A Complexity Approach for Core-Selecting Exchange under Conditionally Lexicographic Preferences

Abstract


 
 
 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.
 
 

An impossibility result for housing markets with fractional endowments

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Strategyproof multi-item exchange under single-minded dichotomous preferences

“…Some positive results depend on the fact that agents have lexicographic preferences over items or items types. Under these assumptions, it is possible to construct extensions of TTC that achieve strategyproofness, individual rationality, and Pareto optimality (see e.g., (Fujita et al, 2015;Sikdar et al, 2017)). The preferences we consider do not assume any of these structural restrictions that are based on lexicographic or conditional lexicographic comparisons.…”

Pareto Optimal Matchings in Many-to-Many Markets with Ties

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