No Holdup in Dynamic Markets

Abstract

Different types of agents make non-contractible investments before bargaining over both who matches to whom and the terms of trade. In thin markets, the holdup problem — that is, underinvestment caused by agents receiving only a fraction of the returns from their investments — is ubiquitous. However, we show that holdup is not a problem in markets that attract traders over time — even when only a few traders are present in the market at any point in time. In particular, we characterize the type-symmetric Markov perfect equilibria of a non-cooperative investment and bargaining game with sequential entry, and we show that — in every such equilibrium — all the agents receive the full returns from their marginal investments in the limit as they become patient. Intuitively, the option to wait for future market participants creates competition — so even apparently-thin markets can be competitive. This provides non-cooperative foundations for the standard price-taking assumption in the literature investigating investment efficiency in competitive matching markets.

Keywords: Holdup, Efficiency, Bargaining, Competition, Dynamic Entry, Outside Options

JEL Classification: C72, C78, D40, D41