Wars of attrition in experimental duopoly markets.

• Author: Phillips, Owen R.

1. Introduction

   Oligopolists often bear large fixed costs. These fixed costs can change, for example through rising property rents, increased taxes, and renegotiated labor contracts. In this paper, we imagine oligopoly market structures that are identical except for the level of fixed costs. Does this level influence the strategic behavior of firms? Since marginal profits are unaffected by fixed costs, one answer is that there should be no change in behavior. Alternatively, firms may seek more cooperative outputs in order to maintain profits. Enough cooperation can even generate bigger profits. But if fixed costs rise to a level where there are too many firms in the market for any seller to earn an adequate profit, a price war could result. Attrition leaves more profits for the survivors and the higher fixed costs are an increased barrier to later entry. Thus, it also can be argued that greater fixed costs engender less cooperation among rivals because agents are fighting over a smaller profit pie.(1)

   Through the use of experimental markets, this paper shows that fixed costs do have an influence on the level of cooperation after they have reached a relatively high level in a duopoly market structure. Subjects (as rivals) engage in price wars. Outputs are kept large - larger than the Cournot level - until a rival exits the market. By contrast, such behavior does not take place when fixed costs are relatively low. This difference in behavior at low and high fixed cost levels is statistically significant. We emphasize that price wars are not observed until fixed costs are relatively high. At low levels, i.e., periods of relatively high profitability, a change in fixed costs seems to make rivals slightly more cooperative, but this effect is not statistically significant.

   The experimental markets are in fact a repeated game in which two symmetric quantity choosing agents face each other over numerous market periods. Behavior is measured by the choices agents make on a payoff table. Row values represent all the output choices rival i can make; column values are the possible output choices of rival j. The intersection of the ith row and the jth column determines the profit of seller i. Agents simultaneously make choices from identical tables and know their rival has the same table, so that payoffs are common knowledge. Subjects are not told when the experiment will end, so the games have an unknown endpoint.(2)

   In these laboratory markets it is possible for agents to make sufficiently high output choices that cumulative profits become negative for at least one agent. If a subject's cumulative profits become negative they are excused from the experiment and the surviving rival is allowed to then behave as a monopoly.(3) Because of bankruptcy, low profitability alters the dynamic payoff structure to agents. In particular, bigger fixed costs reduce the time necessary to drive a counterpart out of the market, and increase the number of periods for monopoly earnings. But other types of behavior can be observed between subject pairs. It is possible that, rather than causing a "war of attrition," larger fixed costs have no impact on choices, as already suggested, or they may even encourage firms to seek higher joint payoff levels. In the latter case, restricted market outputs raise the profits of both sellers, which counteracts the higher costs. We believe oligopoly behavior in the face of rising fixed costs is an empirical issue; the equilibrium of a game may be left unchanged or altered in a number of ways.

   Different fixed costs, and the resulting levels of profitability, do not affect the oneshot Nash solution of the game, i.e., the Cournot equilibrium, but this is not to say that agents either do or will exhibit Cournot behavior under any cost conditions. Indeed, it is widely known that the Nash outcome of the stage game is not a good predictor of behavior in a repeated game. The "Folk Theorem" suggests many outcomes that Pareto-dominate the Cournot solution can be an equilibrium of the supergame [7; 10]. In theory, this is accomplished by players cooperating until cheating on an implicit agreement occurs. Following such a defection, each player moves to a punishment phase, where each receives lower payoffs for a period of time, which may be for the duration of the game.(4) It is possible in this context that defection triggers a war of attrition. Thus, an agent may depart from a cooperative strategy in order to drive the other from the market, or the punishment phase of the strategy may leave only one survivor.

