Fear of Miscoordination and the Robustness of Cooperation in Dynamic Global Games With Exit

This paper develops a framework to assess how fear of miscoordination affects the sustainability of cooperation. Building on theoretical insights from Carlsson and van Damme (1993), it explores the effect of small amounts of private information on a class of dynamic cooperation games with exit. Lack of common knowledge leads players to second guess each other's behavior and makes coordination difficult. This restricts the range of equilibria and highlights the role of miscoordination payoffs in determining whether cooperation is sustainable or not. The paper characterizes the range of perfect Bayesian equilibria as the players' information becomes arbitrarily precise. Unlike in one‐shot two‐by‐two games, the global games information structure does not yield equilibrium uniqueness.     

Repeated Games with Private Monitoring: Two Players

We investigate two‐player infinitely repeated games where the discount factor is less than but close to unity. Monitoring is private and players cannot communicate. We require no condition concerning the accuracy of players' monitoring technology. We show the folk theorem for the prisoners' dilemma with conditional independence. We also investigate more general games where players' private signals are correlated only through an unobservable macro shock. We show that efficiency is sustainable for generic private signal structures when the size of the set of private signals is sufficiently large. Finally, we show that cartel collusion is sustainable in price‐setting duopoly.     

Games with Imperfectly Observable Actions in Continuous Time

This paper investigates a new class of two‐player games in continuous time, in which the players' observations of each other's actions are distorted by Brownian motions. These games are analogous to repeated games with imperfect monitoring in which the players take actions frequently. Using a differential equation, we find the set ℰ(r) of payoff pairs achievable by all public perfect equilibria of the continuous‐time game, where r is the discount rate. The same differential equation allows us to find public perfect equilibria that achieve any value pair on the boundary of the set ℰ(r). These public perfect equilibria are based on a pair of continuation values as a state variable, which moves along the boundary of ℰ(r) during the course of the game. In order to give players incentives to take actions that are not static best responses, the pair of continuation values is stochastically driven by the players' observations of each other's actions along the boundary of the set ℰ(r).     

Reputation for Quality

We propose a model of firm reputation in which a firm can invest or disinvest in product quality and the firm's reputation is defined as the market's belief about this quality. We analyze the relationship between a firm's reputation and its investment incentives, and derive implications for reputational dynamics. Reputational incentives depend on the specification of market learning. When consumers learn about quality through perfect good news signals, incentives decrease in reputation and there is a unique work–shirk equilibrium with ergodic dynamics. When learning is through perfect bad news signals, incentives increase in reputation and there is a continuum of shirk–work equilibria with path‐dependent dynamics. For a class of imperfect Poisson learning processes and low investment costs, we show that there exists a work–shirk equilibrium with ergodic dynamics. For a subclass of these learning processes, any equilibrium must feature working at all low and intermediate levels of reputation and shirking at the top.     

Distributed Decision‐Making in Supply Chains and Private E‐Marketplaces

This paper develops a distributed decision‐making framework for the players in a supply chain or a private e‐marketplace to collaboratively arrive at a global Pareto‐optimal solution. In this model, no player has complete knowledge about all the costs and constraints of the other players. The decision‐making framework employs an iterative procedure, based on the Integer L‐shaped method, in which a master problem is solved to propose global solutions, and each player uses his local problems to construct feasibility and optimality cuts on the master problem. The master problem is modeled as a mixed‐integer program, and the players' local problems are formulated as linear programs. Collaborative planning scenarios in private e‐marketplaces and in supply chains were formulated and solved for test data. The results show that this distributed model is able to achieve near‐optimal solutions considerably faster than the traditional centralized approach.     

Belief‐Free Equilibria in Games With Incomplete Information

We define belief‐free equilibria in two‐player games with incomplete information as sequential equilibria for which players' continuation strategies are best replies after every history, independently of their beliefs about the state of nature. We characterize a set of payoffs that includes all belief‐free equilibrium payoffs. Conversely, any payoff in the interior of this set is a belief‐free equilibrium payoff. The characterization is applied to the analysis of reputations.     

Axiomatic Equilibrium Selection for Generic Two‐Player Games

For a finite game with perfect recall, a refinement of its set of Nash equilibria selects closed connected subsets, called solutions. Assume that each solution's equilibria use undominated strategies and some of its equilibria are quasi‐perfect, and that all solutions are immune to presentation effects; namely, if the game is embedded in a larger game with more pure strategies and more players such that the original players' feasible mixed strategies and expected payoffs are preserved regardless of what other players do, then the larger game's solutions project to the original game's solutions. Then, for a game with two players and generic payoffs, each solution is an essential component of the set of equilibria that use undominated strategies, and thus a stable set of equilibria as defined by Mertens (1989).     

