Recently, the problem of allocating one resource per agent with initial endowments (\emph{house markets}) has seen a renewed interest: indeed, while in the general domain Top Trading Cycle is known to be the only procedure guaranteeing Pareto-optimality, individual rationality, and strategy proofness, the situation differs in single-peaked domains. Bade (2019) presented the Crawler, an alternative procedure enjoying the same properties (with the additional advantage of being implementable in obviously dominant strategies); while Damamme et al. (2015) showed that allowing mutually beneficial swap-deals among the agents was already enough to guarantee Pareto-optimality. In this paper we significantly deepen our understanding of this decentralized procedures: we show in particular that the single-peaked domains happen to be ``maximal'' if one wishes to guarantee this convergence property. Interestingly, we also observe that the set of allocations reachable by swap-deals always contains the outcome of the Crawler. To further investigate how these different mechanisms compare, we pay special attention to the average and minimum rank of the resource obtained by the agents in the outcome allocation. We provide theoretical bounds on the loss potentially induced by these procedures with respect to these criteria, and complement these results with an extensive experimental study which shows how different variants of swap dynamics behave. In fact, even the simplest dynamics exhibit very good results, and it is possible to further guide the process towards our objectives, if one is ready to sacrifice a bit in terms of decentralization. On our way, we also show that a simple variant of the Crawler allows to check efficiently that an allocation is Pareto-optimal in single-peaked domains.

In this paper we study the exchange of indivisible objects where agents’ possible preferences over the objects are strict and share a common structure among all of them, which represents a certain level of asymmetry among objects. A typical example of such an exchange model is a re-scheduling of tasks over several processors, since all task owners are naturally assumed to prefer that their tasks are assigned to fast processors rather than slow ones. We focus on designing exchange rules (a.k.a.mechanisms) that simultaneously satisfy strategyproofness, individual rationality, and Pareto efficiency. We first provide a general impossibility result for agents’ preferences that are determined in an additive manner, and then show an existence of such an exchange rule for further restricted lexicographic preferences. We finally find that for the restricted case, a previously known equivalence between the single-valuedness of the strict core and the existence of such an exchange rule does not carry over.

Core-selection is a crucial property of social choice functions, or rules, in social choice literature. It is also desirable to address the incentive of agents to cheat by misreporting their preferences. This paper investigates an exchange problem where each agent may have multiple indivisible goods, agents' preferences over sets of goods are assumed to be lexicographic, and side payments are not allowed. We propose an exchange rule called augmented top-trading-cycles (ATTC) procedure based on the original TTC procedure. We first show that the ATTC procedure is core-selecting. We then show that finding a beneficial misreport under the ATTC procedure is NP-hard. Under the ATTC procedure, we finally clarify the relationship between preference misreport and splitting, which is a different type of manipulation.

We study a mechanism design problem for exchange economies where each agent is initially endowed with a set of indivisible goods and side payments are not allowed. We assume each agent can withhold some endowments, as well as misreport her preference. Under this assumption, strategyproofness requires that for each agent, reporting her true preference with revealing all her endowments is a dominant strategy, and thus implies individual rationality. Our objective in this paper is to analyze the effect of such private ownership in exchange economies with multiple endowments. As fundamental results, we first show that the revelation principle holds under a natural assumption and that strategyproofness and Pareto efficiency are incompatible even under the lexicographic preference domain. We then propose a class of exchange rules, each of which has a corresponding directed graph to prescribe possible trades, and provide necessary and sufficient conditions on the graph structure so that they satisfy strategyproofness.

Individual rationality, Pareto efficiency, and strategy- proofness are crucial properties of decision making functions, or mechanisms, in social choice literatures. In this paper we investigate mechanisms for exchange models where each agent is initially endowed with a set of goods and may have indifferences on distinct bundles of goods, and monetary transfers are not allowed. Sonmez (1999) showed that in such models, those three properties are not compatible in general. The impossibility, however, only holds under an assumption on preference domains. The main purpose of this paper is to discuss the compatibility of those three properties when the assumption does not hold. We first establish a preference domain called top-only preferences, which violates the assumption, and develop a class of exchange mechanisms that satisfy all those properties. Each mechanism in the class utilizes one instance of the mechanisms introduced by Saban and Sethuraman (2013). We also find a class of preference domains called m-chotomous preferences, where the assumption fails and these properties are incompatible.