Deadlines in the market for lemons
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Deadlines in the market for lemons Heng Liu1 Received: 20 March 2020 / Accepted: 6 June 2020 © Society for the Advancement of Economic Theory 2020
Abstract This paper studies finite-horizon bargaining games with interdependent values. A long-lived seller privately learns the quality of an indivisible good. Short-lived buyers make publicly observable offers to the seller successively until the good is sold. In the two-type case, the prices are always low and only the low-quality good is gradually traded in the unique equilibrium. With a continuum of types and linear values, we characterize asymptotic equilibrium outcomes as the time horizon increases to infinity. While the finite-horizon equilibrium dynamics can be different in these two cases, as the time horizon goes to infinity, the equilibrium outcomes in both settings converge to the bargaining impasse identified by Hörner and Vieille (Econometrica 77: 29–69, 2009) in the infinite-horizon game.
1 Introduction Hörner and Vieille (2009) find that the lemons problem can lead to an impasse in infinite horizon bargaining with privately informed sellers. In settings where infinitely many short-lived buyers make price quotes sequentially to a patient seller, they show that the seller’s signaling incentive through turning down a serious offer to receive more favorable future offers, together with the lemons problem, may result in a complete market breakdown, even when the gains from trade are always positive. This paper examines the robustness of bargaining impasse in finite-horizon bargaining. There are three motivations for this exercise. First, there are deadlines in many markets with adverse selection, such as trading of financial assets with liquidity concerns. It is relevant to understand the impact of deadlines on the trading patterns and information revelation in these markets. Second, in finite-horizon settings,
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s4050 5-020-00185-6) contains supplementary material, which is available to authorized users. * Heng Liu [email protected] 1
Department of Economics, University of Michigan, Ann Arbor, USA
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bargaining impasse (or, complete market failure) cannot hold, since the last buyer will always trade with some sellers as in a static problem. Nonetheless, it is of theoretical interest to ask whether and how the finite-horizon equilibrium outcomes converge to the bargaining impasse as the horizon goes to infinity, to understand the robustness of impasse to the time horizon of bargaining. Finally, the analysis has policy implications when the horizon of trade may be determined by government interventions, which are often crucial in markets suffering from adverse selection, such as the asset market during the recent financial crisis. For instance, it may be welfare improving to reduce the trading opportunities of certain financial asset, if doing so would accelerate transactions.1 Specifically, we introduce a deterministic deadlin
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