Inlern&onul Review of Law and Econotnics (1994) 14, 273-281

Pretrial Negotiations with Asymmetric Information on Risk Preferences

AMY FARMER

Department of Economics, University of Tennessee, Knoxville, Tennessee 37996

AND

PAUL PECORINO*

Department of Economics, Finance and Legal Studies, Tuscaloosa, AL 35487-0224

1. Introduction

University of Alabama,

Why would parties to a dispute fail to reach a bilateral settlement in the face of a costly trial? One possible explanation is that each party to the dispute has different expectations of the probable trial outcome. This is the approach taken by Shave11 (1982) and Hause (1989) among others. Another approach has been to assume some type of informational asymmetry, as in Bebchuk (1984) and Reinganum and Wilde (1986). In addition, Spier (1992) uses this approach to model pretrial bargaining in a multiperiod setting.’

The informational asymmetry considered here is the plaintiff’s attitude toward risk, which is unknown to the defendant.2 This distinction over the type of informational asymmetry assumed is important. In Bebchuk the asymmetry is over the probability of one side prevailing in trial, and in Spier and Reinganum and Wilde it is over the extent of injury. Shave11 (1989) shows that if private information can be credibly revealed on a voluntary basis, then no trials will occur in equilibrium. It is only when private information cannot be credibly established that trials will occur. In light of Shavell’s result, risk preferences, which are difficult to communicate credibly, represent a type of informational asymmetry that is likely to lead to trial in equilibrium.3

The trial award is uncertain, but each party knows the true distribution of outcomes. A trial may result if the defendant makes an offer that attempts to sort between risk types; that is, an offer risk-averse plaintiffs are willing to accept, but that risk-neutral plaintiffs are not. Factors that make the trial outcome more risky raise the probability

*We would like to thank Ronald Harstad and an anonymous referee for helpful comments

‘See Cooter and Rubinfeld (1989) for a survey of this literature. Curry and Pecorino (1993) use informational asymmetries to explain the use of tinal offer arbitration.

‘More generally, one might wish to consider a model with two-sided incomplete information, but the intuition developed from this simpler model would be important in interpreting the more general model.

‘In a somewhat different context, Polinsky and Rubinfeld (1991) model optimal tines for repeat offenders when there is asymmetric information about the offender’s preferences. Again, a key issue is that preferences are not directly observable.

0 1994 Butterworth-Heinemann

274 Pretrial negotiations with asymmetric inforwuztion

of a trial by increasing the gains to making offers that sort between risk types. The effect of the English rule (where the loser pays all legal costs) and the use ofcontingency fees on the incidence of trial are discussed in the context of this result. The model is presented in Section 2, while some policy implications are explored in Section 3. These include the effects of the English rule and contingency fees on settlement rates. In Section 4, the model is extended by considering multiple risk types and multiple bargaining periods. Section 5 concludes.

2. The Model

Assume the defendant (perhaps a large corporation) is risk neutral and that this is common knowledge. The plaintiff may be either risk neutral or risk averse (initially only two types are considered). The attitude toward risk of a particular plaintiff is known by the plaintiff, but not by the defendant. Consider a single bargaining period in which the defendant makes a take-it-or-leave-it offer. The outcome of the trial is uncertain, but the distrib~ltion of outcomes is common knowledge. Since risk-averse plaintiffs are willing to settle for less than the expected trial award, there exists a contract zone between a risk-neutral defendant and a risk-averse plaintiff in which both prefer to settle rather than proceed to trial. If the defendant knows the plaintiff’s attitude toward risk, she will make an offer that extracts the plaintiff’s entire willingness to pay to avoid trial. When the plaintiff’s attitude toward risk is unknown, the defen- dant must weigh the opportunity to extract surplus from a risk-averse plaintiff against the cost of a trial when an aggressive offer is rejected by a risk-neutral plaintiff.

In the context of this model, the assumption that the defendant has the power to make the single offer is an important one. Were the plaintiff given the opportunity to make a take-it-or-leave-it offer, he would extract from the defendant the expected trial outcome plus the defendant’s trial costs. No cases would proceed to trial. Viewed more broadly, however, this assumption is not crucial. If incomplete information is two sided then it should matter less which side is given the power to make the single offer. In a more realistic bargaining setup, the defendant could expect to extract only some of the plaintiff’s willingness to pay to avoid trial.

