War of Attrition: Evidence from a Laboratory Experiment on Market Exit

I. INTRODUCTION Young industries often undergo a process of shakeout (Gort and Klepper 1982 and Klepper 1996), attracting excess firms and gradually shedding them over time. More mature industries are likewise often forced to contract in the face of recession or product specific negative demand shocks. When an overcrowded industry is forced to shrink, which firms exit and which ones survive? The conventional answer in economics is that overcrowded industries tend to shed inefficient firms and retain efficient ones. We might call this "survival of the most efficient", a process analogous to natural selection that can adaptively improve the efficiency of industries over time (Nelson and Winter 1982). Fudenberg and Tirole (1986) model firms' exit decisions in overcrowded duopoly markets as wars of attrition and show that the intuition of survival of the most efficient has merit even if firms have little information regarding their costs relative to their competitors. However, the equilibrium of their game is complex, involving a solution to a system of differential equations. Since neither Fortune 500 chief executive officers in the naturally occurring markets nor undergraduate participants in laboratory markets deliberately solve differential equations when deciding whether or not to exit a declining market, it is an open question as to how well Fudenberg and Tirole's rational reconstruction of the exit decision corresponds to the facts of how people make such decisions. We report the results of a laboratory experiment designed to answer this question. Nearly 200 subjects in 16 sessions participated in a total of 3,800 wars of attrition based on Fudenberg and Tirole's model. At the beginning of each period, subjects were randomly paired and given a private cost draw that (usually) induced negative net per second payoffs in a shared market and positive net payoffs per second in monopoly. Subjects then decided in real time whether and when to exit the market, never to return. Monotonic equilibrium strategy functions predict higher cost (inefficient) participant exit at an earlier time than their lower cost competitor, that is, the relatively efficient competitor survives in the market. We find that Fudenberg and Tirole's model organizes our data surprisingly well, especially considering its complexity. We observe exit by the higher cost firm in 76% of cases. When differences between the costs faced by firms are substantial, the rate of efficient exit rises to nearly 100%. The data on exit times are likewise quite close to the point predictions, particularly in the crucial higher portion of the cost distribution that generally governs exit times. The median deviation from equilibrium exit times falls to zero by the end, and on average subjects earn payouts identical to those predicted in equilibrium. Our design permits tests of two other conjectures in Fudenberg and Tirole. First our data supports Fudenberg and Tirole's core comparative static prediction that a decrease in the ex ante likelihood of actually being in a war of attrition leads to an increase in the speed of exit. (1) Second, half of our sessions use costs framed as Fixed Costs (suffered while in the market) and half use costs framed as Opportunity Costs (earned by exiting the market). There is no evidence that this treatment variable affects exit behavior. This isomorphism between gains and losses, predicted by standard theory, stands in stark contrast to evidence from previous individual decision-making experiments suggesting asymmetries in how people react to potential losses and potential gains. Although wars of attrition have an important place in the game theoretic literature, there are surprisingly few experimental studies directly relating to them. (2,3) Bilodeau, Childs, and Mestelman (2004) study a three-player full information war of attrition (framed as a volunteer game) and report widespread failure of equilibrium predictions (the predicted volunteer in a subgame perfect Nash equilibrium only volunteers 41% of the time). …