environment: ..."
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We consider the problem of efficient operation of a barter exchange platform for indivisible goods. We introduce a dynamic model of barter exchange where in each period one agent arrives with a single item she wants to exchange for a different item. We study a homogeneous and stochastic environment: an agent is interested in the item possessed by another agent with probability p, independently for all pairs of agents. We consider three settings with respect to the types of allowed exchanges: a) Only twoway cycles, in which two agents swap their items, b) Two or threeway cycles, c) (unbounded) chains initiated by altruistic donors who provide an item but expect nothing in return. The goal of the platform is to minimize the average waiting time of an agent. Somewhat surprisingly, we find that in each of these settings, a policy that conducts exchanges in a greedy fashion is near optimal, among a large class of policies that includes batching policies. Further, we find that for small p, allowing threecycles can greatly improve the waiting time over the twocycles only setting, and the presence of altruistic donors can lead to a further large improvement in average waiting time. Specifically, we find that a greedy policy achieves an average waiting time of Θ(1/p2) in setting a), Θ(1/p3/2) in setting b), and Θ(1/p) in setting c). Thus, a platform can achieve the smallest waiting times by using a greedy policy, and by facilitating three cycles and chains, if possible. Our findings are consistent with empirical and computational observations which compare batching policies in the context of kidney exchange programs.
2014): „House Allocation with Overlapping Generations
 In: American Economic Journal – Microeconomics
"... House allocation with overlapping ..."
An Axiomatic Approach to Characterizing and Relaxing Strategyproofness of Onesided Matching Mechanisms.” Working Paper
, 2014
"... We study onesided matching mechanisms where agents have vNM utility functions and report ordinal preferences. We first show that in this domain strategyproof mechanisms are characterized by three intuitive axioms: swap consistency, weak invariance, and lower invariance. Our second result is that dr ..."
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We study onesided matching mechanisms where agents have vNM utility functions and report ordinal preferences. We first show that in this domain strategyproof mechanisms are characterized by three intuitive axioms: swap consistency, weak invariance, and lower invariance. Our second result is that dropping lower invariance leads to an interesting new relaxation of strategyproofness, which we call partial strategyproofness. In particular, we show that mechanisms are swap consistent and weakly invariant if and only if they are strategyproof on a restricted domain where agents have sufficiently different valuations for different objects. Furthermore, we show that this domain restriction is maximal and use it to define a singleparameter measure for the degree of strategyproofness of a manipulable mechanism. We also provide an algorithm that computes this measure. Our new partial strategyproofness concept finds applications in the incentive analysis of nonstrategyproof mechanisms, such as the Probabilistic Serial mechanism, different variants of the Boston mechanism, and the construction of new hybrid mechanisms. 1.
Hierarchical Exchange Rules and the Core in Indivisible Objects Allocation
"... Abstract We study the allocation of indivisible objects under the general endowment structures proposed by Pápai (2000)the consistent inheritance structureswhich specify the initial endowment of objects and also the inheritance of remaining objects after subsets of agents are matched and removed. ..."
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Abstract We study the allocation of indivisible objects under the general endowment structures proposed by Pápai (2000)the consistent inheritance structureswhich specify the initial endowment of objects and also the inheritance of remaining objects after subsets of agents are matched and removed. For any consistent inheritance structure and any given matching, we define the contingent endowment of an agent as the maximal set of objects that she can feasibly inherit given the consistency of endowments. Based on contingent endowment, the concepts of individual rationality and core are then generalized. We show that for each consistent inheritance structure, Pápai's hierarchical exchange rule produces the unique core allocation and is characterized by individual rationality, Pareto efficiency, and strategyproofness. JEL classification: C78, D61, D78, I20 School of Economics, Shanghai University of Finance and Economics, Shanghai, 200433, China. Emails: tangqianfeng198@gmail.com (Q. Tang), yongchao@mail.shufe.edu.cn (Y. Zhang). We thank participants of the SHUFE Market design reading group for helpful comments. All errors are our own. 1
ParetoOptimal Matching Allocation Mechanisms for Boundedly Rational Agents
"... Abstract Is the Pareto optimality of matching mechanisms robust to the introduction of boundedly rational behavior? To address this question I define a restrictive and a permissive notion of Pareto optimality and consider the large set of hierarchical exchange mechanisms which contains serial dicta ..."
