Constrained Signaling in Auction Design

We consider the problem of an auctioneer who faces the task of selling a good (drawn from a known distribution) to a set of buyers, when the auctioneer does not have the capacity to describe to the buyers the exact identity of the good that he is selling. Instead, he must come up with a constrained signalling scheme: a (non injective) mapping from goods to signals, that satisfies the constraints of his setting. For example, the auctioneer may be able to communicate only a bounded length message for each good, or he might be legally constrained in how he can advertise the item being sold. Each candidate signaling scheme induces an incomplete-information game among the buyers, and the goal of the auctioneer is to choose the signaling scheme and accompanying auction format that optimizes welfare. In this paper, we use techniques from submodular function maximization and no-regret learning to give algorithms for computing constrained signaling schemes for a variety of constrained signaling problems

Signaling and indirect taxation

Commodities communicate. Consumers choose a consumption bundle both for its intrinsic characteristics and for what this bundle communicates about their qualities (or .identity.) to spectators. We investigate optimal indirect taxation when consumption choices are motivated by two sorts of concerns: intrinsic consumption and costly signaling. Optimal indirect taxes are introduced into a monotonic signaling game with a finite typespace of consumers. We provide sufficient conditions for the uniqueness of the D1 sequential equilibrium in terms of strategies. In the case of pure costly signaling, signaling goods can in equilibrium be taxed without burden and the optimal quantity taxes on these goods are infinite. When commodities serve both intrinsic consumption and signaling, optimal taxes can be characterized by a generalization of the Ramsey rule, which also deals with the distortions resulting from signaling.Optimal Taxation, Indirect Taxation, Costly Signaling, Identity.

Generalized Second Price Auction with Probabilistic Broad Match

Generalized Second Price (GSP) auctions are widely used by search engines today to sell their ad slots. Most search engines have supported broad match between queries and bid keywords when executing GSP auctions, however, it has been revealed that GSP auction with the standard broad-match mechanism they are currently using (denoted as SBM-GSP) has several theoretical drawbacks (e.g., its theoretical properties are known only for the single-slot case and full-information setting, and even in this simple setting, the corresponding worst-case social welfare can be rather bad). To address this issue, we propose a novel broad-match mechanism, which we call the Probabilistic Broad-Match (PBM) mechanism. Different from SBM that puts together the ads bidding on all the keywords matched to a given query for the GSP auction, the GSP with PBM (denoted as PBM-GSP) randomly samples a keyword according to a predefined probability distribution and only runs the GSP auction for the ads bidding on this sampled keyword. We perform a comprehensive study on the theoretical properties of the PBM-GSP. Specifically, we study its social welfare in the worst equilibrium, in both full-information and Bayesian settings. The results show that PBM-GSP can generate larger welfare than SBM-GSP under mild conditions. Furthermore, we also study the revenue guarantee for PBM-GSP in Bayesian setting. To the best of our knowledge, this is the first work on broad-match mechanisms for GSP that goes beyond the single-slot case and the full-information setting