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



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War of Attrition Evidence from a Laboratory Experiment on Market Exit Ryan Oprea Bart J Wilson Arthur Zillante July 5 2010 Abstract We report an experiment designed to study whether inefficient firms are systematically driven from overcrowded markets Our data set includes series of 3800 wars of attrition of a type modeled in Fudenberg and Tirole 1986 We find that exit tends to be efficient and 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 to those framed in terms of gains JEL Codes D21 L11 C92 Keywords 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 Mason University seminar series and 2006 SEA meetings for comments and suggestions All errors and omissions are our own The data are available upon request 415 Engineering 2 1156 High Street Santa Cruz CA 95064 roprea ucsc edu Economic Science Institute Chapman University One University Dr Orange CA 92866 bartwilson gmail com Dept of Economics 9201 University City Blvd Charlotte NC 28223 azillant uncc edu 1 1 Introduction Young 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 product specific negative demand shocks When an overcrowded industry is forced to shrink which firms exit and which ones survives One popular 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 see e g 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 CEOs in the naturally occurring markets nor undergraduate participants in laboratory markets deliberately solve differential equations when deciding 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 3800 laboratory 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 subjects exit at an earlier time than their lower cost competitors relatively efficient subjects survive 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 percent of cases When differences between the costs faced by firms are substantial the rate of efficient exit rises to nearly 100 percent Point predictions on exit times are likewise quite close to the 2 data particularly in the crucial higher portion of the cost distribution that generally governs exit times The median deviation from equilibrium exit times is zero 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 Second we ran half of our sessions with costs framed as Fixed Costs suffered while in the market and half with 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 subjects 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 relating to them Kirchkamp 2004 studies an all pay auction1 in a near continuous time setting like ours He reports evidence of underbidding and marginal evidence that increased uncertainty regarding costs induces greater bids in contrast to predictions Bilodeau et al 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 SPNE only volunteers 41 of the time Finally Phillips and Mason 1997 consider a quantity choice game 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 simplified version of the Fudenberg Tirole model Section 3 presents our experimental design procedures and predictions In section 4 we present the experimental results and conclude in section 5 1 Bulow and Klemperer 1999 show that all pay auctions are isomorphic to wars of attrition 3 2 Model Consider the following stripped down version of Fudenberg and Tirole 1986 2 Firms i 1 2 compete in a market in continuous time earning duopoly revenues RD while they do If one firm exits the market the remaining firm earns monopoly revenues RM RD forever Firm i incurs a fixed cost ci drawn independently and privately from a common and common knowledge uniform distribution U c c as long as it is in the market Without loss of generality assume c1 c2 Firm i s profits at each instant are i D R ci if both are


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