Litigation with Default Judgments

See Spier (2007) for an excellent survey of these models.

Schwartz and Wickelgren (2009) analyze negative-expected-value defenses in a model with symmetric information. A negative expected value defense reduces the plaintiff’s payoff at trial by less than the cost of the defense. Schwartz and Wickelgren show that such a strategy can be credible if the costs of the defense can be broken up into successive stages where bargaining occurs in between these stages.

There is a second possibility under which the defendant simply accepts the default judgment against all plaintiff types. As a result, no cases proceed to trial.

Nalebuff (1987) finds that some of the comparative statics of Bebchuk (1984) are reversed when the plaintiff’s credibility constraint is binding.

Other work analyzing negative expected value suits in models with asymmetric information includes Katz (1990) and Klement (2003). There is also a literature on negative expected value suits with complete information. See, for example, Rosenberg and Shavell (1985, 2006), Miceli (1993), Bebchuk (1996) and Farmer and Pecorino (1998). Grundfest and Huang (2006) analyze NEV suits in a model in which these suits may be brought because they have a positive option value.

Allowing for risk averse players will affect the expression for the defendant’s credibility condition, but would not alter the general thrust of the results. Under risk neutrality, the defendant compares the expected payoff under a default judgment with the expected payoff of proceeding to trial. Under risk aversion, she would compare the expected utility of these two options. Thus, as under risk neutrality, there will exist some condition under which the defendant will not have a credible threat to proceed to trial.

We associate the plaintiff’s type with the judgment he would receive if victorious at trial.

Nothing in the mathematics forces this assumption, i.e. we could allow for values of k<1 without affecting our analysis in a significant way. However, if k<p, the defendant would always prefer default to defending the suit.

Suppose p=0.5. To raise the borderline type by $10,000 requires raising the offer by $5,000. If p=0.6, then raising the borderline type by $10,000 requires raising the offer by $6,000.

From Result 1, we know that if the credibility constraint does not hold, the cutoff type must be raised so that the constraint can be satisfied. Thus, if the constraint fails to hold at JU∗, it will not hold for a cutoff type below JU∗.

If kJ_>pJU∗−CP, then all plaintiffs reject the offer ODU∗ in favor of the default judgment, and we have the same outcome as when the defendant offers 0. Since the outcome is equivalent to the defendant making an offer of 0, we ignore this possibility in the main text to simplify the exposition.

Recall that the right-hand side of eq. [3] is increasing in the cutoff type. If, as we assume here, the constraint fails to be satisfied at JU∗, then we will have JC∗>JU∗.

Note that k affects JC∗ via eq. [11], but does not appear directly in eq. [13], because default does not occur when the defendant makes the constrained offer.

We have made the standard assumption that the plaintiff is informed about the judgment J, but it should be noted that our result depends upon this assumption. If the plaintiff is informed about the probability p of a judgment in his favor, we would obtain a result in line with the previous literature. The truncated distribution of plaintiff types proceeding to trial would have a high probability of prevailing, and the higher this probability the less likely it is that the defendant’s credibility condition would hold. To restore the credibility condition the defendant would need to make a less generous offer in order to lower the conditional probability that the plaintiffs proceeding to trial will prevail.

The condition in eq. [11] requires that C_D equals k – p times the average judgment of the truncated distribution of plaintiffs proceeding to trial, and JC∗ is the lowest judgment in this truncated distribution.

As k rises, the constraint in eq. [11] is relaxed. The defendant responds to the relaxed constraint by lowering her offer, and this must lower her expected cost from litigation. At the same time, the expected cost of a default from eq. [10] must increase, so that the constrained offer becomes a more attractive option.

For example, if k increases while we are in the unconstrained case and we remain in this case, the incidence of trial will be unchanged.

For all plaintiffs to have a credible threat to proceed to trial it must be the case that pJ_−CP+zpCP−(1−p)CD>0. We assume this condition holds.

The result is first identified by Reinganum and Wilde (1986) in the context of the signaling model, but it also applies in the screening model. For a survey of the literature on fee shifting see Katz and Sanchirico (2010).

A formal restatement of the result would refer to the condition in eq. [20] rather than the condition in eq. [3].

The condition in eq. [24] requires that CD+zpCP−(1−p)CD equals k – p times the average judgment of the truncated distribution of plaintiffs proceeding to trial, and JC∗ is the lowest judgment in this truncated distribution.