auction platform designers

Abstract: We study equilibrium computation in multi-unit trading networks with valuations satisfying generalized full substitutes and agent- and transaction-specific piecewise-linear transfer functions. These transfers model platform fees, taxes, subsidies, and membership discounts in online marketplaces. Our ascending procedure raises prices at different rates and reaches the minimum equilibrium price vector in finitely many iterations, each implementable in strongly polynomial time under our oracle and arithmetic models. An equilibrium allocation can then be recovered efficiently. The method extends primal-dual techniques developed for ascending auctions to handle complementarities between purchases and sales through a submodular flow formulation. In single-seller markets with substitutes and complements, our framework also extends the double-track auctions of Sun and Yang (2009) and Shioura and Yang (2015) to bidder- and good-specific transfers.

Abstract: We show that computing an approximate mixed Bayes-Nash equilibrium in a discrete first-price auction with correlated priors is PPAD-complete. The key intermediate step in our reduction is the PPAD-completeness of computing an approximate Nash equilibrium in a new normal-form game, the hypergraph discrete first-price auction, which may be of independent interest.

Abstract: A single auction can have both a shill-proof equilibrium and a non-shill-proof equilibrium in the model of Komo, Kominers, and Roughgarden. We give an explicit single item example with three bidder positions, publicly observed actions, positive winning prices, and a strictly regular i.i.d.\ value distribution. Real bidders have strict incentives in both equilibria. An initial public action conveys information about whether the final position is real. The resulting belief changes the middle bidder's response and reverses the first shill's strict preference between two actions. We verify both equilibria and compute their expected revenues.

Abstract: When auction bidders misperceive their rivals, a seller can change not only the amount of information rent but also the states in which it is delivered. We ask when this payment-design opportunity survives a finite bidding interface, nonnegative-payment restrictions, and comparison with conventional auctions under the same beliefs. We formulate payment design as a linear program in nonnegative bidder rents. A single state can safely carry a report's rent when it is both cheapest for its intended type and least attractive to potential mimics. We characterize this alignment, bound the cost of a restricted payment architecture when alignment is imperfect, and use shadow prices when the rankings conflict. Own-type projection yields a unique optimal expected-payment rule for a fixed allocation. Contiguous bid bands implement truthful reporting at every value, but create pooling losses and within-band surplus. Under a separate smooth-belief model, feasible truthful rules and revenue upper bounds support comparisons with a first-price equilibrium under the same beliefs. A calibration using 1,000 eBay proof-set auction records illustrates a partition-dependent reversal: first price dominates all exactly truthful, no-subsidy rules on ten equal-probability bands in one scenario, while a richer contingent rule on ten equal-dollar bands outperforms it. An operator should choose interface resolution, payment dependence, and integrity tolerances jointly. Validate the probabilities that support incentives, compare formats under the same beliefs, and distinguish redesign from deployment. Any receipt advantage must cover implementation costs before it can imply a profit advantage.