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### Optimal Regret Minimization in Posted-Price Auctions with Strategic Buyers

We study revenue optimization learning algorithms for posted-price auctions with strategic buyers. We analyze a very broad family of monotone regret minimization algorithms for this problem, which includes the previous best known algorithm, and show that no algorithm in that family admits a strategic regret more favorable than $\Omega(\sqrt{T})$. We then introduce a new algorithm that achieves a strategic regret differing from the lower bound only by a factor in $O(\log T)$, an exponential improvement upon the previous best algorithm. Our new algorithm admits a natural analysis and simpler proofs, and the ideas behind its design are general. We also report the results of empirical evaluations comparing our algorithm with the previous best algorithm and show a consistent exponential improvement in several different scenarios.

### The JCC Bomb-Threat Suspect Had a Client

A federal court has unsealed new documents in the case against an Israeli teenager, Michael Kadar, who has been accused of making at least 245 threatening calls to Jewish Community Centers and schools around the United States. According to the documents, Kadar advertised a "School Email Bomb Threat Service" on AlphaBay, an online marketplace for illicit goods and services that was shut down by the federal government in July. Authorities have identified an individual in California who allegedly ordered and paid for at least some of Kadar's threats. A newly unsealed search warrant alleges that Kadar charged $30 for an email bomb threat to a school, plus a$15 surcharge if the buyer wanted to frame someone for it. "There is no guarantee that the police will question or arrest the framed person," Kadar allegedly wrote in his ad.

### Repeated Contextual Auctions with Strategic Buyers

Motivated by real-time advertising exchanges, we analyze the problem of pricing inventory in a repeated posted-price auction. We consider both the cases of a truthful and surplus-maximizing buyer, where the former makes decisions myopically on every round, and the latter may strategically react to our algorithm, forgoing short-term surplus in order to trick the algorithm into setting better prices in the future. We further assume a buyer’s valuation of a good is a function of a context vector that describes the good being sold. We give the first algorithm attaining sublinear (O(T^{2/3})) regret in the contextual setting against a surplus-maximizing buyer. We also extend this result to repeated second-price auctions with multiple buyers.

### Revenue Optimization against Strategic Buyers

We present a revenue optimization algorithm for posted-price auctions when facing a buyer with random valuations who seeks to optimize his $\gamma$-discounted surplus. To analyze this problem, we introduce the notion of epsilon-strategic buyer, a more natural notion of strategic behavior than what has been used in the past. We improve upon the previous state-of-the-art and achieve an optimal regret bound in $O\Big( \log T + \frac{1}{\log(1/\gamma)} \Big)$ when the seller can offer prices from a finite set $\cP$ and provide a regret bound in $\widetilde O \Big(\sqrt{T} + \frac{T^{1/4}}{\log(1/\gamma)} \Big)$ when the buyer is offered prices from the interval $[0, 1]$.