Strategy-Proof Mechanisms for the k-Winner Selection Problem

The goal of this paper is to develop a strategy-proof (SP) mechanism for the k-winner selection problem, which finds a set of (at most) k winners among participants. Here, we assume the winners can have positive/negative externalities with each other; the gross utility of a winner not only depends on whether she wins, but also on the other winners. If the types of agents, i.e., the gross utilities of agents, are known, we can obtain a Pareto efficient (PE) allocation that maximizes the sum of the gross utilities of winners in polynomial time, assuming k is a constant. On the other hand, when the types of agents are private information, we need a mechanism that can elicit the true types of agents; it must satisfy SP. We first show that there exists no SP mechanism that is PE, individual rational (IR), and non-deficit (ND) in a general setting where we put no restrictions on possible agent types. Thus, we need to give up at least one of these desirable properties.

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