Abstract
The paper explores two-dimensional private information in pre-trial bargaining.
Traditional models of litigation assume private information in a single dimension,
where that information affects the expected judgment at trial (e.g., damages). But
in reality, informed parties could also diverge on other dimensions, and in particular,
concerning properties that do not affect the expected judgment at trial.
While this phenomenon has various manifestations in real-world setups, we
utilize the example of malicious motivations. Plaintiffs could diverge on their
damages, but they can also have different motivations to litigate. While the different
motivations affect the plaintiffs’ “appetite” for trial, they do not affect the
expected judgment at trial. Our analysis reveals that the presence of this second
dimension, informational gaps regarding the plaintiff’s motivations, leads to
surprising effects. First, the familiar fully-revealing result is not sustainable with
bi-dimensional private information. Those who have weaker “appetite” for trial
tend to ”reverse mimic” to the weakest type (and settle with certainty). This effect
may increase the rate of settlements. Second, the uninformed party is counterintuitively
better off — intuitively, the addition of private information in the second
dimension allows her to be more aggressive, which facilitates more generous offers.
Third, bi-dimensional private information gives rise to various equilibria,
semi-fully-revealing, binary (accept/reject), and semi-pooling ones.
Our results bear empirical predictions. We predict “focal” settlement points,
especially at the low-end of the distribution of types; challenge the assumption
regarding monotonicity in settlement rates; and offer a rational explanation for
over-rejection and overly generous offers observed in experiments.
Traditional models of litigation assume private information in a single dimension,
where that information affects the expected judgment at trial (e.g., damages). But
in reality, informed parties could also diverge on other dimensions, and in particular,
concerning properties that do not affect the expected judgment at trial.
While this phenomenon has various manifestations in real-world setups, we
utilize the example of malicious motivations. Plaintiffs could diverge on their
damages, but they can also have different motivations to litigate. While the different
motivations affect the plaintiffs’ “appetite” for trial, they do not affect the
expected judgment at trial. Our analysis reveals that the presence of this second
dimension, informational gaps regarding the plaintiff’s motivations, leads to
surprising effects. First, the familiar fully-revealing result is not sustainable with
bi-dimensional private information. Those who have weaker “appetite” for trial
tend to ”reverse mimic” to the weakest type (and settle with certainty). This effect
may increase the rate of settlements. Second, the uninformed party is counterintuitively
better off — intuitively, the addition of private information in the second
dimension allows her to be more aggressive, which facilitates more generous offers.
Third, bi-dimensional private information gives rise to various equilibria,
semi-fully-revealing, binary (accept/reject), and semi-pooling ones.
Our results bear empirical predictions. We predict “focal” settlement points,
especially at the low-end of the distribution of types; challenge the assumption
regarding monotonicity in settlement rates; and offer a rational explanation for
over-rejection and overly generous offers observed in experiments.