This paper studies social choice under single-peaked preferences, where voters’ participation is voluntary. We say a social choice function satisfies participation if, for any voter, participating by reporting her true preference is weakly better than not participating. For each of two classes of parameterized social choice functions, namely ordered weighted average (OWA) methods and weighted average (WA) methods, we give a necessary and sufficient condition on the parameters to satisfy participation. We also give further discussions on OWAs and WAs, including the necessary and sufficient condition to satisfy a weaker notion of participation called non-obvious abstention (NOA), and the relationship with other properties.

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 [38] 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.

A new paradigm of mechanism design, called mechanism design over social networks, investigates agents’ incentives to diffuse the information of mechanisms to their followers over social networks. In this paper we consider it for two-sided matching, where the agents on one side, say students, are distributed over social networks and thus are not fully observable to the mechanism designer, while the agents on the other side, say colleges, are known a priori. The main purpose of this paper is to clarify the existence of mechanisms that satisfy several properties that are classified into four criteria: incentive constraints, efficiency constraints, stability constraints, and fairness constraints. We proposed three mechanisms and showed that no mechanism is better than these mechanisms, i.e., they are in the Pareto frontier according to the set of properties defined in this paper.

Abstract In many real-life scenarios, a group of agents needs to agree on a common action, e.g., on a location for a public facility, while there is some consistency between their preferences, e.g., all preferences are derived from a common metric space. The facility location problem models such scenarios and it is a well-studied problem in social choice. We study mechanisms for facility location on unweighted undirected graphs that are resistant to manipulations (strategy-proof, abstention-proof, and false-name-proof) by both individuals and coalitions on one hand and anonymous and efficient (Pareto-optimal) on the other. We define a new family of graphs, $$ZV$$ ZV -line graphs, and show a general facility location mechanism for these graphs that satisfies all these desired properties. This mechanism can also be computed in polynomial time and it can equivalently be defined as the first Pareto-optimal location according to some predefined order. Our main result, the $$ZV$$ ZV -line graphs family and the mechanism we present for it, unifies all works in the literature of false-name-proof facility location on discrete graphs including the preliminary (unpublished) works we are aware of. In particular, we show mechanisms for all graphs of at most five vertices, discrete trees, bicliques, and clique tree graphs. Finally, we discuss some generalizations and limitations of our result for facility location problems on other structures: Weighted graphs, large discrete cycles, infinite graphs; and for facility location problems concerning infinite societies.

We study the pairwise organ exchange problem among groups motivated by real-world applications and consider two types of group formulations. Each group represents either a certain type of patient-donor pairs who are compatible with the same set of organs, or a set of patient-donor pairs who reside in the same region. We address a natural research question, which asks how to match a maximum number of pairwise compatible patient-donor pairs in a fair and individually rational way. We first propose a natural fairness concept that is applicable to both types of group formulations and design a polynomial-time algorithm that checks whether a matching exists that satisfies optimality, individual rationality, and fairness. We also present several running time upper bounds for computing such matchings for different graph structures.

We study the Japanese Residency Matching Program (JRMP) in which hospitals are partitioned into disjoint regions and both hospitals and regions are subject to quotas. To achieve a balanced distribution of doctors across regions, hard bounds are imposed by the government to limit the number of doctors who can be placed in each region. However, such hard bounds lead to inefficiency in terms of wasted vacant positions. In this paper, we propose two suitable algorithms to reduce waste with minimal modification to the current system and show that they are superior to the algorithm currently deployed in JRMP by comparing them theoretically and empirically.

Auctions via social network, pioneered by Li et al. (2017), have been attracting considerable attention in the literature of mechanism design for auctions. However, no known mechanism has satisfied strategy-proofness, non-deficit, non-wastefulness, and individual rationality for the multi-unit unit-demand auction, except for some naïve ones. In this paper, we first propose a mechanism that satisfies all the above properties. We then make a comprehensive comparison with two naïve mechanisms, showing that the proposed mechanism dominates them in social surplus, seller's revenue, and incentive of buyers for truth-telling. We also analyze the characteristics of the social surplus and the revenue achieved by the proposed mechanism, including the constant approximability of the worst-case efficiency loss and the complexity of optimizing revenue from the seller's perspective.