Reputation in Continuous‐Time Games

We study reputation dynamics in continuous‐time games in which a large player (e.g., government) faces a population of small players (e.g., households) and the large player's actions are imperfectly observable. The major part of our analysis examines the case in which public signals about the large player's actions are distorted by a Brownian motion and the large player is either a normal type, who plays strategically, or a behavioral type, who is committed to playing a stationary strategy. We obtain a clean characterization of sequential equilibria using ordinary differential equations and identify general conditions for the sequential equilibrium to be unique and Markovian in the small players' posterior belief. We find that a rich equilibrium dynamics arises when the small players assign positive prior probability to the behavioral type. By contrast, when it is common knowledge that the large player is the normal type, every public equilibrium of the continuous‐time game is payoff‐equivalent to one in which a static Nash equilibrium is played after every history. Finally, we examine variations of the model with Poisson signals and multiple behavioral types.     

Efficiency in Repeated Games Revisited: The Role of Private Strategies

Most theoretical or applied research on repeated games with imperfect monitoring has focused on public strategies: strategies that depend solely on the history of publicly observable signals. This paper sheds light on the role of private strategies: strategies that depend not only on public signals, but also on players' own actions in the past. Our main finding is that players can sometimes make better use of information by using private strategies and that efficiency in repeated games can be improved. Our equilibrium private strategy for repeated prisoners' dilemma games consists of two states and has the property that each player's optimal strategy is independent of the other player's state.     

Cursed Equilibrium

There is evidence that people do not fully take into account how other people's actions depend on these other people's information. This paper defines and applies a new equilibrium concept in games with private information, cursed equilibrium, which assumes that each player correctly predicts the distribution of other players' actions, but underestimates the degree to which these actions are correlated with other players' information. We apply the concept to common‐values auctions, where cursed equilibrium captures the widely observed phenomenon of the winner's curse, and to bilateral trade, where cursedness predicts trade in adverse‐selections settings for which conventional analysis predicts no trade. We also apply cursed equilibrium to voting and signalling models. We test a single‐parameter variant of our model that embeds Bayesian Nash equilibrium as a special case and find that parameter values that correspond to cursedness fit a broad range of experimental datasets better than the parameter value that corresponds to Bayesian Nash equilibrium.     

ON‐THE‐JOB SEARCH AND MORAL HAZARD

We analyze the interaction between intertemporal incentive contracts and search frictions associated with on‐the‐job search. In our model, agency problems call for wage contracts with deferred compensation. At the same time workers do on‐the‐job search. Deferred compensation improves workers' incentives to exert effort but distorts their on‐the‐job search decisions. We show that deferred compensation is less attractive when the value to the worker–firm pair of on‐the‐job search is high. Moreover, the interplay between search frictions and wage contracts creates feedback effects. If firms in equilibrium use contracts with deferred compensation, fewer firms with vacancies enter the on‐the‐job search market, and this in turn reduces the distortions created by deferred compensation. These feedback effects between the incentive contracts used and the activity level in the search markets can lead to multiple equilibria: a low‐turnover equilibrium where firms use deferred compensation, and a high‐turnover equilibrium where they do not. Furthermore, the model predicts that firms are more likely to use deferred compensation when search frictions are high and when the gains from on‐the‐job search are small.     

Sequential Estimation of Dynamic Discrete Games

This paper studies the estimation of dynamic discrete games of incomplete information. Two main econometric issues appear in the estimation of these models: the indeterminacy problem associated with the existence of multiple equilibria and the computational burden in the solution of the game. We propose a class of pseudo maximum likelihood (PML) estimators that deals with these problems, and we study the asymptotic and finite sample properties of several estimators in this class. We first focus on two‐step PML estimators, which, although they are attractive for their computational simplicity, have some important limitations: they are seriously biased in small samples; they require consistent nonparametric estimators of players' choice probabilities in the first step, which are not always available; and they are asymptotically inefficient. Second, we show that a recursive extension of the two‐step PML, which we call nested pseudo likelihood (NPL), addresses those drawbacks at a relatively small additional computational cost. The NPL estimator is particularly useful in applications where consistent nonparametric estimates of choice probabilities either are not available or are very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate these methods in Monte Carlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries.     

Competition in Financial Innovation

This paper examines the incentives offered by frictionless markets to innovate asset‐backed securities by owners who maximize the assets' values. Assuming identical preferences across investors with heterogeneous risk‐sharing needs, we characterize economies in which competition provides insufficient incentives to innovate so that, in equilibrium, financial markets are incomplete in all (pure strategy) equilibria, even when innovation is essentially costless. Thus, value maximization does not generally result in complete markets.     

An Efficient Dynamic Mechanism

This paper constructs an efficient, budget‐balanced, Bayesian incentive‐compatible mechanism for a general dynamic environment with quasilinear payoffs in which agents observe private information and decisions are made over countably many periods. First, under the assumption of “private values” (other agents' private information does not directly affect an agent's payoffs), we construct an efficient, ex post incentive‐compatible mechanism, which is not budget‐balanced. Second, under the assumption of “independent types” (the distribution of each agent's private information is not directly affected by other agents' private information), we show how the budget can be balanced without compromising agents' incentives. Finally, we show that the mechanism can be made self‐enforcing when agents are sufficiently patient and the induced stochastic process over types is an ergodic finite Markov chain.     