The specification of the game is as follows:

1. Nature chooses the risk preferences of the plaintiff. 2. The defendant makes an offer x. 3. The plaintiff either accepts or rejects the offer.

a) If the offer is accepted, the plaintiff enjoys utility U(x). b) If the offer is rejected, the case proceeds to trial where the award 0 is deter-

mined. The plaintiff enjoys utility U(fJ - CP), where C, are the plaintiff’s costs of proceeding to trial.

The trial outcome 0 is distributed by the nondegenerate density function g(Q) with a mean 3. Let 2 be the payment received by the plaintiff net of any legal costs so that the plaintiff’s utility may be written as U(Z). If the defendant’s offer is accepted, 2 = x, and if it is refused, Z = 0 - C,. Let x” be the certainty equivalent of trial; that is, the pretrial settlement offer that leaves a risk-averse plaintiff indifferent between settling and proceeding to trial. Then xc6 satisfies equation (1):

By risk aversion, xc’ must satisfy equation (2):

A. FARMER AND I? PECORINO 275

xc* < s - c P’ (2)

Risk-neutral plaintiffs want to maximize their expected net payment and thus will not accept an offer x less than 6 - C,.

Each defendant knows the two types of utility functions that plaintiffs may have and the frequency with which each type is encountered. They do not know the risk preferences of the particular plaintiff to whom they make the settlement offer. Defendants would like to minimize their expected payout and in doing so must decide between making an offer all plaintiffs will accept, x = 6 - C,, or an offer only the risk averse will accept, x = Ye.4 If they offer x” they must take all risk-neutral plaintiffs to court, paying on average 6 + CD, where CD is the defendant’s cost of going to trial. Normalize the number of plaintiffs to 1 and let a denote the percentage who are risk averse. The defendant’s offer will be xcc if and only if equation (3) holds:

cLX[++(l -cX)(e+c,)<G-c,. (3)

Equation (3) may be rewritten as (3a):

cx((G - Cp) - .X?) > (1 - a)(& + CJ. (3a)

The defendant offers xcE when the benefit to sorting, (8 - CP) - x” weighted by (Y, the percentage of risk-averse plaintiffs, is greater than the cost of a trial, Cn + C,, times 1 - a, the percentage of risk-neutral plaintiffs (and the probability of a trial if they sort). Based on the figures cited in Spier (1992), the plaintiff’s trial costs are about 30% of the average award and the defendant’s costs are about 20%, while 90% of cases that are filed settle out of court. Normalizing 3, the expected value of trial, to 1 and letting C, = .3, CD = .2, and OL = .9, the defendant would need to extract 5.5% or more of the expected award ($ - C, - xcL = .055) from risk-averse defendants to justify a sorting strategy.

For risk-averse plaintiffs, the difference between the expected trial award and the certainty equivalent of trial, (G - CP) - xce, is increasing in the riskiness of the trial.5 If trial outcomes are more risky, perhaps due to “capricious” jury awards, the defen- dant’s benefit to sorting is greater, and equation (3) will hold in a larger number of cases. Conversely, policies that reduce the uncertainty of awards could reduce the number of trials. Though the distribution of awards in a particular case is assumed to be common knowledge, there is no reason why it would not vary across case types (auto accident, product liability, etc.) as well as within types due to specific circumstances. In this context it makes sense to consider a generalized version of equation (3) that may hold in some instances but not others.

It may seem counterintuitive that increases in the riskiness of the outcome make trials more likely, because risk-averse plaintiffs will then be willing to pay more to avoid trial. Note, however, that risk-averse plaintiffs always settle before trial. The issue is whether the defendant will make “hard” offers that only the risk averse will accept, or “soft” offers that both risk-averse and risk-neutral plaintiffs will accept. The

‘Note, it is not optimal for the defendant to make an offer between XT and e - C, as this will result in higher payments to the risk averse, but will not prevent any risk neutrals from proceeding to trial.

‘An increase in riskiness in the Rothschild and Stiglitz (1970) sense of a mean preserving spread is a sufficient, but not necessary, condition for this risk premium to increase. See Laffont (1988: 24.30) for a discussion of mean preserving spreads.

276 Pretrial negotiations with asymmetric informntion

more that risk-averse plaintiffs are willing to pay to avoid trial, the greater the number of cases in which the “hard” offer strategy is attractive.

