* Professors of Law, New York University. We acknowledge the generous financial support of the Filomen D'Agostino and Max E. Greenberg Research Fund at the New York University School of Law and the support of the C. V. Starr Center for Applied Economics at New York University. Prior versions of this article were presented at the Conference on the Law and Economics of Environmental Policy, organized by the European Association of Law and Economics and the Geneva Association, Paris, April 1991; at the Comparative Law and Economics Forum, Berkeley, October 1992; and at workshops at the New York University School of Law, University of North Carolina School of Law, and Stanford University Law School. Edward Sherry's extensive comments were very helpful; we also appreciate the valuable suggestions of Marcel Kahan and Kathryn Spier. We are grateful for the research assistance of Kent Chen, Marcel Hawiger, and Jeffrey Spear. ' The classic single-defendant works are John P. Gould, The Economics of Legal Conflicts, 2 J. Legal Stud. 279 (1973); William M. Landes, An Economic Analysis of the Courts, 14 J. Law & Econ. 61 (1971); Richard A. Posner, An Economic Approach to Legal Procedure and Judicial Administration, 2 J. Legal Stud. 399 (1973). The problem of multidefendant settlements is analyzed in Frank H. Easterbrook, William M. Landes, & Richard A. Posner, Contribution among Antitrust Defendants: A Legal and Economic Analysis, 23 J. Law & Econ. 331 (1980); and A. Mitchell Polinsky & Steven Shavell, Contribution and Claim Reduction among Antitrust Defendants: An Economic Analysis, 33 Stan. L. Rev. 447 (1981). These articles deal with a case in which the plaintiff's probabilities of success against each of the defendants are perfectly correlated and thus cover only a narrow slice of the problem that we examine. The approach of the Easterbrook, Landes, & Posner article is followed, without major modification, in Jong Goo Yi, Litigations with Multiple Defendants: How to Settle under Different Apportionment Rules 73-82 (unpublished Ph.D. dissertation, Stanford Univ., February 1991). In a recent paper, Jeffrey Lange studies, in a multiple-defendant context, possible contractual arrangements between a plaintiff and one or more defendants. Jeffrey Lange, Litigation Risk Exchange: An Economic Analysis of Sliding-Scale Settlements (unpublished manuscript, Univ. Pennsylvania Law School 1993). He addresses only the case of perfectly