The FINAL VERSION of this paper will be published in the November, 1994 Santa Clara University Law Review. .

Copyright 1994-95 by the Santa Clara Law Review

[ Intro Page | Table of Contents | Sec. 1 | Sec. 2 | Sec. 3 | Sec. 4 | Sec. 5 | Sec. 6 | Sec. 7 | Law & Econ Page ]

[ Go to Previous Section, Section II | Go to Next Section, Section IV ]

III. Deterrence

This section examines the deterrent effects of the different rules. The first subsection examines the situation where the defendants have symmetric information and thus symmetric beliefs. To begin with, the case where defendants have the same likelihood of loss at trial to the plaintiff and are equally liable for the damage under the contribution rules will be modeled. Then situations where the defendants are not equally liable for damages or do not have the same likelihood of loss at trial are examined. The paper demonstrates that if the defendants have symmetric information, some defendants may face less deterrence under the no contribution rule than under the contribution rules, but at least one defendant will face greater deterrence under the no contribution rule.

The article then analyzes the case where defendants have asymmetric information and different beliefs. The article shows that, where defendants have asymmetric information, neither the no contribution rule nor the contribution rules always lead to more deterrence. However, even where all defendants face less deterrence under the no contribution rule than under the contribution rules, the no contribution rule always leads the plaintiff to expect and receive a higher damage award.

For these two subsections, the focus will be on the deterrence caused by the expected damage payments of the defendants to the plaintiff and not on the deterrence caused by litigation or risk costs.[42] We will assume that a defendant will prefer to settle if its expected settlement payment is less than or equal to its expected loss at trial.

Next the article analyzes defendants' incentives to give information and the plaintiff's incentives to accept information in lieu of monetary compensation. Defendants will provide information under either the no contribution rule or the contribution with claim reduction rule, as both rules have a settlement contribution bar that keeps later trial-losing defendants from obtaining contribution from prior-settling defendants. However, under the contribution with claim reduction rule, the plaintiff has a disincentive to cheaply settle with a defendant who is liable for a high proportion of the damage.

We then examine the deterrent effects caused by risk costs and litigation costs. Finally, the effect of decisionmaker insulation on deterrence will be examined.

A. Symmetric Information

In this subsection, it is assumed that the defendants have symmetric information, and thus symmetric beliefs.[43] Defendants have symmetric beliefs of each defendant's probability of loss to the plaintiff and each defendant's allocation of liability for damages under the contribution rules.[44] It is also assumed that each defendant believes ex ante the conspiracy that the plaintiff will share its beliefs if detection of the conspiracy occurs.[45] What is important with regard to deterrence is the ex ante conspiracy belief of a defendant regarding its expected damages.

This subsection begins with an analysis of cases where defendants are identical. This restriction is then lifted and cases where defendants are liable for different proportions of the damage or face different probabilities of losing at trial are analyzed.

1. Identical Defendants@

Defendants are identical, for purposes of the model, when they have caused the same proportion of damages under the contribution rules, have the same probability of losing at trial to the plaintiff and have the same information and beliefs. The case of identical defendants with symmetric information was thoroughly examined by Easterbrook, Landes and Posner and will be used to demonstrate the model.[46] The following example illustrates how the rules differ in the bargaining process.[47]

Suppose there are two defendants which have each contributed equally to the damage of the plaintiff, and suppose that the probability of each defendant losing at trial is 0.5 and the total damage amount is $100.

Under both of the contribution rules, each defendant will face an expected liability payment of $25, and the plaintiff will receive an expected total damage award of $50.[48] First, suppose that the plaintiff settles with neither defendant and sues only defendant A. In that case, defendant A will have a 50% chance of losing at trial to the plaintiff and paying damages of $100. But if defendant A does pay $100 in damages to the plaintiff, defendant A will be able to get $50 of that back by suing defendant B for contribution. Thus, defendant A will have a 50% chance of paying a net of $50 in damages for an expected liability payment of $25. Defendant B will also have an expected liability of payment of $25, as it will have to pay $50 in contribution to defendant A whenever defendant A loses at trial to the plaintiff, which will occur 50% of the time.

Under the contribution with settlement reduction rule, a defendant has a disincentive to settle individually, as a later trial-losing defendant can obtain contribution from the prior-settling defendants.[49] Thus, unless there is a group or contingent settlement, there will be a trial and the result will be as above.[50]

Under the contribution with claim reduction rule, a defendant will not have a disincentive to settle first. Suppose that the plaintiff settles with defendant A for some amount before suing defendant B. The plaintiff can then sue defendant B for $50, equal to the full damages of $100 less defendant A's attributable share of $50. Since defendant B will have a 50% chance of losing at trial to the plaintiff, defendant B will have an expected damage payment of $25. And because the plaintiff can obtain a damage payment of $50 if it sues one (or both) of the defendants before settling with either, the plaintiff will want to settle with defendant A for at least $25. Defendant A will not be willing to settle for more than $25, its expected damages at trial, and thus the initial settlement between the plaintiff and defendant A will also be for $25.[51] The plaintiff's total expected damage award from the settlements will be $50. Thus, under the contribution with claim reduction rule, whether or not a trial occurs, each defendant will have expected damages of $25.

Under the no contribution rule, the plaintiff can obtain a higher aggregate damage award through settlements than by taking the defendants to trial jointly.[52] The plaintiff can play the two defendants against each other in settlement negotiations and thus the plaintiff will be able to receive a higher expected payment than under the contribution rules.

To see how the plaintiff is able to do this, consider the following scenario. Suppose that the plaintiff is considering settling with defendant A for $25, and then suing defendant B for the remainder of its damages. If the plaintiff settles with defendant A for $25, then the plaintiff can sue defendant B for $75, equaling the total damages of $100, less defendant A's settlement of $25. Since defendant B has a probability of 0.5 of losing at trial to the plaintiff, defendant B will face an expected loss of $37.50.[53] Defendant B will be better off going to the plaintiff and offering to settle for more than defendant A's offer of $25 (before the plaintiff finalizes the settlement with the defendant A). Suppose defendant B offers the plaintiff $30, then the plaintiff will prefer defendant B's offer to defendant A's offer of $25. But if the plaintiff settles with defendant B for $30, then defendant A will face an expected loss of $35.[54] Thus, defendant A would be well-advised to make an offer above $30.

This "bidding war" will continue to spiral upwards until an equilibrium is reached where a defendant's offer to settle first is equal to its expected loss if it does not settle first. In this case, the equilibrium settlement offer will be $33.33, where the first settlement is equal to the expected loss at trial or the second settlement.[55]

It is the defendant's preference of settlement over litigation that causes the upward spiraling of the settlement offers. For example, let c be the cost of trial for a defendant. Both defendants would be better off if neither settled and thus each faced a 50% chance of being taken to trial, giving each an expected liability of $25.[56] But since each defendant will prefer settlement over litigation, a prisoners' dilemma type situation exists. Each defendant will offer a settlement that is equal to its expected liability should it be taken to trial by the plaintiff.

