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Litigation and Selection with Correlated Two-Sided Incomplete Information
Abstract
This article explores the selection of disputes for litigation in a setting with twosided incomplete information and correlated signals. The models analyzed here suggest that Priest and Klein's conclusion that close cases are more likely to go to trial than extreme cases remains largely valid when their model is interpreted as involving correlated, two-sided incomplete information and is updated (i) to incorporate take-it-or-leave-it offers or the Chatterjee-Samuelson mechanism, (ii) to take into account the credibility of the plaintiff's threat to go to trial, and (iii) to allow parties to make sophisticated, Bayesian inferences based on knowledge of the distribution of disputes. On the other hand, Priest and Klein's prediction that the plaintiff will win 50% of litigated cases is sensitive to bargaining and parameter assumptions. © The Author 2018. Published by Oxford University Press on behalf of the American Law and Economics Association. All rights reserved.
... Thus, it is perhaps not surprising that game-theoretical concepts and frameworks have been adopted and translated into the legal domain quite early on. While the vast majority of this work focused upon the application of simple "prisoner's dilemma"-style models [122], there has also been more sophisticated work applying game theoretic models to a range of legal topics including tort law [123][124][125], contract law [126][127][128], the selection of disputes in civil litigation [129][130][131] and the overall law making process [132]. In addition, scholars have attempted to model how judges and courts operate in their own strategic environment. ...
While "complexity science" has achieved significant successes in several interdisciplinary fields such as economics and biology, it is only a very recent observation that legal systems -- from the way legal texts are drafted and connected to the rest of the corpus, up to the level of how judges and courts reach decisions under a variety of conflicting inputs -- share several features with standard Complex Adaptive Systems. This review is meant as a gentle introduction to the use of quantitative tools and techniques of complexity science to describe, analyse, and tame the complex web of human interactions that the Law is supposed to regulate. We offer an overview of the main directions of research undertaken so far as well as an outlook for future research, and we argue that statistical physicists and complexity scientists should not ignore the opportunities offered by the cross-fertilisation between legal scholarship and complex-systems modelling.
... Spier (1992) extended the framework ofBebchuk (1984) by allowing multiple periods of bargaining to explain the "U-shaped" time pattern of settlement.Schweizer (1989),Spier (1994) andKlerman et al. (2018) explored litigation games with two-sided asymmetric information. 10 For the case of medical malpractice in the US, see the review byPeters (2009), which shows that cases with objective evidence of negligent or deficient care are more likely to settle.Content courtesy of Springer Nature, terms of use apply. ...
In this paper, we investigate how loss aversion affects people’s behavior in private litigation. We find that a loss-averse plaintiff demands a higher settlement for intermediate claims to maintain her threat to proceed to trial following rejection compared to a loss-neutral plaintiff. For larger claims, a loss-averse plaintiff demands a lower offer to increase the settlement probability as loss pains her extra in trial. We also investigate how various policies affect loss-averse litigants’ settlement decisions. Only a reduction in the asymmetry of information about trial odds uniformly leads to higher settlement rates.
... 26 Such idiosyncratic asymmetry seems to be realistic as an assumption, and enables the model to both remain simple and explain some puzzling features of trial outcome statistics. Moreover, since idiosyncratic, uncorrelated errors (or informational asymmetries) are at the core of the Priest-Klein framework (Klerman and Lee, 2014;Lee and Klerman, 2016;Klerman, Lee, Liu, 2018), this model combines elements of the Priest-Klein and systemic asymmetric information approaches. ...
Litigation is costly because information is not free. Given that information is costly and perfect information prohibitively costly, courts will occasionally err. Finally, the fact that information is costly implies an unavoidable degree of informational asymmetry between disputants. This paper presents a model of the civil justice system that incorporates these features and probes its implications for compliance with the law, efficiency of law, accuracy in adjudication, trial outcome statistics, and the evolution of legal standards. The model’s claims are applied to and tested against the relevant empirical and legal literature.