3. Policy Implications

3. I Contingency Fees

Under a contingency fee, the plaintiff’s lawyer fees are a fixed percentage, y, of the trial award. In our model, the effect of such a fee on the incidence of trial depends upon how the fee is administered. Initially imagine a contingency fee in which the percentage paid to the lawyer rises the further a case proceeds so as to compensate the lawyer for the greater costs. ’ To match the assumptions of our model where all costs are incurred at trial, assume that y = 0 if the case settles out of court and that if a trial occurs, y is set so that ye = C,. As a result, the expected payment to be received by the lawyer is the same as under a flat fee. While the average fee is the same, the fee paid in any particular case depends on the realization of 9 (i.e., the fee in case j is $I,).

Under these assumptions, the sorting condition in (3a) is still valid. The certainty equivalent of a trial can be computed from (1) except that U[(l - y) 61 replaces LJ(0 - Cr) in the integrand. The systematic fashion in which the lawyer’s fee varies with the trial award makes the net award to the plaintiff less risky in that the net payment for every realization of 9 is pushed closer to the mean. Thus, a fixed fee constitutes a mean preserving spread relative to a contingency fee.’ The introduction of a contin- gency fee reduces the premium that risk-averse plaintiffs are willing to pay to avoid trial. Therefore, equation (3a) is less likely to hold and fewer trials will result.”

If the value of y is the same whether or not a trial results and is set so that ye = C, (raising the total expected lawyer fee), the risk-reducing feature of contingency fees will still be present, but there will be other factors tha_t will tend to increase the incidence of trial. Risk-neutral plaintiffs expect to receive e( 1 - y) if they proceed to trial and, x( 1 - y) if they accept an offer x made prior to the trial. Thus, they will accept no less than e prior to trial. The certainty equivalent of trial is computed as in the preceding paragraph, and risk-averse plaintiffs will accept no less than x”l(1 - y) prior to trial. As a result of these changes, the sorting condition in (3a) is replaced

by (3b).

cY(G - c, - P) > (1 - y)( 1 - U)CD f3b)

Relative to (3a), the left-hand side of this equation is smaller because trials are less risky, but the right-hand side is also smaller, and this factor makes it more likely that the condition will be satisfied. Under the flat fee, the defendant attempts to extract the plaintiff’s trial cost by her settlement offer. If the case proceeds to trial, this surplus

“The use of such a sliding scale is cited in Miller (1987: 201). Al’ so see MacKinnon (1964: 184-185).

‘The trial without contingency fees is more risky than the trial with contingency fees in the Kothschild and Stiglitz

(I 970) sense of a mean preserving spread.

“This ignores possibie agency problems. For example, if the client is risk averse and the lawyer is risk neutral, the lawyer may push for the larger, risk-neutral settlement. Miller (1987) discusses the opposite problem. Under a

contingency fee, lawyers may have incentive to settle cases too early (from the piaintiB’s perspective) if they incur

costs from proceeding further with the case.

A. FARMER AND l? PECORINO 277

is lost, and the defendant takes this into account in deciding whether or not to sort. Under the current assumptions, the plaintiff is committed to paying his lawyer whether or not there is a trial, so these costs cannot be extracted by the defendant’s offer. To the defendant, the plaintiff’s trial costs no longer represent part of the cost of having a hard offer refused and proceeding to trial. Thus, sorting becomes a more attractive strategy. The overall effect of contingency fees on the incidence of trial is ambiguous in this case.

An important issue not addressed here is why contingency fee contracts arise in equilibrium. For example, in our model with no informational asymmetries between the lawyer and client, a risk-averse client would want to sell a 100% stake in the case to a risk-neutral lawyer. In this case, the sorting motive would disappear entirely, and no cases would end in trial.Y

The issue of optimal contingency fee arrangements is examined in Rubinfeld and Scotchmer (1993), where contingency fee contracts can arise as a result of informational asymmetries between the lawyer and her client. Contingency fee contracts can be used by the client to signal the quality of his case, and by the lawyer to signal her ability. Generally, the lawyer’s contingency percentage is less than 100% under these contracts. It might be possible in some larger model to incorporate both the informa- tional asymmetries that exist between the lawyer and her client as well as those between the plaintiff and the defendant (i.e., attitude toward risk among others).