Unless the defendants act in concert during their negotiations, the plaintiff will be able to use the defendants' preference for settlement over litigation to create a wedge that induces each defendant to settle for the equilibrium amount of $33.33.[57]

Since, under the no contribution rule, each defendant has an expected payment of $33.33 while under the contribution rules each defendant has an expected payment of only $25, the deterrence faced by the defendants will be greater under the no contribution rule.[58] A comparison of the rules in this example gives us the following:

Thus, for the case of identical defendants with symmetric information, the no contribution rule leads to increased deterrence and a higher expected reward for the plaintiff.[59]

2. Dissimilar Defendants@

This subsection examines two ways defendants can be different in the model. First, the defendants may be liable for different proportions of the plaintiff's damage. Second, the defendants may have different probabilities of losing to the plaintiff at trial. These differences will be examined separately below. Given that the parties have symmetric information, even if the defendants are different, the no contribution rule, as compared with the contribution rules, will lead to an increased expected damage payment for at least one defendant and a higher aggregate expected damage award for the plaintiff. We now examine the two ways defendants can differ in the model.

a. Different Liability Responsibility@

First we examine the case where the defendants cause different proportions of the damage. Under the contribution rules, if liability is allocated by comparative fault, then the defendants may be liable for different proportions of the damage.[60] The underlying assumption remains: each defendant has the same probability of losing at trial; and the defendants have symmetric information that leads them to the same beliefs of these probabilities and each defendant's proportion of liability.

Under the no contribution rule, liability is not allocated. The plaintiff can seek the entire amount of damages from any defendant, regardless of the proportion of damage that defendant caused. Under the contribution rules, the expected damage payment faced by each defendant is dependent on the allocation of liability for the damages among the defendants. If liability is allocated by comparative fault, a defendant that has caused more damage will have a higher expected damage payment than a defendant who has caused less damage. Under the contribution rules, the expected damage payment of each defendant is equal to the probability that the plaintiff will win at trial multiplied by the amount of damage for which the defendant is liable.

Since, under the no contribution rule, the expected damage payment of a defendant is independent of the proportion of damages attributable to the defendant, while under the contribution rules the expected damage payment of a defendant is directly proportional to the damages attributable to the defendant, it should not be surprising that those defendants causing a high proportion of damage may pay less under the no contribution rule than under the contribution rules.[61] The total damage award received by the plaintiff where defendants have caused different proportions of the damage will be the same as where each defendant caused the same share of the damage for both the no contribution rule and contribution rules. Only the division of damages among the defendants under the contribution rules changes. Slightly modifying the numerical example of the previous section, by changing the amount of the damage attributable to each defendant, shows the effects of the defendants being liable for different shares of the damages under the contribution rules.

Suppose two defendants each have a probability of losing to the plaintiff at trial of 0.5, total damages are $100, defendant A is liable for 90% of the damages and defendant B is liable for 10% of the damages. Under the no contribution rule, each defendant has expected damages of $33.33, and the total expected damage award to the plaintiff will be $66.66.[62] Even though the defendants have caused greatly different amounts of damage, the result is the same as where both defendants had caused an equal proportion of the damage. This is because under the no contribution rule each defendant's expected damage payment is a function of the total damages caused to the plaintiff, not a defendant's attributable share of the damages.

Under the contribution rules, a defendant's expected damage payment is equal to the probability of losing at trial multiplied by the damages attributable to the defendant. Thus, defendant A will have expected damages of $45,[63] and defendant B will have expected damages of $5.[64] The total expected damage award to the plaintiff is equal to the sum of the defendants' expected damage payments, and is thus $50.[65] Under the contribution rules, the expected damage payments are a function of the amount of damage caused by each defendant, and, therefore, individual damage payments are different than those where each defendant causes an equal amount of the damage. However, the total damage payment of $50 remains the same.

In this example, the no contribution rule, as compared to the contribution rules, will lead to less deterrence for defendant A, given its expected damages ($33.33 vs. $45), while defendant B will face more deterrence under the no contribution rule given its expected damages ($33.33 vs. $5). The total expected damages awarded to the plaintiff will be greater under the no contribution rule than under the contribution rules ($66.66 vs. $50), just as in the example of the previous section where defendants caused an equal proportion of damage. A comparison of the rules in this example gives us the following:

Yet, just because the defendant causing more damage pays the same amount as the defendant causing less damage under the no contribution rule, it does not follow that the former defendant is always paying less under the no contribution rule than under the contribution rules. We can show this by modifying the example above such that defendant A is liable for 60% of the damages, while defendant B is liable for 40% of the damages. Defendant A and defendant B will, again, both have expected damage payments of $33.33 under the no contribution rule. Under the contribution rules, defendant A will have an expected damage payment of $30,[66] while defendant B will have an expected damage payment of $20.[67] Under the no contribution rule, defendant A has the same expected damage payment, of $33.33, as defendant B, but defendant A still has a higher expected damage payment under the no contribution rule than under the contribution rules. A comparison of the rules in this example gives us the following:

When parties have symmetric information, there are two separate effects of the no contribution rule. First, the proportion of damages paid by any particular defendant is independent of the damages caused by that defendant. Thus, the no contribution rule may lessen the expected damage payment of a defendant that causes a high proportion of the damages by shifting some of the liability to other defendants. This was shown in the first example in this section. Second, there are higher aggregate damages paid by all of the defendants because of the whipsaw bargaining under the no contribution rule. As shown in the second example, it is possible that the increased penalty paid by all defendants outweighs the shifting effect of who pays under the contribution rules. Thus, all defendants may pay more under the no contribution rule than under the contribution rules, even though some defendants have higher expected damages than others under the contribution rules.

Although the no contribution rule will always lead to an increased expected damage payment for the low damage causing defendants, it is not true that the high damage causing defendants will always face less deterrence. But the higher the proportion of damage a defendant has caused, the more likely it will have a smaller expected damage payment under the no contribution rule than under the contribution rules.

b. Different Probabilities of Loss at Trial@

We will now examine the case where the defendants have different probabilities of loss at trial. For this subsection, we will assume that each defendant has caused the same proportion of damages and that the defendants have symmetric information that leads them to the same beliefs of these probabilities and each defendant's proportion of liability.