A popular narrative suggests that, in the wake of the rise of the Chicago School, the judiciary has grown increasingly lax, making it difficult for antitrust agencies to successfully challenge mergers in court. We develop a theoretical framework to yield propositions regarding merger challenges, settlements, and outcomes under varying judicial standards. We then undertake an empirical investigation of all mergers, challenges, and litigated outcomes in the United States over 1982–2021 to test for the presence of shifting judicial standards. Contrary to the popular narrative, we find evidence that judicial standards have become increasingly pro-enforcement over the past four decades.
We consider a simple model of litigation contests in which each party dedicates both “case-advancing” efforts that directly increase her probability of winning, as well as “adversarial” efforts, which harm her opponent’s strategy and decrease his likelihood of prevailing. Our model characterizes adversarial litigation efforts and the equilibrium investment in such efforts by both parties, subject to the value of winning and the costs of adversarial efforts vis-à-vis case-advancing ones. We find that litigation will always involve adversarial efforts if awards are sufficiently high, and that litigation in which most efforts are adversarial is a plausible scenario. Furthermore, in a relatively symmetric litigation that involves high awards, adversarial efforts increase the parties' likelihood of reaching a settlement agreement. In asymmetric cases, however, the existence of adversarial efforts inhibits settlement irrespective of the awards at stake.
Law and economics theorists have long advanced theories of litigation and settlement, including the canonical Landes–Posner–Gould (LPG) and Priest and Klein (PK) models. Famously, PK predict that, as settlement rates rise, plaintiff win rates approach 50%. So far, though, empirical testing of these models has been hampered by two major limitations: first, these models make clear predictions about the effect of case stakes on settlement rates and plaintiff win rates, but lack of reliable data on stakes means these predictions have gone untested. Second, most of the studies have used data from the United States, a high-settlement, high-litigation-costs setting, and the generalizability of these models to other institutional settings has been less explored. We use a novel data set of Taiwanese court data to test previously untested predictions of the LPG and PK models and explore the extent to which these models apply to a low-settlement, low-litigation-cost setting. We find strong support for the predictions of the LPG model that we test but at best weak support for the 50% hypothesis of the PK model, consistent with recent research suggesting that the hypothesis will have limited applicability in a low-settlement, low-litigation-cost environment. These results suggest directions for research and provide guidance to policy on the role that stakes play in the filing and settlement of claims.
We study the effect of fee shifting rules on litigation. First, we build a model to study the theoretical effect of a change in cost-recovery rules on case filings, (postfiling) settlement, win rates, and plaintiffs’ average litigation expenditures. We then undertake an empirical analysis of the introduction of an intermediate cost shifting rule that falls between the English and American Rules: a reform that limits the size of fee awards to successful litigants in cases decided by the Intellectual Property Enterprise Court (IPEC), one of two venues where IP cases may be filed in England and Wales. Our empirical analysis takes advantage of heterogeneity among case types and compares IPEC cases with intellectual property cases litigated at the PHC of England and Wales, which was not subject to this reform. We find that patent case filings increased following the IPEC’s shift from a pure English Rule to a rule that caps costs awards. Consistent with our model’s predictions, we also find evidence that smaller plaintiffs both won less often and settled more often postreform, as well as evidence that larger plaintiffs spent less on litigation postreform.
When adjudication is not perfectly accurate, litigants with unmeritorious cases may benefit from court errors, which in turn may result in a dilution of incentives for primary behavior and frivolous litigation. We study how shifting the court fees to the loser may improve the accuracy of adjudication. If litigation costs are high, the American rule performs better than the English rule, and vice versa if litigation costs are low. Yet, the optimal rule typically lies in between the American and the English rule, allowing the court to modulate fee shifting based on the accuracy of the evidence submitted by the parties. Our results rationalize observed patterns of use of fee shifting. In the United States, fee shifting is less common than in Europe, where litigation costs are lower. When used, fee shifting commonly depends on the accuracy of the evidence. Moreover, fee shifting filters extreme cases out of litigation, resulting in a more representative set of cases—including also more extreme ones—being adjudicated under the American rule as compared to the English rule. Finally, we identify a characteristic of fee-shifting rules, their “flatness”, which guarantees that fee shifting does not affect the settlement rate and show that flatness is a feature of an optimal mechanism.