2. War of Attrition Models

   Tirole [33] argues that modern analysis on wars of attrition originated in the theoretical biology literature with Maynard Smith [31] and Bishop, Cannings, and Smith [3]. The fundamental idea, beginning with Darwin [5], is that when the survival of a species is threatened, attrition leaves only the most fit, and it is the most fit that hasten the demise of the weak in order to survive. With respect to markets, this idea may have preceded Darwin's treatise. For example, in their classical works on markets, Adam Smith [30] and David Ricardo [23] noted in different contexts that low cost producers will naturally drive out high cost producers as competition fosters market efficiency. Later, Joseph Schumpeter [28] wrote that entrepreneurship would leave even the most secure monopolies vulnerable to obsolescence. In effect, no firm is safe from threatened extinction.

   Several papers provide technical models of wars of attrition, starting with Kreps and Wilson [17] and Fudenberg and Tirole [9]. In Tirole [33, 311-15, 380-84] fixed costs play a crucial role in the firm's decision to continue with the status quo or fight to the death over greater control of the market. Modeling the exit decision, Tirole shows that the higher is a firm's fixed cost, the sooner will there be a war of attrition and the more quickly a weaker firm will exit as a casualty. Relatively high fixed costs move duopolists toward war because profits are low and survival is threatened. Also because it takes less time to force a rival's exit, there are greater discounted returns for the survivor provided there is no threat of future entry.

   But wars of attrition are inherently risky ventures. The time at which one firm will exit is generally unknown because the financial reserves and resolve of the weaker firm are unknown. Market demand and future costs also may be subject to random shocks. Finally, if we consider a game theoretic setting, play could be finite with a random endpoint reflecting a number of real market risks. Such risks include the uncertain nature of the product life cycle or an unexpected innovation that suddenly reduces market size. Thus net gains from a war of attrition may plausibly be regarded as stochastic, and so risk averse agents will require a large expected premium over current returns before they instigate a war of attrition. Nevertheless as survival is threatened by increasing fixed costs, a war of attrition becomes a more likely event in an industry [33, Chapters 8 and 9].

   Wars of attrition bear a resemblance to predatory behavior.(5) Both concepts involve one firm attacking another firm to induce exit from the market. Both suggest that the period of war (or predation) be carried out in the short run. Otherwise the future gains may not be sufficient to cover the wartime losses. One important difference between predatory behavior and wars of attrition, however, is that predation by definition entails a dominant firm driving smaller firms (or entrants) from the market in order to protect or build upon market share. A war of attrition is a fight for survival that could take place between any rival firms, be they of the same or different size. Before the war begins no agent has high or above-normal profitability. It is the dismal future that prompts the war.

   It has been difficult for the theoretical literature to describe the market conditions that cause wars of attrition. Furthermore, it is not clear that such wars have been observed in naturally occurring markets [21]. Indeed there is noticeable skepticism among economists that wars of attrition or acts of predation should ever be observed among market rivals [32]. Carlton and Perloff [4] review several cases, and conclude the evidence supporting any sort of price war behavior is weak. On the existence of these wars they write [4, 407] that allegations "often reflect the complaint of one rival about another's fierce (and socially desirable) competition." The motivation for selling large quantities at low prices generally can be attributed to fiercely competitive behavior; after all, competition is a fight for survival. In uncontrolled market environments there can be many reasons for different levels of competitive behavior, and the level of competitive behavior itself can be difficult to observe and measure from field data.

   We believe the effective use of field data to study the market conditions that induce aggressive behavior on the part of rivals is hindered by a variety of factors that cannot be controlled. For just one example, shifts in underlying basic demand or cost conditions can be both deterministic and random, and so present substantial difficulties for constructing good estimators. An alternative to collecting field data is to obtain data from laboratory markets. Our laboratory markets are based on a simple design that captures the essential ingredients of an oligopoly environment; the environment is controlled. In these markets there are no shocks to the system, no vertical or horizontal influences, no escalations in cost or changes in technology, no threat of entry. By using a sufficiently simple framework, the effects resulting from a change in some preselected treatment variable across markets can be isolated. As we explain below, this allows the rigorous testing of hypotheses relating to the behavior of agents as...