Suppose there are two defendants that are equally liable for the plaintiff's total damages of $100. Assume the probability of defendant A losing at trial to the plaintiff is 0.2, and the probability of defendant B losing at trial to the plaintiff is 0.6. Under the no contribution rule, defendant A will have expected damages of $9.09, and defendant B will have expected damages of $54.55.[68] The total damage award to the plaintiff will be $63.64.[69] Under the contribution rules, defendant A will have expected damages of $30,[70] and defendant B will also have expected damages of $30.[71] The total damage award to the plaintiff will be $60.[72]

In this example, the no contribution rule, as compared with the contribution rules, will lead to less deterrence for defendant A as its expected damages will be less under the no contribution rule than under the contribution rules ($9.09 vs. $30). Likewise, the no contribution rule will lead to more deterrence for defendant B as its expected damages will be more under the no contribution rule than under the contribution rules ($54.55 vs. $30). The total expected damages awarded to the plaintiff will be greater under the no contribution rule than under the contribution rules ($63.64 vs. $60). A comparison of the rules in this example gives us the following:

Thus, where defendants have symmetric information, for some defendants the no contribution rule may lead to less deterrence than the contribution rules. However, it should be noted that for at least one defendant the deterrence will be greater under the no contribution rule. We now examine defendants having asymmetric information and asymmetric beliefs, where the variety of possible outcomes is greater.

B. Asymmetric Information

In the real world, individuals and firms often have different information that can lead to different beliefs.[73] Thus, examining cases where asymmetric information exists among the actors is a necessary addition to the model. This subsection will show that asymmetric information may lead to less deterrence for all of the defendants under the no contribution rule as compared with contribution rule in some informational settings.[74]

To see how asymmetric information can affect deterrence, and why the symmetric information model is unsatisfactory in many situations, we reexamine an example used by Professors Easterbrook, Landes and Posner.[75]

Professors Easterbrook, Landes and Posner set up their example as follows. Suppose that three firms, firm A, firm B and firm C are considering a plan to fix prices that will raise the price of a good, giving the firms a total profit of one billion dollars. Assume that firm A, firm B and firm C have 50%, 30% and 20% of the market respectively, and that profits from the conspiracy will be split according to market share. If detected, the conspiracy will have to pay total antitrust damages of three billion dollars.[76] Further, assume that if there is a lawsuit, the consumers will have a 50% chance of prevailing at trial. Finally, suppose that firm A and firm B believe that if there is a lawsuit, consumers will sue firm C for the entire amount.

Given these assumptions, we must now determine whether a conspiracy will take place. Professors Easterbrook, Landes and Posner assert that a conspiracy will not take place because firm C will never enter into the conspiracy as its expected profit of $200 million is less than its expected liability of $1.5 billion.[77]

But, Professors Easterbrook, Landes and Posner have assumed that firm C also believes that the consumers will sue only firm C for their damages.[78] Firm C, however, could have different beliefs than firms A and B. Suppose firm C expects the consumers to sue only firm A for all of their damages, in which case firm C will face $0 in expected liability, and will gladly join the price-fixing conspiracy with firms A and B. Just because firms A and B believe that firm C faces a high risk of liability in damages, this does not necessarily imply that firm C will also believe that it faces the same high risk of liability. It is firm C's belief about its liability (not firm A's or firm B's beliefs) that is critical to firm C when it decides whether to enter into a conspiracy.

Of course, if firm C believes that the consumers will sue only firm A, while firm A and firm B believe the consumers will sue only firm C, then the firms disagree as to whom the consumers will sue. But the firms can still enter into a price-fixing conspiracy while disagreeing as to whom the consumers will sue. In a price-fixing conspiracy, it is only necessary that the firms agree on the price.

When asymmetric information is added to the model, one can see that it is possible for the no contribution rule to lead to less deterrence for all defendants than either of the contribution rules. It is quite possible that different parties could enter into a conspiracy under the no contribution rule with a plan to settle quickly and cheaply with the plaintiff should the conspiracy be detected. Thus, the agreeing parties would face little in the way of deterrence and expect the other party to be sued for the larger proportion of the damages by the plaintiff. Of course, if each party believes it will be sued by consumers for all of the damages, then they could all face more deterrence under the no contribution rule than under the contribution rules. The point is that neither the no contribution, nor the contribution rules leads to more deterrence under all information scenarios. Although not using an economic model, Judge Hanson, in his dissent in Professional Beauty Supply, Inc. v. National Beauty Supply, Inc.,[79] came to the same conclusion regarding the ambiguous nature of deterrence provided by the different rules when he stated:

[80]

In the model, asymmetric information will be reflected by allowing the defendants to have different beliefs about either the proportion of damages that each defendant has caused or the probabilities that each defendant will lose at trial. The defendants' beliefs about these two factors will affect the defendants' beliefs of their expected liabilities if the conspiracy is detected.

Defendants may also have asymmetric information of the probability of detection, the conspirators' relationships with the potential plaintiff, the total amount of damage caused and many other factors. In addition, the collecting and hiding of information can lead to asymmetric information and asymmetric beliefs among defendants.[81]

In the section above, it was shown that given symmetric information, and thus symmetric beliefs, it is possible that the expected damage payment and deterrence of a particular defendant can be less under the no contribution rule than under the contribution rules.[82] Now, if each defendant holds the belief that it will be held responsible for relatively little, then all defendants will be more likely to enter into a conspiracy under the no contribution rule than under the contribution rules. That the defendants have different information may lead them to divergent beliefs and, in turn, diminished deterrence. Modifying the symmetric information numerical examples will show that neither the no contribution rule nor the contribution rules always leads to more deterrence.

1. Different Beliefs of Liability Responsibility

It could be the case that each defendant believes that it is liable for a small portion of the damage under the contribution rules.[83] In such a case, the conspiracy will be more likely to take place under the contribution rules than under the no contribution rule.[84] For example, suppose each defendant believes that it is liable for 10% of the damage and the other defendant is liable for 90% of the damage. Under the no contribution rule, each defendant will have expected damages of $33.33.[85] Under the contribution rules, each defendant will have expected damages of $5,[86] while each defendant will believe that the other defendant will have expected damages of $45.[87] However, it is the defendant's own beliefs, not those of another defendant, that determine deterrence. Thus, each defendant will face less deterrence under the contribution rules than under the no contribution rule. A comparison of the rules in this example gives us the following:

Of course, if each defendant believes it has caused most of the damages, then the defendants will face more deterrence under the contribution rules than under the no contribution rule. For example, suppose each defendant believes that it will be liable for 90% of the damages under the contribution rules. As the no contribution rule reaches the same outcome regardless of the allocation of damages, each defendant will again face expected damages of $33.33.[88] Under the contribution rules, each defendant will face expected damages of $45,[89] while each defendant will believe that the other defendant will have expected damages of $5.[90] Again, it is the defendant's own beliefs, not those of another defendant, that determine deterrence. In this case, each defendant will face more deterrence under the contribution rules than under the no contribution rule. A comparison of the rules in this example gives us the following:

2. Different Beliefs of Probabilities of Loss at Trial@

We now examine the case where the defendants have different beliefs as to their chances of losing to the plaintiff at trial. The beliefs about the probabilities of loss at trial may be different because a defendant is planning to supply the plaintiff with information to be used against the other defendants, while unaware of others' plans to do likewise.[91]

In this section, the assumption is that the defendants have different beliefs about their probabilities of losing at trial, but the same beliefs about the proportion of damages that are caused by each defendant. Some numerical examples show how asymmetric information may affect deterrence.