An informed (prospective) plaintiff can send a take-it-or-leave-it demand to an uninformed (prospective) defendant with the threat of a lawsuit that may not be credible. In this context, the well-known perfect separating equilibrium in litigation bargaining game (Reinganum andWilde, 1986) no longer exists, and all perfect Bayesian equilibria with pre-filing settlements exhibit a cutoff feature. These equilibria offer an explanation for the distinctive behaviors of Litigation PAEs, who aggressively file lawsuits for settlements, and Portfolio PAEs, who obtain licensing revenues through pre-filing settlements. Our comparative statics results lead to testable hypotheses regarding how litigation costs and the plaintiff’s reputation affect the settlement amount before and after the cases are filed, and the frequency of lawsuits from a given plaintiff.
Labor courts may influence firing costs. Apart from the procedural costs, there is the likelihood that labor courts declare firings as unfair or nil, which significantly increase severance payments over those established for fair dismissals by Employment Protection Legislation. In this paper we model the determinants of the wedge between mandated and effective firing costs arising from labor courts resolution of dismissals, and show how it is affected by EPL reforms, looking at recent EPL reforms in Spain (implemented in 2010 and 2012) that significantly widened the definition of fair economic dismissals.
Pretrial negotiation is a structured environment in which to study bargaining with incomplete information. When a plaintiff believes that a defendant owes him damages, he may first attempt to reach a private settlement before resorting to a costly court-imposed judgment. A central issue in their negotiations is whether the plaintiff's threat to litigate is credible. It is possible for the plaintiff to undermine the credibility of his litigation threat by making a settlement demand that is insufficient. As a result, the plaintiff must raise his settlement demand to limit the amount of bad news he can learn if his offer is rejected. When this credibility constraint is binding, traditional comparative static results are reversed. In addition, even though the defendant is being sued, he wants the plaintiff's threat to be credible.
This article examines a model of settlement and litigation in which the plaintiff makes a settlement demand based upon his true level of damages; the defendant infers the plaintiff's true damage level and decides whether to go to trial. When both parties share common beliefs about the likelihood of judgment in favor of the plaintiff (but not necessarily about the expected award) and when the plaintiff retains the entire settlement, then the system for allocating litigation costs does not affect the equilibrium probability of trial. If either of these two assumptions is violated, then the litigation cost allocation system becomes an important determinant of the equilibrium probability of trial.
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 Nash
equilibrium and characterize its conditional trial probabilities and judgments. Some of the results are intuitive. For example,
an increase in trial cost (or a decrease in the range of possible outcomes) reduces the probability of a trial. We obtain
a precise nonlinear expression for the relationship. 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, middling cases (rather than extreme cases) are more likely to settle.
This article examines the strategic interaction between a defendant and a prosecutor during the plea bargaining process. A four-stage game of incomplete information is developed where the defendant's guilt or innocence is private information but the amount of resources available to the prosecutor is common knowledge. The basic result of the article is that equilibrium is semiseparating; the plea offer is accepted by a proportion of the guilty defendants and is rejected by all of the innocent defendants and the remaining guilty defendants. In this model an increase in the resources available to the prosecutor increases the proportion of guilty defendants who accept plea offers. Although the prosecutor is unable to generate complete separation of the guilty and innocent defendants through the plea bargaining process, prosecutorial resources are beneficial from a societal standpoint. Copyright 2001 by Oxford University Press.
New York closing-statement data provide unique insight into settlement and selection. The distributions of settlements and adjudicated damages are remarkably similar, and the average settlement is very close to the average judgment. One interpretation is that selection effects may be small or nonexistent. Because existing litigation models all predict selection bias, we develop a simple, no-selection-bias model that is consistent with the data. Nevertheless, we show that the data can also be explained by generalized versions of screening, signaling, and Priest– Klein models.
