Litigation with symmetric bargaining and two-sided incomplete information

We construct game theoretic foundations for bargaining in the shadow of a trial. Plaintiff and defendant both have noisy signals of a common-value trial judgment and make simultaneous offers to settle. If the offers cross, they settle on the average offer; otherwise, both litigants incur an additional cost and the judgment is imposed at trial. We obtain an essentially unique NE and characterize its conditional trial probabilities and judgments. Some of the results are intuitive, e.g., an increase in trial cost (or a decrease in the range of possible outcomes) reduces the probability of a trial. Other results reverse findings from previous literature. For example, trials are possible even when the defendant's signal indicates a higher potential judgment than the plaintiff's signal, and when trial costs are low, the middling cases (rather than the extreme cases) are more likely to settle.