Suppose there are two defendants, each defendant is equally liable for the plaintiff's damages, and the total damages are $100. Suppose defendant A believes that the probability of it losing at trial is 0.2 and the probability of defendant B losing at trial is 0.6. Then, under the no contribution rule, defendant A will believe that it will have an expected damage payment of $9.09.[92] Under the contribution rules, defendant A will believe it has an expected damage payment of $30.[93] Thus, defendant A will believe it faces less in expected damages, and thus less deterrence under the no contribution rule than under the contribution rules.

Now if defendant B believes that its probability of losing at trial is 0.2 and the probability of defendant A losing at trial is 0.6, then defendant B will also believe that it will have an expected damage payment of $9.09 under the no contribution rule,[94] and $30 under the rules of contribution.[95] Thus, defendant B will also face less deterrence under the no contribution rule than under the contribution rules. These results are summarized below. A comparison of the rules in this example gives us the following:

In the example above, defendant A expects defendant B to face $54.55 in damages, and defendant B expects defendant A to face $54.55 in damages. But again, what is important to defendant A is what it believes it faces in damages ($9.09). Likewise, what is important for defendant B is its own beliefs as to the damages it faces. Therefore, both defendants have beliefs that will increase the likelihood of them entering into a conspiracy under the no contribution rule than under the contribution rule.

Of course, more deterrence for all defendants is also possible under the no contribution rule. In the example above, if each defendant believes that it has a probability of losing at trial of 0.6 and that the other defendant has a probability of losing at trial of 0.2, then each defendant will believe that it faces more deterrence under the no contribution rules than under the contribution rules, as $54.55 > $30.[96] These results are summarized below. A comparison of the rules in this example gives us the following:

Thus, we have seen situations where the no contribution rule and the contribution rules have each led to more deterrence for all defendants. There could also be a conspiracy where some conspirators are deterred more by the no contribution rule and others are deterred more by the contribution rules.[97]

One might think that, in cases where both defendants face less deterrence under the no contribution rule than under the contribution rules, the plaintiff's total damage award will also be less. However, regardless of the beliefs of the defendants, the no contribution rule will always lead the plaintiff to expect and receive a higher total damage award than that which could be obtained under the contribution rules. When defendants have asymmetric beliefs, they cannot both be correct; one or both must be wrong about the outcome. There will be only one actual outcome, and the results that occur will be consistent. One might think of this actual outcome as imposing consistent ex post beliefs on all of the parties involved. As can be noted from the examples in the symmetric information section, where the beliefs of the outcome are consistent, the plaintiff will always receive more in damages.[98] Thus, if compensating the plaintiff is a high priority in the choice of the rule, then the no contribution rule may be favored over the contribution rules. Of course, one could always place a multiplier on damages under the contribution rules in order to obtain the same higher damage award that the plaintiff could have received under the no contribution rule without a multiplier.

C. Information Exchange in Settlements

In conspiracy situations, it is frequently the case that earlier settling defendants settle for less than later settling defendants.[99] This is often because settling with one defendant improves the plaintiff's chances of winning at trial against the remaining defendants. Thus, an early settlement is more valuable to the plaintiff than just the monetary amount received from the defendant. A defendant settling early may provide the plaintiff with information about the conspiracy that can be used against the other defendants.[100] The initial settlement money itself may improve the plaintiff's prospects against the other defendants by allowing the plaintiff to continue with a case that might otherwise have to be dropped for lack of resources.[101] Additionally, the plaintiff may settle either to break up a united front among defendants,[102] or to remove a defendant that caused minor portion of the damages from the trial[103] or could negatively affect the plaintiff's case at trial.[104]

As noted above, one reason that a defendant may have low expected damages when entering into a conspiracy is that the defendant has a belief that it will be able to settle with the plaintiff cheaply by supplying the plaintiff with information to be used against other defendants (while discounting the likelihood that the other defendants will do the same). Different defendants in a conspiracy may each believe that they will be the first to settle cheaply.[105]

However, the different rules give the defendants different incentives to provide this information, and give the plaintiff different incentives to accept the information, in lieu of monetary compensation. These different incentives can influence the conspirators' beliefs of their expected liability before entering into the conspiracy.

The defendants will be willing to supply the plaintiff with information under both the no contribution and contribution with claim reduction rules because of the settlement-bar to contribution from later trial-losing defendants. But, under the contribution with claim reduction rule, the plaintiff will have a disincentive to settle cheaply with a defendant who is liable for a high proportion of the damage.

Under both the no contribution and contribution with claim reduction rules, a defendant who knows the culpability of its act may be able to settle for less than ignorant defendants because, ex ante the conspiracy, the culpable defendant will have a greater incentive to collect information that can be supplied to the plaintiff in the event that the conspiracy is detected.

We now proceed by more formally analyzing certain disparate effects of the rules: the defendants' incentives to provide information; the plaintiff's willingness to offer financial incentives to obtain the information; and the defendants' incentives to collect and hide the information to be given to the plaintiff. Finally, we integrate the above in attempting to determine which rule will be better for deterrence.

1. Defendants' Incentives to Provide Information@

The defendants will be willing to supply the plaintiff with information under both the no contribution and contribution with claim reduction rules because of the settlement-bar to contribution from later trial-losing defendants. The defendants will not be willing to provide information under the contribution with settlement reduction rule, as there is no settlement-bar to contribution. The plaintiff, under the contribution with claim reduction rule, will have to provide the defendant with an incentive to reveal information, such as a lower monetary settlement amount. However, the plaintiff will not have to provide an incentive under the no contribution rule.

The defendant's willingness to supply the plaintiff with information can lead to a prisoners' dilemma situation among the defendants.[106] However, often the information that a defendant might provide could be used against it. Thus, before providing the plaintiff with the information, a defendant will want a settlement agreement. Therefore, the plaintiff may be unable to effectuate the ideal prisoners' dilemma situation of using each defendant's information against the other to improve its strategic position. The following examples illustrate the incentives for defendants to provide information.

Suppose there are two defendants, each defendant equally liable for the damage of the plaintiff. The probability of each defendant losing at trial is 0.2 if no information is given, and 0.8 if information is given. The total damage caused is $100. Each defendant can either disclose or not disclose information to the plaintiff. This gives us four cases for which we can compute the expected damage payments depending on whether none, one or both of the defendants provides the plaintiff with information. The four cases are shown below.

a. No Contribution Rule

First, we examine the settlement outcomes under the no contribution rule. Initially, assume that the information which a defendant provides the plaintiff cannot be used against the information-providing defendant. If neither discloses information, then each defendant will have a probability of loss at trial of 0.2, and each will have expected damages of $16.67.[107]

If only defendant A discloses information, then defendant B will have a probability of losing at trial of 0.8, while defendant A will have a probability of losing at trial of 0.2. The resulting expected damage payments will be $4.76 for defendant A and $76.19 for defendant B.[108] Likewise, if only defendant B discloses information, then the resulting expected damage payments will be $76.19 for defendant A and $4.76 for defendant B.

