War of Attrition: Evidence from a LaboratoryExperiment on Market Exit∗Ryan Oprea†Bart J. Wilson‡Arthur Zillante§July 5, 2010AbstractWe report an experiment designed to study whether inefficient firms are systematicallydriven from overcrowded markets. Our data set includes series of 3800 wars of attritionof a type modeled in Fudenberg and Tirole (1986). We find that exit tends to be efficientand exit times conform surprisingly well to point predictions of the model. Moreover,subjects respond similarly to implementations framed in terms of losses as they do tothose framed in terms of gains.JEL Codes: D21, L11, C92Keywords: Market exit, war of attrition, timing games, experimental economics∗We would like to thank John Dickhaut and Dan Houser, as well as participants of the George MasonUniversity seminar series and 2006 SEA meetings, for comments and suggestions. All errors and omissionsare our own. The data are available upon request.†415 Engineering 2, 1156 High Street, Santa Cruz, CA, 95064. [email protected]‡Economic Science Institute,Chapman University, One University Dr., Orange, CA 92866 . [email protected]§Dept. of Economics, 9201 University City Blvd., Charlotte, NC 28223. [email protected] IntroductionYoung industries often undergo a process of shakeout (see for example 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 productspecific negative demand shocks. When an overcrowded industry is forced to shrink, whichfirms exit and which ones survives? One popular answer in economics is that overcrowdedindustries tend to shed inefficient firms and retain efficient ones. We might call this “survivalof the most efficient”, a process analogous to natural selection that can adaptively improvethe efficiency of industries over time (see e.g. Nelson and Winter, 1982).Fudenberg and Tirole (1986) model firms’ exit decisions in overcrowded duopoly marketsas wars of attrition and show that the intuition of survival of the most efficient has meriteven if firms have little information regarding their costs relative to their competitors. How-ever, the equilibrium of their game is complex, involving a solution to a system of differentialequations. Since neither Fortune 500 CEOs in the naturally occurring markets nor under-graduate participants in laboratory markets deliberately solve differential equations whendeciding to exit a declining market, it is an open question as to how well Fudenberg andTirole’s rational reconstruction of the exit decision corresponds to the facts of how peoplemake such decisions.We report the results of a laboratory experiment designed to answer this question. Nearly200 subjects in 16 sessions participated in a total of 3800 laboratory wars of attrition basedon Fudenberg and Tirole’s model. At the beginning of each period, subjects were randomlypaired and given a private cost draw that (usually) induced negative net per second payoffsin a shared market and positive net payoffs per second in monopoly. Subjects then decidedin real time whether and when to exit the market, never to return. Monotonic equilibriumstrategy functions predict higher cost (inefficient) subjects exit at an earlier time than theirlower cost competitors; relatively efficient subjects survive in the market.We find that Fudenberg and Tirole’s model organizes our data surprisingly well, especiallyconsidering its complexity. We observe exit by the higher cost firm in 76 percent of cases.When differences between the costs faced by firms are substantial, the rate of efficient exitrises to nearly 100 percent. Point predictions on exit times are likewise quite close to the2data, particularly in the crucial higher portion of the cost distribution that generally governsexit times. The median deviation from equilibrium exit times is zero and on average subjectsearn payouts identical to those predicted in equilibrium.Our design permits tests of two other conjectures in Fudenberg and Tirole. First ourdata supports Fudenberg and Tirole’s core comparative static prediction that a decrease inthe ex ante likelihood of actually being in a war of attrition leads to an increase in the speedof exit.Second, we ran half of our sessions with costs framed as Fixed Costs (suffered whilein the market) and half with costs framed as Opportunity Costs (earned by exiting themarket). There is no evidence that this treatment variable affects exit behavior. Thisisomorphism between gains and losses, predicted by standard theory, stands in stark contrastto evidence from previous individual decision making experiments suggesting asymmetriesin how subjects react to potential losses and potential gains.Although wars of attrition have an important place in the game theoretic literature, thereare surprisingly few experimental studies relating to them. Kirchkamp (2004) studies an allpay auction1in a near-continuous time setting like ours. He reports evidence of underbid-ding and marginal evidence that increased uncertainty regarding costs induces greater bids(in contrast to predictions). Bilodeau et al. (2004) study a three player full informationwar of attrition (framed as a volunteer game) and report widespread failure of equilibriumpredictions (the predicted volunteer in a subgame perfect Nash equilibrium (SPNE) onlyvolunteers 41% of the time). Finally Phillips and Mason (1997) consider a quantity choicegame and vary whether fixed costs lead to wars of attrition at Cournot equilibrium outputs.They report evidence that subjects voluntarily enter wars of attrition in this setting.The remainder of this paper is organized as follows. In section 2, we describe a sim-plified version of the Fudenberg-Tirole model. Section 3 presents our experimental design,procedures, and predictions. In section 4 we present the experimental results and concludein section 5.1Bulow and Klemperer (1999) show that all pay auctions are isomorphic to wars of attrition.32 ModelConsider the following stripped down version of Fudenberg and Tirole (1986).2Firms i = 1, 2compete in a market in continuous time, earning duopoly revenues RDwhile they do. If onefirm exits the market, the remaining firm earns monopoly revenues RM> RDforever. Firmi incurs a fixed cost cidrawn independently and privately from a common (and commonknowledge) uniform distribution U [c, c] as long as it is in the