We present a refinement of the set of sequential equilibria [Kreps & Wilson (1982)] for generic signaling games based on rationality postulates for off-the-equilibrium-path beliefs. This refinement concept eliminates equilibria which Kreps (1985) and others dismiss on intuitive grounds. In addition, we derive a characterization of the set of stable equilibria [Kohlberg and Mertens (1982)] for generic signaling games in terms of equilibrium strategies and restrictions on beliefs. Examples are given which differentiate the predictions of these equilibrium concepts.
Priest and Klein's 1984 article, "The Selection of Disputes for Litigation," famously hypothesized a "tendency toward 50 percent plaintiff victories" among litigated cases. Despite the article's enduring influence, its results have never been formally proved, and doubts remain about their meaning, validity, and generality. This article makes two main contributions. First, it distinguishes six hypotheses plausibly attributable to Priest and Klein. Second, it mathematically proves or disproves the hypotheses under a generalized version of Priest and Klein's model. The Fifty-Percent Limit Hypothesis and three other hypotheses attributable to Priest and Klein (1984) are mathematically well-founded and true under the assumptions made by Priest and Klein. In fact, they are true under a wider array of assumptions. More specifically, the Trial Selection Hypothesis, Fifty-Percent Limit Hypothesis, Asymmetric Stakes Hypothesis, and Irrelevance of Dispute Distribution Hypothesis are true for any distribution of disputes that is bounded, strictly positive, and continuous. The Fifty-Percent Bias Hypothesis is true when the parties are veil/accurate in estimating case outcomes, but only sometimes true when they are less accurate. As shown in Klerman and Lee (2014), the No Inferences Hypothesis is false.
Priest and Klein’s 1984 article, “The Selection of Disputes for Litigation,” famously hypothesized a “tendency toward 50 percent plaintiff victories” among litigated cases. Despite the article’s enduring influence, its results have never been formally proved, and doubts remain about their meaning, validity, and generality. This article makes two main contributions. First, it distinguishes six hypotheses plausibly attributable to Priest and Klein. Second, it mathematically proves or disproves the hypotheses under a generalized version of Priest and Klein’s model. The Fifty-Percent Limit Hypothesis and three other hypotheses attributable to Priest and Klein (1984) are mathematically well-founded and true under the assumptions made by Priest and Klein. In fact, they are true under a wider array of assumptions. More specifically, the Trial Selection Hypothesis, Fifty-Percent Limit Hypothesis, Asymmetric Stakes Hypothesis, and Irrelevance of Dispute Distribution Hypothesis are true for any distribution of disputes that is bounded, strictly positive, and continuous. The Fifty-Percent Bias Hypothesis is true when the parties are very accurate in estimating case outcomes, but only sometimes true when they are less accurate. As shown in Klerman and Lee (2014), the No Inferences Hypothesis is false.
Prior efforts to specify and then empirically estimate structural models of the outcomes of tort lawsuits involve only two parties-plaintiff and defendant. We incorporate the defendant's insurer and its "duty to settle" into a three-party settlement model. In medical malpractice cases, there is both anecdotal and quantitative evidence that policy limits and the insurer's duty to settle are central parts of settlement bargaining. We estimate the model using a Texas database of closed, paid medical malpractice claims. Both the data and our model predict a mass of cases with a settlement offer by the plaintiff exactly at limits; a smaller but still sizeable mass of cases with payout exactly at limits (both in pre-trial settlements and after trial), and substantial haircuts (payout<damages) in tried cases with damages > limits. In counterfactual analysis, we predict that, as dutyto-settle liability becomes stricter, there will be: more at-limits offers, fewer trials, fewer at-limits payments in tried cases, more insurer payments above limits, and smaller haircuts. (JEL K13, K41)
This article develops a simple but general model of suit and settlement given symmetric information. Plaintiffs and defendants
can choose when and to what extent they sink litigation costs through the use of retainers and detailed pleading. I demonstrate
sharp asymmetries in the ability of plaintiffs and defendants to use sunk costs strategically to obtain or deter nuisance-value
settlements. The model accounts for the roles of the merits, litigation costs, and bargaining power; incorporates complaints
and answers for which parties’ investments in pleading detail are endogenously determined; permits strategic default by the
defendant; and nests several existing models of negative-expected-value litigation as special cases. It generates testable,
counterintuitive, empirical predictions, and facilitates normative analysis. For example, the model predicts that plausibility