If defendant A and defendant B each disclose information, then both will have a probability of 0.8 of losing at trial to the plaintiff, and both will have expected damages of $44.44.[109]

Examining the decision to disclose information leads to the following normal form game where the strictly dominant strategy is to disclose the information. This is a prisoners' dilemma situation in which both defendants will be better off if they can agree not to provide information. Absent such an agreement, each has an incentive to supply information.

Under the no contribution rule, defendant A is better off if the plaintiff can collect a high damage amount from defendant B (and vice versa). If the plaintiff can collect a high damage amount from defendant B, then the plaintiff will not be able to sue defendant A for as much as it could have if it had collected a low damage amount from defendant B. This is because any suit against defendant A would be reduced by defendant B's settlement amount. Thus, increased expected damages for defendant B will lead to defendant A having lower expected damages.

If defendant A can be sure that the information it gives the plaintiff can only be used against defendant B, and not be used against itself, then defendant A will freely give the plaintiff the information. Defendant A is better off if the probability of defendant B losing at trial is higher. The lower expected damage payment for defendant A will not come through an incentive offer by the plaintiff to obtain the information, but will be due to defendant B's higher expected damage payment (and thus higher settlement payment) and the corresponding reduced damages that can be sought from defendant A. The lower expected damage payment is not necessarily an enticement from the plaintiff to disclose the information but merely the outcome of the new equilibrium settlement pattern.[110]

Information exchange often occurs during or after settlement to prevent the information from being used against the defendant who supplies it. In many situations, it is unlikely the plaintiff will be able get both defendants to reveal information against the other defendant before either defendant has settled.[111]

However, it may not be necessary for the plaintiff to have the actual information in order to obtain the higher settlement. The plaintiff may be able to create a bidding war among the defendants to be the first defendant to provide information. In that case, where the parties agree on the value of the information, the plaintiff will secure the prisoners' dilemma equilibrium amount. The plaintiff, before it has any information, can ask each defendant how much it will be willing to settle for, on the condition of providing information.

Suppose defendant A offers to settle for $4.76 and to provide information against defendant B. Defendant B will then face expected damages of $76.19. Thus, defendant B will offer to pay more than $4.76, say $20. But then defendant A will face expected damages of $64,[112] and will want to raise its settlement offer above defendant B's settlement offer of $20. This will continue until each defendant offers to settle for $44.44, which is the equilibrium settlement under the no contribution rule where both defendants provide information.

If the plaintiff and the defendants are unable to agree on the value of the information, then the plaintiff will settle with the defendant that gives the plaintiff the highest expected value of the lawsuit. The plaintiff will have to weigh both the value of the information and the monetary value of the settlement in deciding with whom to settle first.

b. Contribution with Claim Reduction Rule

We now examine the settlement outcomes under the contribution with claim reduction rule. If neither defendant discloses information, then each defendant will have a probability of loss at trial of 0.2, and each will have expected damages of $10.[113] If only defendant A discloses information, then defendant B will have a probability of losing at trial of 0.8, while defendant A will have a probability of losing at trial of 0.2. The resulting expected damage payments will be $10 for defendant A and $40 for defendant B.[114] Likewise, if only defendant B discloses information, then the resulting expected damage payments will be $40 for defendant A and $10 for defendant B. If defendant A and defendant B each disclose information, then both will have a probability of 0.8 of losing to the plaintiff at trial and both will have expected damages of $40.

Examining the decision to disclose information leads to the following normal form game where neither player has a dominant strategy to disclose the information. This is not a prisoners' dilemma situation, as each defendant is indifferent as to whether it reveals or withholds information.

However, the plaintiff can make this situation a prisoners' dilemma case by giving each defendant a small monetary incentive for disclosing information.[115] If we let this incentive be e, then we will have the following normal form game which will be a prisoners' dilemma.

With the incentive e, each defendant now has a dominant strategy to disclose information. This incentive can, theoretically, be very small. Thus, the plaintiff should be able to receive nearly the expected damage award it could obtain if it had all of the information.[116]

As is the case under the no contribution rule, under the contribution with claim reduction rule, the plaintiff will want to use the information of each defendant against the other. The plaintiff may need to settle with a defendant in order to obtain the information and, thereafter, convey the information's value to the other defendant. But if the value of the information is known to the plaintiff and the defendants before the plaintiff obtains it, then the plaintiff may use a bidding war between the defendants in order to achieve the prisoners' dilemma amount.

2. Plaintiff's Willingness to Accept Information in Lieu of a Monetary Settlement@

Above, we showed that if the plaintiff and the defendants agree on the value of the information that the defendants can provide, then the plaintiff will be able to use this to start a bidding war between the defendants and achieve the prisoners' dilemma maximum. But it may be the case that the plaintiff does not know the value of the information or is unable to convey the value of the information to defendants without actually having the information. In such a case, the plaintiff might have to settle with one defendant first to be able to use the information in a suit against the other defendant.[117] If such is the case, the plaintiff will have different incentives as to which defendant it settles with first under the no contribution rule as compared with contribution with claim reduction rule.

Under the no contribution rule, the plaintiff will be indifferent as to how much damage is caused by the defendant it settles with because the amount of damages that the plaintiff can seek from the other defendant is only reduced by the settlement amount.[118] Under the contribution with claim reduction rule, the plaintiff will have a disincentive to settle cheaply with a defendant that is liable for a large proportion of the total damage, as the amount it can seek against other defendants will be reduced by the settling defendant's high proportion of the damages.[119] The following numerical examples show the differences between the two rules.

a. No Contribution Rule

Suppose we have the same situation as above, but that defendant A has caused 90% of the damages and defendant B has caused 10% of the damages. Assume that the plaintiff needs to settle with a defendant in order to obtain that defendant's information, which can then be used against a non-settling defendant. Under the no contribution rule, we would have the following payoff matrix.

Under the no contribution rule, the plaintiff is indifferent as to whether it settles first with defendant A or defendant B. In each case, the plaintiff will have an expected damage award of $80.95.[120]

b. Contribution with Claim Reduction Rule

As noted in the previous section, under the contribution with claim reduction rule the plaintiff will need to provide each defendant with an incentive e, in the form of a reduced monetary payment, to induce the defendants to provide information. If liability is allocated by comparative fault under the contribution with claim reduction rule, then the plaintiff will not be indifferent as to which defendant it settles with first and receives its information from.

