Core-selection is a crucial property of rules in the literature of resource allocation. It is also desirable, from the perspective of mechanism design, to address the incentive of agents to cheat by misreporting their preferences. This paper investigates the exchange problem where (i) each agent is initially endowed with (possibly multiple) indivisible goods, (ii) agents' preferences are assumed to be conditionally lexicographic, and (iii) side payments are prohibited. We propose an exchange rule called augmented top-trading-cycles (ATTC), based on the original TTC procedure. We first show that ATTC is core-selecting and runs in polynomial time with respect to the number of goods. We then show that finding a beneficial misreport under ATTC is NP-hard. We finally clarify relationship of misreporting with splitting and hiding, two different types of manipulations, under ATTC.

This paper considers a mechanism design problem for locating two identical facilities on an interval, in which an agent can pretend to be multiple agents. A mechanism selects a pair of locations on the interval according to the declared single-peaked preferences of agents. An agent's utility is determined by the location of the better one (typically the closer to her ideal point). This model can represent various application domains. For example, assume a company is going to release two models of its product line and performs a questionnaire survey in an online forum to determine their detailed specs. Typically, a customer will buy only one model, but she can answer multiple times by logging onto the forum under several email accounts. We first characterize possible outcomes of mechanisms that satisfy false-name-proofness, as well as some mild conditions. By extending the result, we completely characterize the class of false-name-proof mechanisms when locating two facilities on a circle. We then clarify the approximation ratios of the false-name-proof mechanisms on a line metric for the social and maximum costs.

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.

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.