pleading standards will have modest effects in deterring low-merit suits but may be harmful to plaintiffs and defendants settling stronger cases. (JEL K41)
Many analyses of courts within the economic analysis of law are indistinguishable from those produced by positive political theorists; they consider how judges control, exploit, or resolve conflicts of interest among judges. This article considers three contributions by economic analysts of law outside this common, positive, political theoretic model but which still exploit the tools of rational-choice theory. These contributions either integrate appellate decisio -making within a more comprehensive model of litigant and trial behavior; assume that judges constitute a team with shared preferences; or assume that judges decide cases rather than announce or implement policies. These three elements yield a substantively different understanding of courts than the standard model of positive political theory (PPT). The assumption of shared preferences explicitly rejects the principal-agent model that is standard in PPT. The integration of appellate decision making with other aspects of the disputing process and the shift from policies to cases are consistent with, but potentially transformative of, the standard principal-agent models of adjudication.
Priest and Klein (1984) argued that, because of selection effects, the percentage of litigated cases won by plaintiffs will not vary with the legal standard. Many researchers thereafter concluded that one could not make valid inferences about the character of the law from the percentage of cases plaintiffs won, nor could one measure legal change by observing changes in that percentage. This article argues that, even taking selection effects into account, one may be able to make valid inferences from the percentage of plaintiff trial victories. First, it analyzes selection effects under asymmetric information models. It shows that, under a wide array of plausible assumptions, the standard screening and settlement models predict that a sufficiently more pro-plaintiff legal standard will lead to a larger percentage of plaintiff trial victories. Second, it reexamines Priest and Klein’s own model. The prediction that the plaintiff trial win rate will not vary with the legal standard is a limiting result which holds only as the variance of the parties’ prediction errors goes to zero. Nevertheless, this limiting result is not necessarily relevant to empirical work, because, as the variance of the parties’ prediction errors goes to zero, the number of litigated cases also goes to zero. Thus, whenever one is doing empirical work on litigated cases, one is necessarily dealing with a situation in which prediction errors are positive. Under a wide range of plausible parameters and distributions of disputes, plaintiff trial win rates increase as the law becomes sufficiently more pro-plaintiff, and this effect will be large enough to be detected in samples of reasonable size. Third, it examines the effect of an increase or decrease in damages. It concludes that unlike a shift in the standard of liability, changes relating to damages produce ambiguous, yet testable, predictions regarding the plaintiff trial win rate.
This survey of the modeling of pretrial settlement bargaining organizes current main themes and recent developments. The basic concepts used are outlined as core models and then several variations on these core models are discussed. The focus is on articles that emphasize formal models of settlement negotiation and the presentation in the survey is organized in game-theoretic terms, this now being the principal tool employed by analyses in this area, but the discussion is aimed at the not-terribly-technical non-specialist. The survey also illustrates some of the basic notions and assumptions of information economics and of (cooperative and noncooperative) game theory.
This paper provides a formal model of the Priest-Klein trial selection hypothesis, and extends the hypothesis as well. We derive the conditions under which the hypothesis is valid, and examine implications for the relationship between trial outcome uncertainty and litigation.
A basic question about litigation concerns the frequency of plaintiff victory at trial and how cases that go to trial relate to settled cases. In a stimulating paper, Priest and Klein advanced a model in which there is a tendency for plaintiffs to prevail at trial with probability 50 percent. However, this note demonstrates that, in a simple, frequently employed model of litigation, it is possible for the cases that go to trial to result in plaintiff victory with any probability. Moreover, given any probability of plaintiff victory at trial, the probability of plaintiff victory among settled cases (had they been tried) may be any other probability. Further, data on the frequency of plaintiff victory does not clearly support the 50 percent tendency. In consequence, this note concludes that it does not seem appropriate to regard 50 percent plaintiff victories as a central tendency, either in theory or in fact. Copyright 1996 by the University of Chicago.