If the plaintiff settles first with defendant A for $18 - e, then the plaintiff can only sue defendant B for $10, as defendant A's attributable share of the damages is $90.[121] Thus, even if defendant A gives the plaintiff information that improves the plaintiff's probability of winning at trial against defendant B from 0.2 to 0.8, the expected trial award against defendant B is only increased from $2 to $8.

If the plaintiff settles first with defendant B for $2 - e, then the plaintiff can sue defendant A for $90, as defendant B's attributable share of the damages is only $10.[122] If defendant B gives the plaintiff information that improves the plaintiff's probability of winning at trial against defendant A from 0.2 to 0.8, the expected trial award against defendant A is increased from $18 to $72.

Assuming that a defendant will not provide information until it has settled, we will have the following payoff matrix under the contribution with claim reduction rule.

If the plaintiff cannot obtain a defendant's information to use against another defendant without settling with the defendant, and each defendant can provide the same quality of information, then the plaintiff will prefer to settle first with those defendants that cause less damage. In this case, the plaintiff will wish to settle with defendant B before settling with defendant A because it will give the plaintiff a greater aggregate damage award.

To the extent that it is necessary to deter those conspirators that cause, and are liable for, large proportions of the damage, the contribution with claim reduction rule will make it less likely that these conspirators believe that they can settle cheaply. For they will know that the plaintiff has a disincentive to settle cheaply with them. In some situations, we will want to deter conspirators that are liable for larger proportions of the damage more than conspirators liable for smaller proportions of the damage. For instance, we will want to increase deterrence for a larger conspirator that coerces other smaller actors into the conspiracy. In such cases, the smaller actors may be unable to avoid entering into the conspiracy without being punished by the large damage causing actor.[123] In these situations, it will be the large damage causing actor that should be deterred in order to stop the conspiracy.[124]

In addition, it may be a defendant that caused a large proportion of damage that is in the best position to frustrate a conspiracy's objectives. For example, in a price-fixing conspiracy, a non-participating large firm would be in a superior position to a non-participating small firm to undercut a conspiracy's output restraint that is needed for the success of the conspiracy. A non-participating small firm might not be able to increase output quickly enough to undercut the conspiracy's ability to inflict damage on consumers.[125] Thus, deterring a large firm from entering into the conspiracy may have a greater effect on thwarting the conspiracy's objectives than deterring a small firm.

3. Defendants' Incentives to Collect and Hide Information@ Under both the no contribution rule and the contribution with claim reduction rule, defendants may wish to provide the plaintiff with information in order to lower their monetary settlement amount. How much a defendant can save on its monetary settlement will, to some degree, depend upon the quality of the information and evidence it can provide to the plaintiff. We might not expect each defendant to have the same quality of information to be used against other defendants. One reason for the divergent quality of information is that the defendants may have different incentives to collect the information.

A pessimistic defendant that enters a conspiracy believing that the probability of detection is high, and that it is likely to be found liable to the plaintiff, will have a strong incentive to collect information that can be used against the other defendants. A pessimistic defendant's strategy will be to enter into the conspiracy, collect information and, if detected, provide the information to the plaintiff in exchange for a lower monetary settlement. The pessimistic defendant will also try to hide information that can be used against it.

On the other hand, an optimistic defendant that enters a conspiracy believing it unlikely that the conspiracy will be detected, or that, should detection occur, it is unlikely liability will be imposed, will have less incentive to collect information to be used against other defendants. In addition, an optimistic defendant will not try as hard as a pessimistic defendant to hide the information that can be used against it.

Whether a conspirator is optimistic or pessimistic will depend upon many factors. One such factor is the conspirator's knowledge of the illegality of its action. Conspirators that believe that their actions are legal are likely to be optimistic as to the outcome of the conspiracy, as they will believe that if a trial takes place they will be victorious. Conspirators that believe their actions are clearly illegal are likely to be pessimistic. However, in a conspiracy between optimistic and pessimistic conspirators, the pessimistic conspirators are likely to be the ones that have the best information to be used against others and to have hidden the information that can be used against themselves. Thus, the pessimistic conspirators may be able to reach a cheaper settlement with the plaintiff than optimistic conspirators.[126]

It may seem unjust that the conspirators who know the wrongness of their actions are able to settle for a cheaper amount than conspirators that seem less culpable.[127] But this will provide an incentive to actors to determine the legality of their action ex ante the conspiracy. Whether this is a proper incentive depends on whether we believe that parties already spend enough in resources trying to determine the legality of their potential actions. It is doubtful that we want actors to have to contact lawyers before they perform any action, but in some areas of activity, it is desirable that these actors become better informed than they currently are.

Both the no contribution rule and the contribution with claim reduction rule, because they may lead to situations where defendants provide information that is adverse to other defendants, will lead to situations where culpable defendants are able to settle for less than non-culpable defendants. Neither rule will be fair in the sense that the most culpable defendant is forced to pay more than less culpable defendants. Of course, a jury may find the most reprehensible defendants liable for more damages because of their culpability, but in many situations, it may be culpable defendants who appear the cleanest.

As for differences among the rules, the contribution with claim reduction rule will make it more likely that a defendant liable for a large proportion of the plaintiff's damage will face more deterrence. To the extent that one believes that such defendants are also more culpable, possibly because they have more resources to determine the legality of their actions, there will be more deterrence on more culpable defendants under the contribution with claim reduction rule. However, in situations where the more culpable defendant is liable for only a small proportion of the damages, then the contribution with claim reduction rule favors the more culpable defendant.

D. The Effect of Risk Aversion on Deterrence

The no contribution rule, as compared with the contribution rules, imposes additional risk costs on risk averse defendants.[128] In addition to the risk a defendant faces of winning or losing at trial, the no contribution rule leads to additional risk by causing uncertainty as to the amount of damages that a defendant may be forced to pay. While these higher risk costs increase the deterrence faced by the defendant ex ante the conspiracy, should there be a conspiracy, the risk costs themselves are a social waste. There is a trade-off between the benefit of increased deterrence when a conspiracy does not form and the social waste of the risk costs when a conspiracy does form.[129]

We can avoid these risk costs by setting liability damages under either of the contribution rules such that the same ex ante deterrence is achieved as under the no contribution rule.[130] The plaintiff will then receive a greater expected damage award, instead of the risk costs vanishing as a social waste when a conspiracy does occur.