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Abstract Is the Pareto optimality of matching mechanisms robust to the introduction of boundedly rational behavior? To address this question I define a restrictive and a permissive notion of Pareto optimality and consider the large set of hierarchical exchange mechanisms which contains serial dictatorship as well as Gales top trading cycles. Fix a housing problems with boundedly rational agents and a hierarchical exchange mechanism. Consider the set of matchings that arise under all possible assignments of agents to initial endowments in this mechanism. I show that this set is nested between the sets of Pareto optima according to the restrictive and the permissive notion. These containment relations are generally strict, even when deviations from rationality are minimal. In a similar vein, minimal deviations from rationality suffice for the set of outcomes of Gale's top trading cycles for all possible initial endowments to differ from the set of outcomes of serial dictatorship for all possible orders of agents as dictators.
Trading Cycles for School Choice
, 2011
"... In this note we study the allocation and exchange of discrete resources in environments in which monetary transfers are not allowed. We allow each discrete resource to be represented by several copies, extend onto this environment the trading cycles mechanisms of Pycia and Ünver [2009], and show tha ..."
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In this note we study the allocation and exchange of discrete resources in environments in which monetary transfers are not allowed. We allow each discrete resource to be represented by several copies, extend onto this environment the trading cycles mechanisms of Pycia and Ünver [2009], and show that the extended mechanisms are Pareto efficient and strategyproof. In particular, we construct the counterpart of Pápai [2000] hiererachical exchange mechanisms for environments with copies.
Size versus truthfulness in the House Allocation problem
, 2014
"... We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary tran ..."
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We study the House Allocation problem (also known as the Assignment problem), i.e., the problem of allocating a set of objects among a set of agents, where each agent has ordinal preferences (possibly involving ties) over a subset of the objects. We focus on truthful mechanisms without monetary transfers for finding large Pareto optimal matchings. It is straightforward to show that no deterministic truthful mechanism can approximate a maximum cardinality Pareto optimal matching with ratio better than 2. We thus consider randomized mechanisms. We give a natural and explicit extension of the classical Random Serial Dictatorship Mechanism (RSDM) specifically for the House Allocation problem where preference lists can include ties. We thus obtain a universally truthful randomized mechanism for finding a Pareto optimal matching and show that it achieves an approximation ratio of ee−1. The same bound holds even when agents have priorities (weights) and our goal is to find a maximum weight (as opposed to maximum cardinality) Pareto optimal matching. On the other hand we give a lower bound of 1813 on the approximation ratio of any universally truthful Pareto optimal mechanism in settings with strict preferences. In the case that the mechanism must additionally be nonbossy, an improved lower bound of ee−1 holds. This lower bound is tight given that RSDM for strict preference lists is nonbossy. We moreover interpret our problem in terms of the classical secretary problem and prove that our mechanism provides the best randomized strategy of the administrator who interviews the applicants.
Hybrid Mechanisms: Trading off Efficiency and Strategyproofness in OneSided Matching˚
, 2014
"... We study onesided matching mechanisms where agents have vNM utility functions and report ordinal preferences. Strong impossibility results restrict the design space os strategyproof mechanisms in this domain. Improving on efficiency beyond the expost efficiency of Random Serial Dictatorship (RSD) ..."
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We study onesided matching mechanisms where agents have vNM utility functions and report ordinal preferences. Strong impossibility results restrict the design space os strategyproof mechanisms in this domain. Improving on efficiency beyond the expost efficiency of Random Serial Dictatorship (RSD) generally requires tradeoffs. In this paper, we introduce hybrid mechanisms, which are convex combinations of existing mechanism, and we show that they are a powerful yet simple method for trading off strategyproofness and efficiency. We present conditions under which hybrid mechanisms remain partially strategyproof with respect to a given bound for the degree of strategyproofness. At the same time, these hybrids have better efficiency properties than the less efficient component. Our approach can be successfully applied to create hybrids of RSD and the Probabilistic Serial mechanism (PS), as well as hybrids of RSD and the adaptive Boston mechanism (ABM). We provide numerical results demonstrating that the improvements can be significant. 1.