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We study stationary equilibria in a sequential auction setting. A seller runs a sequence of standard first-price or second-price auctions to sell an indivisible object to potential buyers. The seller can commit to the rule of the auction and the reserve price of the current period but not to reserve prices of future periods. We prove the existence of stationary equilibria and establish a uniform Coase conjecture—at any point in time and in any stationary equilibrium, the seller’s profit from running sequential auctions converges to the profit of running an efficient auction as the period length goes to zero. 

We review the nascent field of matching with incomplete information and its connections to other areas of research. We also discuss open questions and argue that cooperative solution concepts offer new perspectives for applications. 

This paper analyses a model of strategic exploration in which competing players independently explore a set of alternatives. The model features a multiple-player multiple-armed bandit problem and captures a strategic trade-off between pre-emption—covert exploration of alternatives that the opponent will explore in the future—and prioritization—exploration of the most promising alternatives. Our results explain how the strategic trade-off shapes equilibrium behaviours and outcomes, for example, in technology races between superpowers and R&D competitions between firms. We show that players compete on the same set of alternatives, leading to duplicated exploration from start to finish, and they explore alternatives that are a priori less promising before more promising ones are exhausted. The model also predicts that competition induces players to implement unreliable technologies too early, even though they should wait for the technologies to mature. Coordinated exploration is impossible even if the alternatives are equally promising, but it can emerge in equilibrium following a phase of pre-emptive competition if there is a short deadline. With asymmetric capacities of exploration, the weak player conducts extensive instead of intensive exploration—exploring as many alternatives as the strong player does but never fully exploring any. 

We propose a criterion of stability for two-sided markets with asymmetric information. A central idea is to formulate off-path beliefs conditional on counterfactual pairwise deviations and on-path beliefs in the absence of such deviations. A matching-belief configuration is stable if the matching is individually rational with respect to the system of on-path beliefs and is not blocked with respect to the system of off-path beliefs. The formulation provides a language for assessing matching outcomes with respect to their supporting beliefs and opens the door to further belief-based refinements. The main refinement analyzed in the paper requires the Bayesian consistency of on-path and off-path beliefs with prior beliefs. We define concepts of Bayesian efficiency, the rational expectations competitive equilibrium, and the core. Their contrast with pairwise stability manifests the role of information asymmetry in matching formation. (JEL C78, D40, D82, D83) 

We study the role of limited commitment in a standard auction environment. In each period, the seller can commit to an auction with a reserve price but not to future reserve prices. We characterize the set of equilibrium profits attainable for the seller as the period length vanishes. An immediate sale by efficient auction is optimal when there are at least three buyers. For many natural distributions two buyers is enough. Otherwise, we give conditions under which the maximal profit is attained through continuously declining reserve prices. (JEL D44, D82)