E. The Effect of Litigation Costs on Deterrence

The contribution rules both require that the liability be allocated among the defendants, while the no contribution rule does not require a division of damages. Thus, the contribution rules may cause additional expenditures of legal resources to determine the allocation of damages.[131] These additional litigation costs under the contribution rules can be minimized by using a per capita liability allocation rule as opposed to the comparative fault or comparative benefit liability allocation rules.[132]

The contribution rules may also lead to greater litigation costs because there may be more outstanding defendants if a trial occurs.[133] Under the no contribution rule, the plaintiff will always want to settle with all but one defendant.[134] Under the contribution with settlement reduction rule, defendants will have an incentive not to settle individually. Thus, there may be many defendants if a trial takes place. The contribution with claim reduction rule falls between these two rules, as the defendants will not have a disincentive to settle individually, but the plaintiff will not have an incentive to settle with all but one of the defendants. Thus, it would seem that the contribution with settlement reduction rule would lead to more total litigation costs than the contribution with claim reduction rule, which would lead to more total litigation costs than the no contribution rule.[135]

Just as risk costs are a social waste, the same may be said of litigation costs. Although higher legal costs will increase the amount of deterrence faced by the defendants, as in the case of risk costs, a balance exists between the benefit the litigation costs bring as a deterrent to the activity and the waste that occurs when there is a trial.[136] However, unlike the waste of risk costs which do not affect risk-neutral defendants, litigation expenses raise the costs of risk-neutral as well as risk-averse defendants.

We seem to have a trade off between wasteful litigation costs under the contribution rules and wasteful risk costs under the no contribution rule (for risk-averse defendants). Which rule leads to less total waste is an empirical question that may be different depending on which law is being examined. If we knew which type of costs dominated, we could apply the rule that minimized those costs and set the liability level to achieve the appropriate amount of deterrence. The least wasteful way to increase deterrence is to increase the liability of the defendants.

F. Insulation of Decisionmakers

Decisionmakers of an organization found liable for damages may be insulated from the full extent of the liability since they do not pay the organization's total damages.[137] A decisionmaker may be indifferent as to whether the organization faces a large or small punishment. In such a situation, an organization may be deterred more if each of the organizations is liable for some of the damages, rather than one organization being liable for all of the damages. In such cases, the contribution rules would be favored. This has been formally analyzed by Polinsky and Shavell.[138]

Easterbrook, Landes and Posner note that if there is some minimal level of liability that the organization must face in order for the decisionmaker to be punished, then the no contribution rule may lead to more deterrence.[139] In some situations, the minimum level of organizational liability that leads to decisionmaker deterrence may be achieved if an organization would pay all the conspiracy's damages under the no contribution rule. But that level would not be reached where the organization pays only its share under the contribution rules.

If the damage amount caused by each defendant is large, then the contribution rules will likely lead to more deterrence for decisionmakers. If there is a minimum threshold of damage payment leading to a punishment for the decisionmaker, and the conspiracy's damages are low, then the no contribution rule may lead to more deterrence. The problem of decisionmaker insulation could be addressed by changing the rule used, depending on the expected amount of total liability (or liability per firm). One could use a contribution rule where damages are large, and thus ensure that all decisionmakers face some deterrence. Where total damages are small, the no contribution rule could be applied to ensure that at least one decisionmaker is punished. Additionally, if there is a limited amount of punishment an organization can impose on a decisionmaker, it may be better for society to impose fines or imprisonment on the decisionmaker directly.[140]

[ Go to Previous Section, Section II | Go to Next Section, Section IV ]

Notes

It is also not necessary that the parties have symmetric information in order to have the same beliefs. But if the parties do have symmetric information then they will have the same beliefs. Return to text

If a defendant believes that a plaintiff will disagree with the defendant's beliefs, then the defendant will have to take into account how it expects the plaintiff to behave in order to determine its expected damages. For example, if the defendant believes that the plaintiff will settle with every defendant for one cent, then the defendant will face little in the way of deterrence, regardless of the defendant's belief of the plaintiff's probability of winning at trial, as the defendant will plan on settling with the plaintiff for one cent. On the other hand, if the defendant believes that the plaintiff will never settle with any defendant, then the defendant will have to determine how this strategy by the plaintiff will affect the defendant's expected damage payment. Return to text

Suppose the plaintiff settles with neither defendant, then it will have an expected award of $50, equal to the probability that it prevails at trial multiplied by the total damages. Now suppose defendant A offers to settle with the plaintiff for only $1. The plaintiff will be better off accepting the $1 and suing defendant B for the remainder of $99. This will give the plaintiff expected damages of $50.50 which is higher than the expected damages of $50 the plaintiff will receive if it goes to trial against defendant A. Of course, defendant B will now have expected damages of $49.50, and will bid against defendant A to settle first. Thus, we will be in a bidding war as described below.

Under a rule where contribution is only allowed among non-settled defendants, the result will be the same. In the analysis, the plaintiff will again wish to settle with all but one of the defendants before trial, as the plaintiff gains nothing when there is more than one outstanding defendant and its probabilities of winning at trial are correlated. Thus, there will remain only one non-settled defendant if there is a trial. But as in the case of the no contribution rule, under this modified contribution rule, if a defendant settles it cannot be sued for contribution. Thus, there will be no non-settled defendants from whom a trial-losing defendant can seek contribution. The result is the same as where the no contribution rule had been in effect. See id. at 363. Return to text

Under the no contribution rule, the plaintiff will have an incentive to settle with all but one defendant before any trial occurs, as the plaintiff will gain nothing by having more than one outstanding defendant in a trial. Both the plaintiff and the defendants will know this. This knowledge will affect the bargaining. The following example will show why a plaintiff might be disadvantaged in sequential settlement negotiations.

Suppose that defendant A and defendant B cause $100 in total damages and each has a 50% probability of losing at trial to the plaintiff. Suppose the plaintiff wants to first sue defendant A and then sue defendant B. The plaintiff and defendant A will agree that defendant A will have an expected payment of $50 in damages if a trial occurs. The plaintiff will want to settle with defendant A for defendant A's expected damages at trial of $50 and then sue defendant B for the remaining $50. If the plaintiff and defendant A settle for $50, then the plaintiff and defendant B would agree that the expected outcome at their trial would lead to expected damages of $25 and thus, they would settle for $25. This negotiating pattern will give the plaintiff an expected award of $75 from the sequential bargaining, which is greater than the $66.66 likely received from the simultaneous bargaining.

However, if the plaintiff commits to the sequential bargaining ex ante the negotiations, then the plaintiff will be better off accepting any positive offer from defendant A than risking a trial. For example, if defendant A offers the plaintiff only $1 to settle, the plaintiff will be better off accepting the $1 and suing defendant B for the remainder of $99. This will give the plaintiff expected damages of $50.50, which is greater than the expected damages of $50 the plaintiff could expect if it goes to trial against defendant A.

Thus, defendant A is better off settling for up to $50 than going to trial and facing expected damages of $50 and trial costs. The plaintiff is in a better position if it settles for any positive amount, as opposed to going to trial against defendant A. The actual bargaining agreement between the plaintiff and defendant A will be somewhere between $0 and $50. Where the actual agreement occurs depends on the parties risk preferences, time preferences for money and possibly psychological factors. See generally Ariel Rubinstien, Perfect Equilibrium in a Bargaining Model, 50 Econometrica 97 (1982); Ariel Rubinstien, A Bargaining Model with Incomplete Information About Time Preferences, 53 Econometrica 1151 (1985); Drew Fudenberg & Jean Tirole, Game Theory, chapters 4.4, 4.6 and 10, at 113-17, 128-30, 397-428 (1991).

