online auction platforms

Abstract: The design of credible auctions---mechanisms where a revenue-maximizing auctioneer has no incentive to deviate from the protocol---faces a fundamental cryptographic barrier when the auctioneer controls shill bidders. While a natural approach is to use Secure Multi-Party Computation (MPC) to remove the trusted auctioneer, the impossibility of fair coin flipping of Cleve (1986) implies that monolithic MPC protocols grant the auctioneer a "free option": they can learn the auction's outcome and unilaterally abort if the revenue is unsatisfactory. Cryptographic commitments with ex-ante penalties mitigate this abort asymmetry, but no finite penalty suffices for heavy-tailed distributions. We circumvent this barrier by introducing the MPC Decomposition Principle. Rather than encrypting the entire mechanism, we use MPC strictly as an information-restriction tool. We isolate the winner determination problem into a minimal MPC gadget that computes and reveals the winner's identity but no payment information. This qualitative restriction mathematically bounds the information leaked upon an abort. By combining this gadget with sequential revelation and finite economic penalties, we design the Sequential Revelation Auction (SRA). We prove that bounding the information leakage strictly bounds the value of the free option, showing that a penalty of $k \geq \sum_{i=1}^n Rev(F_i)$ is sufficient for credibility, and tight: for equal-revenue distributions, every smaller penalty admits a profitable deviation. Using constant-round MPC, the SRA resolves an open question of Akbarpour and Li (2020) and Ferreira and Weinberg (2020) by providing a constant-round, incentive-compatible, revenue-optimal credible auction for all product distributions with vanishing revenue tails

Abstract: We study Bulow-Klemperer-style competition complexity in two-sided double auctions with $m$ unit-demand buyers drawn i.i.d. from $F_B$ and $n$ unit-supply sellers drawn i.i.d. from $F_S$. When $m \ge n$ and buyer valuations first-order stochastically dominate seller costs ($F_B \succeq_{\mathrm{FSD}} F_S$), we prove that recruiting just two additional sellers enables Seller Trade Reduction (STR), a prior-independent mechanism, to achieve expected Gains From Trade (GFT) at least the first-best GFT of the original market. When the buyer side is the smaller side of the market ($m \le n$), an analogous result holds for Buyer Trade Reduction with 2 additional buyers. This resolves open questions of Babaioff, Goldner, and Gonczarowski (SODA 2020) and Cai, Liaw, Mehta, and Zhao (STOC 2024). We complement our upper bound by showing that this uniform bound is optimal: already for $m = n = 1$, no prior-free mechanism (deterministic or randomized) that is dominant-strategy incentive-compatible, individually rational, and weakly budget-balanced can match the first-best GFT by recruiting only one additional seller.

Abstract: We study repeated prophet inequalities under prefix feedback. In each of $T$ rounds, a learner encounters fresh values drawn independently from $n$ boxes with unknown $[0,1]$-supported distributions in a fixed order and must irrevocably accept one, observing only the prefix up to its stopping box. Regret is measured against the optimal stopping policy that knows the distributions. We give an efficient algorithm achieving $\widetilde O(\sqrt{T})$ expected regret, matching the lower bound up to logarithmic factors. Our algorithm explores directly through near-optimal policies, combining empirical backward induction with box-specific reach bonuses. A relative-drop aggregation rule then exploits the nesting structure of observed prefixes to preserve exploration, thereby removing the polynomial dependence on the box number $n$. This resolves an open question posed by Liu et al. (2025).