Pretrial bargaining with asymmetric information: unilateral versus bilateral payoff relevance.

• Author: Farmer, Amy

1. Introduction

   Asymmetric information is a leading explanation for bargaining failure, and the role of asymmetric information has been extensively analyzed in the civil litigation literature. (1) Most of this literature concerns information that has bilateral payoff relevance in the sense that the information in question affects the expected payoff at trial of both the plaintiff and defendant. When there is bilateral payoff relevance, trials may be predicted in the equilibrium of the bargaining game, regardless of whether the informed or uninformed party makes the offer. In this article, we analyze information that has unilateral payoff relevance, meaning that it affects the expected payoff of one of the two parties to the dispute, but not the other. As an example, suppose the plaintiff has private information on her risk preferences. This affects her expected payoff at trial but not the defendant's. When there is unilateral payoff relevance, there are never inefficient trials in the equilibrium of the game where the informed party makes the offer. (2) However, there may still be costly disputes in the equilibrium of the game in which the uninformed party makes the offer.

   Examples of information with bilateral payoff relevance include information on the probability that the plaintiff will prevail at trial, and information on the amount of the judgment to be awarded at trial in the event the plaintiff is victorious. In both cases, the information clearly affects the expected payoff of both the plaintiff and defendant at trial, and these are the types of informational asymmetry considered most often in the literature. What type of information has only unilateral payoff relevance? One example, mentioned above, is information on risk preferences. Farmer and Pecorino (1994), Swanson and Mason (1998), and Heyes, Rickman, and Tzavara (2004) all examine asymmetric information on risk preferences within the context of the screening model in which the uninformed party makes the offer. (3) In each case, trials are predicted in the equilibrium of these models, as long as trials are not too costly for the participants. However, other types of information also have only unilateral .payoff relevance. A large literature on the ultimatum game has provided convincing evidence that under certain circumstances individuals will express a preference for being treated fairly. (4) This preference may be expressed specifically by the percentage of her own court costs a player is willing to concede to her opponent via his settlement offer. (5) Since this preference is not observable and presumably differs across individuals, the proposer in a screening game must decide how much of the joint surplus of settlement he will attempt to extract without knowledge of how low he can go before triggering a rejection.

   Suppose the judgment is $100,000 and the plaintiff's court costs are $30,000. A plaintiff without a taste for fairness will accept an offer of $70,000 rather than proceed to trial. A plaintiff with a taste for fairness might (as an example) accept no less than $90,000. The defendant then must choose between an offer of $90,000 and $70,000 without knowledge of whether the other party has a taste for fairness or not. The defendant will make the low offer if he believes it will be accepted with a sufficiently high probability; if the plaintiff does indeed have a taste for fairness, she will reject the low offer and a trial will result. Presumably a mechanism along these lines explains the persistence of disputes in ultimatum game experiments.

   Another example of information with unilateral payoff relevance is the degree of litigiousness, which can be modeled as differences in perceived court costs on the part of the plaintiff (Eisenberg and Farber 1997). A litigious plaintiff perceives lower trial costs than a nonlitigious plaintiff who may incur psychological or other intangible costs from pursuing trial. Since the degree of litigiousness is not directly observable, the defendant would have to choose between a low offer that only the nonlitigious would accept and a higher offer acceptable to both plaintiff types. Also note that the plaintiff's degree of litigiousness does not affect the defendant's payoff at trial.

   A fourth example concerns self-serving bias. Individuals suffering from a self-serving bias may interpret the facts of a case in a way which is favorable toward themselves. This phenomenon has been documented in the experimental literature, and an excellent survey of this literature is provided by Babcock and Lowenstein (1997). The extent of an individual's self-serving bias is not directly observable. Moreover, if the plaintiff has a self-serving bias, this affects her perceived payoff from trial but not the payoff for the defendant. Self-serving bias has been addressed in theoretical models by Farmer and Pecorino (2002), Bar-Gill (2006), and Langlais (2008). Langlais models the extent of self-serving bias as a form of asymmetric information that can lead to trials in equilibrium. As with the work on risk preferences, this is done in a model in which the uninformed player makes the offer.