If the plaintiff can decide whether or not it wants to commit to sequential bargaining, it will only do so if it leads to an expected total damage award greater than the $66.66 it could obtain through simultaneous bargaining. Thus, the plaintiff will have to believe before committing that it is in a strong bargaining position with the first defendant in a sequential negotiation settlement pattern. Return to text

We will compare two mythical states that use the no contribution rule to show how the number of conspirators affects each conspirator's expected damage payment. In state A, there is one conspiracy composed of four members, each conspirator is equally liable for the $200 in total damages. In state B, there are two conspiracies of two conspirators each, each conspiracy causes $100 in total damages and in each conspiracy, each conspirator is equally liable for the damages. Thus, in both states, the total damages are $200 and the damage per conspirator is $50. Assume all conspirators are likely to lose to a plaintiff at trial with probability 0.5.

In state A, the total damage that the four conspirators cause is $200. In equilibrium, each defendant will settle for the damages it would expect if it were the last non-settled defendant left and threatened with trial. In this case under the no contribution rule, each conspirator will be willing to settle for s equal to $40 in damages. $40 = (0.5) x ($200 - 3s) = (0.5) x ($200 - $120). Under the contribution rules, each defendant will have expected damages of $25. $25 = (0.5) x [(0.25) x ($200)].

In state B, the total damages that the four conspirators cause is also $200. But in state B each conspiracy consists of only two members. Thus, as above in the text, in equilibrium each conspirator will offer to settle for s equal to $33.33. $33.33 = (0.5) x ($100 - s) = (0.5) x ($100 - $33.33). And under the contribution rules each defendant will settle for $25. $25 = (0.5) x [(0.5) x ($100)].

In both states, conspiracies cause $200 in total damages, but because there is only one conspiracy in state A, each defendant faces expected damages of $40 under the no contribution rule. However, in state B where there are 2 conspiracies, each conspirator faces expected damages of $33.33 under the no contribution rule. The effect of the no contribution rule on expected damages is not consistent when the conspiracy size is varied. Conspirators must take into account the amount of damage caused along with the number of defendants. As can be seen above, joining a conspiracy with twice as many members that causes twice as much total damage leads to greater expected liability, even if the benefit to each conspirator is the same in each conspiracy.

In the model, the no contribution rule provides greater deterrence for larger conspiracies than for smaller conspiracies. For some situations, such as price fixing, this seems contradictory from a policy point of view, as one would expect larger conspiracies to be more likely to break down than smaller conspiracies. Thus, it would seem that smaller conspiracies are more significant to deter than larger ones. That the damages vary with conspiracy size will also cause problems in trying to set the correct multiplier on damages, such as the chosen multiplier of 3 for antitrust damage. The main point is that the no contribution rule adds the size of the conspiracy as a factor when determining the expected damages through bargaining, which may lead to some odd results as the examples in this footnote demonstrate. Return to text

The plaintiff's total damage award under the no contribution rule is such that $66.66 = $33.33 + $33.33. Return to text

Under the no contribution rule, defendant A's settlement will be $9.09 such that $9.09 = (0.2) x ($100 - $54.55), while defendant B's settlement will be $54.55 such that $54.55 = (0.6) x ($100 - $9.09). Return to text

If played by individuals who have a variety of knowledge and skill, poker can be seen as an example of an asymmetric information game. I will compare the two games to show the differences between symmetric and asymmetric information.

A bet based on a roulette wheel is a game of symmetric information. Suppose that two players decide to play a game in which if the ball lands on black, player 1 wins and if the ball lands of red, player 2 wins (assume that 0 and 00 or green leads to a re-spin of the wheel and ball). Before we send the ball onto the wheel, both players can agree on the likelihood of each party winning as each party has the same information, namely that 50% of the slots are red and 50% of the slots are black.

Poker on the other hand is a game of asymmetric information. Before the card hand is dealt, each player will have private information regarding its skill in the game of poker. This private information can lead to different beliefs. Suppose that player 1 and player 2 both majored in English at college, that very few English majors understand probability theory, and that both players know that the other player was also an English major. In addition, suppose that both player 1 and player 2 took probability courses in college for the sole purpose of playing poker, but that neither player knows that the other player took the probability courses. In this case, the players will have asymmetric information.

Player 1 will be placing its bet with the knowledge that it, player 1, has taken probability courses, while believing that it is unlikely that player 2 has much knowledge of probability (as player 1 knows that player 2 majored in English). Similarly player 2 will be placing its bet with the knowledge that it, player 2, has taken probability courses, while assuming that it is unlikely that player 1 has much knowledge of probability (as player 2 also knows that player 1 majored in English).

In this case, each player might be rather confident that it will do well (win with a probability greater than 50%) in a poker match, even though only one player can win. The players, each expecting to win and the other to lose, have inconsistent beliefs. That the beliefs are inconsistent should be obvious because both defendants cannot have a probability of over 50% of winning in a two player zero sum game. The players have these different beliefs because of their private information. It is not necessary for beliefs to be consistent as between players.

In the real world, all of the information will not be known by all parties, and in many cases, such as in the game of poker, each party will have private information unavailable to the other party. It is possible that each party has the belief that it will win the game, whether that game is poker, football or settling cheaply in an antitrust conspiracy trial. While Professor Easterbrook's roulette wheel example does explain what a lottery is, it is not as useful in describing the situation faced by antitrust or other conspirators, who are playing a game more like the game of poker. Return to text

Where I expect defendants are most likely to have differing beliefs (even in antitrust cases) is in their belief that each defendant will settle cheaply with the plaintiff by giving the plaintiff information to be used against other defendants. It is entirely plausible that each defendant believes that it will be the first to settle cheaply. In fact, under the no contribution rule and contribution with claim reduction rule, the strategy of a conspirator who enters into a conspiracy should be to settle quickly and cheaply as soon as the conspiracy is detected, and if necessary to provide the plaintiff with information on the other conspirators in order to obtain a cheap settlement. See infra part Return to text

They do note that if each defendant believes that it is unlikely to be sued by the plaintiff, each defendant will then be likely to enter into the conspiracy under the no contribution rule. The example is modified to take into account the belief that a firm is unlikely to be sued. See id. at 350-51 & n.48 (indicating that such a situation would arise infrequently because participants generally have similar information leading to symmetric beliefs).

I believe such assymetric beliefs among defendants might occur more frequently than Easterbrook, Landes and Posner suggest because defendants may hide information relevant to forming symmetric beliefs and/or defendants may collect data leading to asymmetric beliefs. See infra Return to text