Myerson on a Network
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The auction of a single indivisible item is one of the most celebrated problems in mechanism design with transfers. Despite its simplicity, it provides arguably the cleanest and most insightful results in the literature. When the information of the auction is available to every participant, Myerson [17] provided a seminal result to characterize the incentive-compatible auctions along with revenue optimality. However, such a result does not hold in an auction on a network, where the information of the auction is spread via the agents, and they need incentives to forward the information. In recent times, a few auctions (e.g., [10, 15]) were designed that appropriately incentivize the intermediate nodes on the network to promulgate the information to potentially more valuable bidders. In this paper, we provide a Myerson-like characterization of incentive-compatible auctions on a network and show that the currently known auctions fall within this larger class of randomized auctions. We obtain the structure of the revenue optimal auction for i.i.d. bidders on arbitrary trees. We discuss the possibilities of addressing more general settings. Through experiments, we show that auctions following this characterization can provide a higher revenue than the currently known auctions on networks.
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