   In each of the examples above, the information in question directly affects the payoff of the individual who holds the information. (6) For example, the plaintiff's risk preferences affect the plaintiff's expected payoff at trial but not the defendant's. When unilateral payoff relevance takes this form, we find that disputes can occur when the uninformed party makes the offer but not when the informed party makes the offer. When there is a two-sided informational asymmetry, where each piece of information has only unilateral payoff relevance, the solution to the game involves only screening elements. When there is bilateral payoff relevance, the corresponding solution involves both signaling and screening elements. As we will demonstrate, solving a model with a two-sided asymmetry is much easier under unilateral payoff relevance than under bilateral payoff relevance. (7) In addition, in this setting disputes may occur regardless of which party makes the offer.

   Our last example differs from those above, because it involves a situation where the defendant holds information that affects the plaintiff's expected payoff at trial but not his own. In particular, the defendant may know whether the plaintiff will incur high costs or low costs in enforcing a judgment should she prevail at trial. For example, the defendant may know how difficult it will be for the plaintiff to uncover the defendant's assets so as to force payment of the judgment. Kaplan and Sadka (2008) analyze data from Mexican labor courts and find that many plaintiff awards go uncollected because of enforcement costs. (8) This suggests that enforcement costs are both uncertain and potentially large. When the defendant has information that affects the plaintiff's payoff but not his own, we find that there will be 100% settlement regardless of who makes the offer.

   It should be clear from this discussion that there are a wide variety of circumstances in which the distinction between unilateral and bilateral payoff relevance is of importance. Furthermore, the full implications of unilateral payoff relevance are not well understood in the literature. In particular, although models have been worked out for several of the examples mentioned, these typically have the uninformed party making the offer. The models in which the informed party makes the offer have not been analyzed with one exception. In a nontechnical discussion of the model with asymmetric information on risk preferences, Daughety (2000, p. 145-6) notes that trial will not occur if the informed party makes the offer. Thus, Daughety is the first to make this point in regard to the model with asymmetric information on risk preferences. We provide a more formal analysis and extend this insight to an entire information class, that is, to the class of information with unilateral payoff relevance. In addition, we also consider informational structures, which (to our knowledge) have not been previously analyzed in a model in which there is unilateral payoff relevance. These include two-sided informational asymmetries and a model in which private information is held by one player but affects only the payoff of the other player.

2. Some Preliminaries

   In most of the literature on pretrial bargaining, private information has bilateral payoff relevance. To fully understand the implications of unilateral payoff relevance, we will cover a number of cases in what follows. Here we introduce a relatively simple but general notation that characterizes all the cases we discuss. To keep the analysis simple there will be no more than two player types for both the plaintiff and defendant. The plaintiff's expected payoff at trial is denoted [PI], and the defendant's expected cost at trial is denoted C. Note that we are defining C to be the defendant's total expected cost at trial (inclusive of the expected judgment), and not simply court costs as is often the case in this literature.

   A plaintiff may either have a high expected payoff at trial [[PI].sup.H], or a low expected payoff [[PI].sup.L] > 0. (9) These are referred to as type H and type L plaintiffs, respectively. In some of our games there will be two defendant types. Those with a high expected cost at trial [C.sup.H] will be called type H defendants, and those with a low expected cost [C.sup.L] will be referred to as type L. In the case of bilateral payoff relevance, there is a 100% correlation in player types. In other words, when the plaintiff is type H and therefore expects a high payoff at trial, this implies that the defendant is also type H and has a high expected cost at trial. Similarly, a type L plaintiff implies a type L defendant under bilateral payoff relevance. Note that a player need not know his or her own type but at a minimum will know the unconditional...