This paper provides a survey on studies that analyze the macroeconomic effects of intellectual property rights (IPR). The first part of this paper introduces different patent policy instruments and reviews their effects on R&D and economic growth. This part also discusses the distortionary effects and distributional consequences of IPR protection as well as empirical evidence on the effects of patent rights. Then, the second part considers the international aspects of IPR protection. In summary, this paper draws the following conclusions from the literature. Firstly, different patent policy instruments have different effects on R&D and growth. Secondly, there is empirical evidence supporting a positive relationship between IPR protection and innovation, but the evidence is stronger for developed countries than for developing countries. Thirdly, the optimal level of IPR protection should tradeoff the social benefits of enhanced innovation against the social costs of multiple distortions and income inequality. Finally, in an open economy, achieving the globally optimal level of protection requires an international coordination (rather than the harmonization) of IPR protection.
Games in which one party conveys private information to a second through messages typically admit large numbers of sequential
equilibria, as the second party may entertain a wealth of beliefs in response to out-of-equilibrium messages. By restricting
those out-of-equilibrium beliefs, one can sometimes eliminate many unintuitive equilibria. We present a number of formal restrictions
of this sort, investigate their behavior in specific examples, and relate these restrictions to Kohlberg and Mertens' notion
of stability.
A model of parties' litigation and settlement decisions under imperfect information is studied. The model shows how informational asymmetry influences parties' decisions, and how it might lead to parties' failure to settle. The model is used to identify how the likelihood of settlement and the settlement amount are shaped by various factors--the size of the amount at stake, the magnitude of the parties' litigation costs, and the nature of the parties' information. The model is also used to examine how the likelihood of settlement is affected by various legal rules, such as those governing the allocation of litigation costs.
Previous studies of litigation have sidestepped the strategic element in the decisions to file suit, and to settle or go to trial. This article develops a model of strategic behavior in litigation, which reveals how information is exploited and how the litigants' strategies are interdependent. The model is analyzed to derive conditions on the parameters under which suit is filed, action is settled, and the action is tried. Further, it is applied to begin to study the question of whether there is excessive litigation in the U.S. legal system. It is found that in certain cases, the outcome of the litigation process does not satisfy private efficiency; that is, in some cases, even ignoring effects on the rest of society, the outcome is not efficient for the litigants.
A model of plea bargaining with asymmetric information is presented. The prosecutor's private information consists of the strength of the case, while the defendant's private information consists of h is guilt or innocence. In equilibrium, a fraction of cases are dismis sed because they are too likely to involve an innocent defendant; in the remaining cases, the prosecutor's offer of a sentence in exchange for a plea of guilty reveals the strength of the case. It is shown t hat unlimited prosecutorial discretion may be socially disadvantageou s since it carries with it the requirement of sequential rationality. Copyright 1988 by American Economic Association.
There are many economic problems which, when modelled as games of incomplete information, give rise to many sequential equilibria, severely limiting the usefulness of the model. There has recently been a large literature devoted to "refining" the set of equilibria in order to reduce this multiplicity by restricting the set of admissible disequilibrium beliefs. This paper argues that the logical foundations of some refinements and the equilibria they focus on are problematic and, further, proposes an alternative refinement that avoids the difficulties. We also provide an existence theorem covering a broad class of signalling games often studied in economics. Journal of Economic Literature Classification Numbers: C72, C70, D82.
I study a budget-constrained, private-valuation, sealed-bid sequential auction with two incompletely-informed, risk-neutral bidders in which the valuations and income may be non-monotonic functions of a bidder's type. Multiple equilibrium symmetric bidding functions may exist that differ in allocation, efficiency and revenue. The sequence of sale affects the competition for a good and therefore also affects revenue and the prices of each good in a systematic way that depends on the relationship among the valuations and incomes of bidders. The sequence of sale may affect prices and revenue even when the number of bidders is large relative to the number of goods. If a particular good, say [alpha], is allocated to a strong bidder independent of the sequence of sale, then auction revenue and the price of good [alpha] are higher when good [alpha] is sold first.