EFFICIENT TUITION FEES AND EXAMINATIONS

We assume that students observe only a private, noisy signal of their ability and that universities can condition admission decisions on the results of noisy tests. If the university observes a private signal of each student's ability, which is soft information, then asymmetries of information are two‐sided, and the optimal admission policy involves a mix of pricing and pre‐entry selection, based on the university's private information. In contrast, if all test results are public knowledge, then there is no sorting on the basis of test scores: Tuition alone does the job of implementing an optimal degree of student self‐selection. These results do not depend on the existence of peer effects. The optimal tuition follows a classic marginal social‐cost pricing rule. (JEL: D82, H42, I22, J24)     

The Effect of Changes in Risk Attitude on Strategic Behavior

We study families of normal‐form games with fixed preferences over pure action profiles but varied preferences over lotteries. That is, we subject players' utilities to monotone but nonlinear transformations and examine changes in the rationalizable set and set of equilibria. Among our results: The rationalizable set always grows under concave transformations (risk aversion) and shrinks under convex transformations (risk love). The rationalizable set reaches an upper bound under extreme risk aversion, and lower bound under risk love, and both of these bounds are characterized by elimination processes. For generic two‐player games, under extreme risk love or aversion, all Nash equilibria are close to pure and the limiting set of equilibria can be described using preferences over pure action profiles.     

Signaling and Election Motivations in a Voting Model with Common Values and Responsive Candidates

In this paper we focus on strategic voting behavior when both an election and a signaling motivation affect voters' behavior. We analyze a model of elections with two candidates competing on a one‐dimensional policy space. Voters are privately and imperfectly informed about a common shock affecting the electorate's preferences. Candidates are assumed to choose policy in response to information gleaned from election results and according to exogenous factors that may lead to polarization in candidates' policy choices. We analyze a subset of symmetric equilibria in which strategies are symmetric to candidates' names and private signals (CSS equilibria). We show that signaling and election motivations pull voters to vote in different directions. We provide conditions that show the relation between the amount of information aggregated in the election and the motivation that influences voting behavior the most. Finally, we show that when candidates are responsive and polarized, all CSS equilibria are inefficient in the limit.     

The Economic Value of Market Information for Farmers in Developing Economies

In developing countries, farmers lack information for making informed production, manufacturing/selling decisions to improve their earnings. To alleviate poverty, various non‐governmental organizations (NGOs) and for‐profit companies have developed different ways to distribute information about market price, crop advisory and farming technique to farmers. We investigate a fundamental question: will information create economic value for farmers? We construct a stylized model in which farmers face an uncertain market price (demand) and must make production decisions before the market price is realized. Each farmer has an imprecise private signal and an imprecise public signal to estimate the actual market price. By examining the equilibrium outcomes associated with a Cournot competition game, we show that private signals do create value by improving farmers' welfare. However, this value deteriorates as the public signal becomes available (or more precise). In contrast, in the presence of private signals, the public signal does not always create value for the farmers. Nevertheless, both private and public signals will reduce price variation. We also consider two separate extensions that involve non‐identical private signal precisions and farmers' risk‐aversion, and we find that the same results continue to hold. More importantly, we find that the public signal can reduce welfare inequality when farmers have non‐identical private signal precisions. Also, risk‐aversion can dampen the value created by private or public information.     

Insurance,Public Assistance,and Household Flood Risk Reduction: A Comparative Study of Austria,England, and Romania

In light of increasing losses from floods, many researchers and policymakers are looking for ways to encourage flood risk reduction among communities, business, and households. In this study, we investigate risk‐reduction behavior at the household level in three European Union Member States with fundamentally different insurance and compensation schemes. We try to understand if and how insurance and public assistance influence private risk‐reduction behavior. Data were collected using a telephone survey (n = 1,849) of household decisionmakers in flood‐prone areas. We show that insurance overall is positively associated with private risk‐reduction behavior. Warranties, premium discounts, and information provision with respect to risk reduction may be an explanation for this positive relationship in the case of structural measures. Public incentives for risk‐reduction measures by means of financial and in‐kind support, and particularly through the provision of information, are also associated with enhancing risk reduction. In this study, public compensation is not negatively associated with private risk‐reduction behavior. This does not disprove such a relationship, but the negative effect may be mitigated by factors related to respondents' capacity to implement measures or social norms that were not included in the analysis. The data suggest that large‐scale flood protection infrastructure creates a sense of security that is associated with a lower level of preparedness. Across the board there is ample room to improve both public and private policies to provide effective incentives for household‐level risk reduction.     

TRUST,COORDINATION, AND THE INDUSTRIAL ORGANIZATION OF POLITICAL ACTIVISM

We study political activism by several interest groups with private signals. When their ideological distance to the policymaker is small, a “low‐trust” regime prevails: agents frequently lobby even when it is unwarranted, taking advantage of the confirmation provided by others' activism; conversely, the policymaker responds only to generalized pressure. When ideological distance is large, a “high‐trust” regime prevails: lobbying behavior is disciplined by the potential contradiction from abstainers, and the policymaker's response threshold is correspondingly lower. Within some intermediate range, both equilibria coexist. We then study the optimal organization of influence activities, contrasting welfare levels when interest groups act independently and when they coordinate. (JEL: D72, D78, D82)