False-name-proof combinatorial auction design via single-minded decomposition

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

Limited Verification of Identities to Induce False-Name-Proofness

In open, anonymous environments such as the Internet, mechanism design is complicated by the fact that a single agent can participate in the mechanism under multiple identifiers. One way to address this is to design false-name-proof mechanisms, which choose the outcome in such a way that agents have no incentive to use more than one identifier. Unfortunately, there are inherent limitations on what can be achieved with false-name-proof mechanisms, and at least in some cases, these limitations are crippling. An alternative approach is to verify the identities of all agents. This imposes significant overhead and removes any benefits from anonymity. In this paper, we propose a middle ground. Based on the reported preferences, we check, for various subsets of the reports, whether the reports in the subset were all submitted by different agents. If they were not, then we discard some of them. We characterize when such a limited verification protocol induces false-name-proofness for a mechanism, that is, when the combination of the mechanism and the verification protocol gives the agents no incentive to use multiple identi- fiers. This characterization leads to various optimization problems for minimizing verification effort. We study how to solve these problems. Throughout, we use combinatorial auctions (using the Clarke mechanism) and majority voting as examples

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

International audienceCore-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

Anonymity-proof voting rules

Abstract. A (randomized, anonymous) voting rule maps any multiset of total orders (aka. votes) over a fixed set of alternatives to a probability distribution over these alternatives. A voting rule f is false-name-proof if no voter ever benefits from casting more than one vote. It is anonymity-proof if it satisfies voluntary participation and it is false-name-proof. We show that the class of anonymityproof neutral voting rules consists exactly of the rules of the following form. With some probability kf ∈ [0, 1], the rule chooses an alternative uniformly at random. With probability 1 − kf, the rule first draws a pair of alternatives uniformly at random. If every vote prefers the same alternative between the two (and there is at least one vote), then the rule chooses that alternative. Otherwise, the rule flips a fair coin to decide between the two alternatives. We also show how the characterization changes if group strategy-proofness is added as a requirement.