Abstract Weanalyze,a settlement and litigation game,inwhi ch,both parties possess private information relevant to the value of a claim. The plaintiff knows the level of damages, while the defendant knows the probability he will be held liable for those damages. We consider two alternatives: (1) the plaintiff proposes a settlement, which the defendant accepts or rejects; and (2) the defendant proposes a settlement, which the plaintiff accepts or rejects. Despite the extensive symmetry of the model, these alternatives will generally result in different equilibrium expected frequencies of trial, and therefore different social efficiencies. November, 1992
This paper deals with a simple game of litigation and settlement with incomplete information. Parties are assumed to have
the choice between settling their dispute out of court or resorting to costly litigation. The set of sequential equilibria
is characterized and conditions are given under which an efficient equilibrium does exist. Efficient equilibria, however,
will be ruled out by various tests of refinement. A comparative statics analysis is carried out with respect to the quality
of private information which parties are assumed to receive before any moves have to be made.
The authors introduce a new solution concept, divine equilibrium, which refines the set of sequential equilibria in signaling games by requiring that off-the-equilibrium-path beliefs satisfy an additional restriction. This restriction rules out implausible sequential equilibria in examples. Divine equilibria exist because a sequential equilibrium that fails to be divine cannot be in a stable component. The authors demonstrate through examples that the stable component of signaling games is typically smaller than the set of divine equilibria and present a characterization of the set of stable outcomes in generic signaling games. Copyright 1987 by The Econometric Society.
Global games are games of incomplete information whose type space is determined by the players each observing a noisy signal of the underlying state. With strategic complementarities, global games often have a unique, dominance solvable equilibrium, allowing analysis of a number of economic models of coordination failure. For symmetric binary action global games, equilibrium strategies in the limit (as noise becomes negligible) are simple to characterize in terms of 'diffuse' beliefs over the actions of others. We describe a number of economic applications that fall in this category. We also explore the distinctive roles of public and private information in this setting, review results for general global games, discuss the relationship between global games and a literature on higher order beliefs in game theory and describe the relationship to local interaction games and dynamic games with payoff shocks.
A model of sequential bargaining with one-sided incomplete information is analyzed where, if an agreement is not reached,
the agents go to court. A “deadline effect” emerges where much settlement occurs just prior to the trial, and many cases proceed
to court. If fixed costs are incurred during each bargaining period, a “U-shaped” pattern of settlement emerges. These patterns
persist in the limit as the time between offers approaches zero. A model with an endogenous trial date is also considered,
and it is shown that even with complete information, there exist inefficient equilibria where disputes are resolved in court.
This article examines the conflict of interest between shareholders and bondholders in a setting in which firms can renegotiate the terms of existing debt with public debtholders. In particular, we consider one of the most common types of debt restructuring: the exit‐exchange offer. Our analysis explores the relation between exit‐exchange offers and investment choice by the manager, and it concludes that managers, acting strategically on behalf of shareholders, may select inefficient investment projects in order to enhance their bargaining position vis‐a‐vis creditors. Holding the upside potential of an investment project fixed, managers/shareholders prefer projects with lower payoffs in states of bankruptcy because it induces individual bondholders to accept poorer terms in a debt‐for‐debt exit‐exchange offer, thus generating a greater residual for shareholders in states of solvency. Additionally, we show how the investment inefficiencies in our analysis depend on (i) the inability of bondholders to coordinate their actions; (ii) the ability of managers to commit to suboptimal investment projects; and (iii) the coupling of an individual bondholder's decision to tender and her decision to consent to allow the firm to strip fiduciary covenants. We suggest conditions under which a ban on coupled exit‐exchange offers—or alternatively, constraints on “debt‐for‐debt” exchanges—would be efficiency‐enhancing.
- Morris H Degroot
DeGroot, Morris H. 2004. Optimal Statistical Decisions. Hoboken, NJ: Wiley
Interscience.