3.2 The EngZish Rule

The English rule requires that the loser pay all legal costs. For the plaintiff, a move to the English rule will affect both the mean net payment received and the uncertainty associated with that payment. We will discuss each effect separately, starting with the effect on the riskiness of trial, holding the mean net payment constant. Consider a distribution of trial awards such that there is a discrete probability that the jury finds for the defendant (i.e., 0 = 0). When each side pays its own legal costs, the plaintiff’s net payoff is -C, when 0 = 0 and 8 - C, when 0 > 0. Under the English rule, these payoffs change to - (C, + C,J when 0 = 0 and 0 when 0 > 0.

In general it is not possible to rank the riskiness of the two resulting distributions of net payments in the sense of a mean preserving spread (this criterion gives an incomplete ranking). This is true because, even if both the distribution of 8 and (as is unlikely) the mean payment are unchanged, there may be positive awards below the mean that are pushed closer to the mean under the English rule.‘” Thus, it is not possible to make a completely general statement about the effect of the English rule on the riskiness of trial.

Because the English rule considerably lowers the plaintiff’s worst outcome (B = 0) and considerabiy raises all other outcomes (8 > 0), there seems some presumption that it would raise the risk premium plaintiffs will pay to avoid trial. If this were the case, trials would become more likely (holding the mean net payment constant). Only if the English rule reduces the risk premium plaintiffs will pay to avoid trial will it result in fewer trials. If the intuition behind the use of the English rule is that it will

“This was p&ted out to us by an ~~~~y~*~s referee.

‘There do, ofwurse, exist distributions for which thr chartge to the English rule would constitute a tltean presew- ing spread.

278 Pretrial negotiations with asymmetric information

make trials less likely by making the outcomes more risky, the analysis here suggests that this intuition is wrong.

Because use of the English rule will change the mean net payment to the plaintiff, the mix of cases that reach the litigate/settle stage will also change. As discussed in Snyder and Hughes (1990), the English rule tends to encourage low stakes cases with a high probability of success (i.e., some positive award) and to discourage high stakes cases with a low probability of success. ” Since the former are less risky than the latter, our model suggests that the change in the mix of cases reaching the litigate/settle stage should favor settlement. Since this runs counter to the effect of riskier trials, the overall effect of the English rule on the incidence of trial is ambiguous.

These inferences from the model seem to correspond to the empirical findings of Snyder and Hughes (1990), who examine the effect of the English rule in Florida in the early 1980s. They find at the litigate/settle stage that a given claim is more likely to be litigated under the English rule but that more cases are dropped. In addition, the change in the composition of cases that reach the litigate/settle stage leads to fewer trials. This results as cases most likely to be litigated were more prevalent among the cases that were dropped. They estimate that the overall effect is a lower total incidence of trial.

In previous theoretical work, the effect of the English rule on the incidence of trial has varied considerably from model to model. Reinganum and Wilde (19%) find that when there is only uncertainty over the extent of irtjury, the probability of a trial is unaffected by a move to the English rule. Bebchuk (1984) finds that the English rule increases the probability of a trial in a model where there is asymmetric information on the probability the plaintiff will prevail. Bebchuk suggests that this result might be overturned by the introduction of risk aversion, but our analysis indicates that this depends on the resulting changes in the riskiness of trial and mean net payment.

In Shave11 (1982), where the trial occurs due to optimism over the probability of prevailing at the trial, the English rule raises the probability of trial. In a similar model, but with endogenous litigation costs, Hause (1989) shows that the English rule increases the likelihood of settlement, but also increases the expenditure of resources on those cases that go to trialI

4. Extensions of the Model

The defendant’s problem is similar if additional risk types are added. Let there be three types of plaintiffs: risk neutral, and ones exhibiting greater and lesser degrees of risk aversion. Let U’ (Z) be the utility function of those exhibiting a lesser degree of risk aversion, while Uz (Z) is the utility function of those displaying a greater degree of risk aversion. Let the total risk averse be CY, with IX’ of type 1 and a’ of type 2 (or = a’ + cr*). The certainty equivalents of trial for types 1 and 2 are determined from equation (2) and denoted xi and x2, where x2 < x’. The defendant must choose among offering xi, x2, and e - C,. The benefit of offering xz is the lower settlement accepted by the very risk averse, but the cost is additional cases going to trial and a lost

“Also, see Katz (1987) on the effects of the English rule

“Snyder and Hughes (1990) find an increase in expenditures at trial

A. FAKMERAND l? PECORINO 279

opportunity to extract surplus from less risk-averse plaintiffs, who proceed to trial. The defendant will offer x2 if (4a-b) hold.