We consider the problem of locating a single facility on a vertex in a given graph based on agents' preferences, where the domain of the preferences is either single-peaked or single-dipped, depending on whether they want to access the facility (a public good) or be far from it (a public bad). Our main interest is the existence of deterministic social choice functions that are Pareto efficient and false-name-proof, i.e., resistant to fake votes. We show that regardless of whether preferences are single-peaked or single-dipped, such a social choice function exists (i) for any tree graph, and (ii) for a cycle graph if and only if its length is less than six. We also show that when the preferences are single-peaked, such a social choice function exists for any ladder (i.e., 2 × m grid) graph, and does not exist for any larger (hyper)grid.

This paper studies minimum cost spanning tree (MCST) problems, in which an agent can behave as multiple agents by adding fake accounts. Since such split manipulations may increase the cost of MCST, it is important to (i) design a cost allocation rule under which no agent has an incentive to split her accounts, and (ii) analyze the resistance of the existing cost allocation rules against split manipulations. We first show that there exists no cost allocation rule that is both efficient and split-proof under the general domain. We then focus on the MCST problems with monotonic weight functions and show that there exists a cost allocation rule that is efficient, core-selecting, and split-proof. We finally analyze the resistance of the Bird rule, one of the most studied cost allocation rules in the literature, against split manipulations from three different perspectives: the mixed price of anarchy, the computational difficulty of manipulation, and domain restrictions.

My research is summarized as mechanism design with uncertainty. Traditional mechanism design focuses on static environments where all the (possibly probabilistic) information about the agents are observable by the mechanism designer. In practice, however, it is possible that the set of participating agents and/or some of teheir actions are not observable a priori. We therefore focused on various kinds of uncertainty in mechanism design and developed/analyzed several market mechanisms that incentivise agents to behave in a sincere way.

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.

In this paper, we study the service exchange problem where each agent is willing to provide her service in order to receive in exchange the service of someone else. We assume that agent's preference depends both on the service that she receives and the person who receives her service. This framework is an extension of the housing market problem to preferences including a degree of externalities. We investigate the complexity of computing an individually rational and Pareto efficient allocation of services to agents for ordinal preferences, and the complexity of computing an allocation which maximizes either the utility sum or the utility of the least served agent for cardinal preferences.

The cake cutting problem is concerned with the fair allocation of a divisible good among agents whose preferences vary over it. Recently, designing strategy-proof cake cutting mechanisms has caught considerable attention from AI and MAS researchers. Previous works assumed that an agent’s utility fu nction is additive so that theoretical analysis becomes tractable. However, in practice, agents have non-additive utility over a resource. In this paper, we consider the all-or-nothing utility function as a representative example of non-additive utility because it can widely cover agents’ preferences for such real-world resources as the usage of meeting rooms, time slots for computational resources, bandwidth usage, and so on. We first show the incompatibility between envy-freeness and Pareto efficiency when each agent has all-or-nothing utility. We next propose two strategy-proof mechanisms that satisfy Pareto efficiency, which are based on the serial dictatorship mechanism, at the sacrifice of envy-freeness. To address computational feasibility, we propose a heuristic-based allocation algorithm to find a near-optimal allocation in time polynomial in the number of agents, since the problem of finding a Pareto efficient allocation is NP-hard. As another approach that abandons Pareto efficiency, we develop an envy-free mechanism and show that one of our serial dictatorship based mechanisms satisfies proportionality in expectation, which is a weaker definition of proportionality. Finally, we evaluate the efficiency obtained by our proposed mechanisms by computational experiments.

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.

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.

This paper proposes a new approach to building false-name-proof (FNP) combinatorial auctions from those that are FNP only with single-minded bidders, each of whom requires only one particular bundle. Under this approach, a general bidder is decomposed into a set of single-minded bidders, and after the decomposition the price and the allocation are determined by the FNP auctions for single-minded bidders. We first show that the auctions we get with the single-minded decomposition are FNP if those for single-minded bidders satisfy a condition called PIA. We then show that another condition, weaker than PIA, is necessary for the decomposition to build FNP auctions. To close the gap between the two conditions, we have found another sufficient condition weaker than PIA for the decomposition to produce strategy-proof mechanisms. Furthermore, we demonstrate that once we have PIA, the mechanisms created by the decomposition actually satisfy a stronger version of false-name-proofness, called false-name-proofness with withdrawal.

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.