Facility location games provide an abstract model of mechanism design. In such games, a mechanism takes a profile of $n$ single-peaked preferences over an interval as an input and determines the location of a facility on the interval. In this paper, we restrict our attention to distance-based single-peaked preferences and focus on a well-known class of parameterized mechanisms called ordered weighted average methods, which is proposed by Yager in 1988 and contains several practical implementations such as the standard average and the Olympic average. We comprehensively analyze their performance in terms of both incentives and fairness. More specifically, we provide necessary and sufficient conditions on their parameters to achieve strategy-proofness, non-obvious manipulability, individual fair share, and proportional fairness, respectively.

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.

In this paper, we propose a fractional preference model for the facility location game with two facilities that serve the similar purpose on a line where each agent has his location information as well as fractional preference to indicate how well they prefer the facilities. The preference for each facility is in the range of [0, L] such that the sum of the preference for all facilities is equal to 1. The utility is measured by subtracting the sum of the cost of both facilities from the total length L where the cost of facilities is defined as the multiplication of the fractional preference and the distance between the agent and the facilities. We first show that the lower bound for the objective of minimizing total cost is at least Ω(n^1/3). Hence, we use the utility function to analyze the agents' satification. Our objective is to place two facilities on [0, L] to maximize the social utility or the minimum utility. For each objective function, we propose deterministic strategy-proof mechanisms. For the objective of maximizing the social utility, we present an optimal deterministic strategy-proof mechanism in the case where agents can only misreport their locations. In the case where agents can only misreport their preferences, we present a 2-approximation deterministic strategy-proof mechanism. Finally, we present a 4-approximation deterministic strategy-proof mechanism and a randomized strategy-proof mechanism with an approximation ratio of 2 where agents can misreport both the preference and location information. Moreover, we also give a lower-bound of 1.06. For the objective of maximizing the minimum utility, we give a lower-bound of 1.5 and present a 2-approximation deterministic strategy-proof mechanism where agents can misreport both the preference and location.

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.

This paper studies a mechanism to incentivize agents who predict their own future actions and truthfully declare their predictions. In a crowdsouring setting (e.g., participatory sensing), obtaining an accurate prediction of the actions of workers/agents is valuable for a requester who is collecting real-world information from the crowd. If an agent predicts an external event that she cannot control herself (e.g., tomorrow's weather), any proper scoring rule can give an accurate incentive. In our problem setting, an agent needs to predict her own action (e.g., what time tomorrow she will take a photo of a specific place) that she can control to maximize her utility. Also, her (gross) utility can vary based on an eternal event. We first prove that a mechanism can satisfy our goal if and only if it utilizes a strictly proper scoring rule, assuming that an agent can find an optimal declaration that maximizes her expected utility. This declaration is self-fulfilling; if she acts to maximize her utility, the probabilistic distribution of her action matches her declaration, assuming her prediction about the external event is correct. Furthermore, we develop a heuristic algorithm that efficiently finds a semi-optimal declaration, and show that this declaration is still self-fulfilling. We also examine our heuristic algorithm's performance and describe how an agent acts when she faces an unexpected scenario.

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.