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. Our main interest is the existence of deterministic social choice functions (SCFs) 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 an SCF 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 an SCF exists for any ladder (i.e., 2-by-m grid) graph, and does not exist for any larger hypergrid.
Over the last decade, false-name-proofness has been scrutinized in various mechanism design problems @cite_27 @cite_18 @cite_25 @cite_8 , as a refinement of truthfulness for such open and anonymous environments, as the internet. Bu @cite_19 clarified a connection between false-name-proofness and population monotonicity in general social choice. @cite_2 also addressed FNP SCFs that are associated with monetary compensation. @cite_21 considered the case of locating two homogeneous facilities. @cite_4 studied some discrete structures, but focused on randomized SCFs. One of the most similar works to this paper is @cite_17 , who also clarified the network structures under which FNP and PE SCFs exist for single-peaked preferences. One clear difference from ours is that, in their paper proposed a new class of graphs, called a ZV-line, as a generalization of path graphs. In our paper we investigate well-known existing structures, namely tree, hypergrid, and cycle graphs. ZV-line graphs contain any tree and ladder (i.e., @math -grid for arbitrary @math ), but do not cover any other graphs considered in this paper, such as larger (hyper-)grid graphs and cycle graphs with lengths over three.
@cite_18 @cite_4 @cite_8 @cite_21 @cite_19 @cite_27 @cite_2 @cite_25 @cite_17
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An important aspect of mechanism design in social choice protocols and multiagent systems is to discourage insincere and manipulative behaviour. We examine the computational complexity of false-name manipulation in weighted voting games which are an important class of coalitional voting games. Weighted voting games have received increased interest in the multiagent community due to their compact representation and ability to model coalitional formation scenarios. Bachrach and Elkind in their AAMAS 2008 paper examined divide and conquer false-name manipulation in weighted voting games from the point of view of Shapley-Shubik index. We analyse the corresponding case of the Banzhaf index and check how much the Banzhaf index of a player increases or decreases if it splits up into sub-players. A pseudo-polynomial algorithm to find the optimal split is also provided. Bachrach and Elkind also mentioned manipulation via merging as an open problem. In the paper, we examine the cases where a player annexes other players or merges with them to increase their Banzhaf index or Shapley-Shubik index payoff. We characterize the computational complexity of such manipulations and provide limits to the manipulation. The annexation non-monotonicity paradox is also discovered in the case of the Banzhaf index. The results give insight into coalition formation and manipulation. We consider the problem of locating facilities on a discrete acyclic graph, where agents’ locations are publicly known and the agents are requested to report their demands, i.e., which facilities they want to access. In this paper, we study the effect of manipulations by agents that utilize vacant vertices. Such manipulations are called rename or false-name manipulations in game theory and mechanism design literature. For locating one facility on a path, we carefully compare our model with traditional ones and clarify their differences by pointing out that some existing results in the traditional model do not carry over to our model. For locating two facilities, we analyze the existing and new mechanisms from a perspective of approximation ratio and provide non-trivial lower bounds. Finally, we introduce a new mechanism design model where richer information is available to the mechanism designer and show that under the new model false-name-proofness does not always imply population monotonicity. Cake cutting has been recognized as a fundamental model in fair division and several envy-free cake cutting algorithms have been proposed Recent works from the computer science field proposed novel mechanisms for cake cutting, whose approaches are based on the theory of mechanism design; these mechanisms are strategy-proof, i.e., no agent has any incentive to misrepresent her utility function, as well as envy-free. We consider a different type of manipulations; each agent might create fake identities to cheat the mechanism. Such manipulation have been called Sybils or false-name manipulations, and designing robust mechanisms against them, i.e., false-name-proof, is a challenging problem in mechanism design literature. We first show that no randomized false-name-proof cake cutting mechanism simultaneously satisfies ex-post envy-freeness and Pareto efficiency We then propose a new randomized mechanism that is optimal in terms of worst-case loss among those that satisfy false-name-proofness, ex-post envy-freeness, and a new weaker efficiency property. However, it reduces the amount of allocations for an agent exponentially with respect to the number of agents. To overcome this negative result, we provide another new cake cutting mechanism that satisfies a weaker notion of false-name-proofness, as well as ex-post envy freeness and Pareto efficiency. 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. Matching a set of agents to a set of objects has many real applications. One well-studied framework is that of priority-based matching, in which each object is assumed to have a priority order over the agents. The Deferred Acceptance (DA) and Top-Trading-Cycle (TTC) mechanisms are the best-known strategy-proof mechanisms. However, in highly anonymous environments, the set of agents is not known a priori, and it is more natural for objects to instead have priorities over characteristics (e.g., the student's GPA or home address). In this paper, we extend the model so that each agent reports not only its preferences over objects, but also its characteristic. We derive results for various notions of strategy-proofness and false-name-proofness, corresponding to whether agents can only report weaker characteristics or also incomparable or stronger ones, and whether agents can only claim objects allocated to their true accounts or also those allocated to their fake accounts. Among other results, we show that DA and TTC satisfy a weak version of false-name-proofness. Furthermore, DA also satisfies a strong version of false-name-proofness, while TTC fails to satisfy it without an acyclicity assumption on priorities. We examine the effect of false-name bids on combinatorial auction protocols. False-name bids are bids submitted by a single bidder using multiple identifiers such as multiple e-mail addresses. The obtained results are summarized as follows: (1) the Vickrey–Clarke–Groves (VCG) mechanism, which is strategy-proof and Pareto efficient when there exists no false-name bid, is not falsename-proof; (2) there exists no false-name-proof combinatorial auction protocol that satisfies Pareto efficiency; (3) one sufficient condition where the VCG mechanism is false-name-proof is identified, i.e., the concavity of a surplus function over bidders. The class of Groves mechanisms has been attracting much attention in called social welfare maximization) and dominant strategy incentive compatibility. However, when strategic agents can create multiple fake identities and reveal more than one preference under them, a refined characteristic called false-name-proofness is required. Utilitarian efficiency and false-name-proofness are incompatible in combinatorial auctions, if we also have individual rationality as a desired condition. However, although individual rationality is strongly desirable, if participation is mandatory due to social norms or reputations, a mechanism without individual rationality can be sustained. In this paper we investigate the relationship between utilitarian efficiency and false-name-proofness in a social choice environment with monetary transfers. We show that in our modelization no mechanism simultaneously satisfies utilitarian efficiency, false-name-proofness, and individual rationality. Considering this fact, we ignore individual rationality and design various mechanisms that simultaneously satisfy the other two properties. We also compare our different mechanisms in terms of the distance to individual rationality. Finally we illustrate our mechanisms on a facility location problem. 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, which are resistant to manipulations (strategyproof, abstention-proof, and false-name-proof ) by both individuals and coalitions and are efficient (Pareto optimal). We define a family of graphs, ZV -line graphs, and show a general facility location mechanism for these graphs which satisfies all these desired properties. Moreover, we show that this mechanism can be computed in polynomial time, the mechanism is anonymous, and it can equivalently be defined as the first Pareto optimal location according to some predefined order. Our main result, the ZV -line graphs family and the mechanism we present for it, unifies the few current works in the literature of false-name-proof facility location on discrete graphs, including the preliminary (unpublished) works we are aware of. Finally, we discuss some generalizations and limitations of our result for problems of facility location on other structures.