a*~* + (1 - a*)(3 + C,) < (cx’ + a2)x’ + (1 - (Y’ - a’)(6 + C,) (a) (4) c&J + (1 - fX’)(G + C,) < e - c, (b)

Condition (4a) ensures that offering xp is preferable to offering x1 and (4b) ensures that offering x2 is preferable to offering 6 - Cp and settling with everyone. If (4a) does not hold and (3a) does (for x = x’ and a = a’ + cx’), the-defendant offers x’ and only the risk neutral proceed to trial. Otherwise she offers 0 - C, and no one proceeds to trial. The earlier result that only risk-neutral plaintiffs proceed to trial does not hold in general, but plaintiffs who reach trial will be less risk averse than those who settle.

4.2 Multiple Pretrial Negotiating Periods

In Farmer and Pecorino (1993) the model is extended to consider multiple pretrial negotiating periods, the results of which are summarized here.‘” In this extension it is assumed that some information about the likely trial outcome is revealed at the end of each pretrial bargaining period. This new information could represent new evidence, a judge’s ruling on admissibility of evidence, or a decision in a similar case. During each period, the defendant makes an offer. If the offer is accepted, the game ends, and if it is rejected the game proceeds to the next period. Rejection in the final period leads to a trial.

The surplus to be extracted from risk-averse plaintiffs is largest in the initial bar- gaining period, prior to the resolution of any of the uncertainty associated with the case. However, the need to maintain credible threats (i.e., subgame perfection) puts constraints on the defendant’s ability to settle with all risk-averse plaintiffs in period 1. Consider two bargaining periods and two types of plaintiffs: risk neutral and risk averse. The defendant would like to settle with risk-averse plaintiffs in period 1, while maintaining a credible threat of a hard offer in period 2. This hard offer would force risk-averse plaintiffs to pay (in the form of a lower settlement) for the uncertainties associated with the trial itself.

If all risk-averse plaintiffs settle in period 1, then the threat of a hard offer in period 2 is not credible. Risk-averse plaintiffs, anticipating a soft offer in the second period, will demand more to settle in period 1. If it is desirable to maintain a credible threat of a hard offer in period 2 (and this is not certain), equilibrium will generally require a double mixed strategy. Some risk-averse plaintiffs will settle in period 1 and others in period 2. The defendant will use a mixed strategy in deciding whether or not to make a hard offer in period 2.

Trials result when a hard period 2 offer is rejected by a risk-neutral plaintiff. If trial costs are large, substantial numbers of risk-averse plaintiffs must remain to be sorted in period 2 for a hard offer to be an optimal strategy. As a result, in a model with many bargaining periods where some trials occur, there should be a spike in settlements in the final period for the same reasons as in Spier (1992).

Since it is risky for plaintiffs to wait until later periods to settle (they may receive bad news about the likely trial outcome in earlier periods), the expected offer will

‘“Farmer and Pecorino (1993) is the working paper version of this article.

280 Pretrial negotiations with asymmetric information

rise over time.14 If plaintiffs can exhibit many degrees of risk aversion, then the most risk averse will tend to settle earliest in the process. The existence of many bargaining periods increases the ability of the defendant to make offers that discriminate among risk types. This would further reinforce the tendency of the expected settlement to rise over time.

5. Conclusion

Risk preference is not a directly observable characteristic, nor is it likely to be revealed during pretrial discovery. Trials may result if risk-neutral defendants make offers that sort between risk-neutral and risk-averse plaintiffs. Policies that raise the riskiness of the trial outcome can increase the frequency of trial by increasing the incentive to sort between risk types. The effects of the English rule and contingency fees on the incidence of trial have been analyzed in the context of this result. An empirical implication of the model is that types of cases (perhaps malpractice versus automobile accidents) in which the trial outcome is more risky, should be taken to trial more often. Similarly, a state whose laws lead to a greater uncertainty in trial awards should have a higher percentage of cases that go to trial.

It is likely that considerations other than asymmetric information with respect to risk preference are important in explaining settlement patterns and the probability of trial. It is quite possible, however, that this particular asymmetry will play an important role in any more complete story. Regardless of what other factors are considered, attitude toward risk is inherently difficult to observe, thereby providing a positive incentive to make offers that sort among risk types.

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