Imperfect Monitoring Research Articles

Collusion Under Imperfect Monitoring with Asymmetric Firms

AbstractWe explore the effects of asymmetries in capacity constraints on collusion where market demand is uncertain and where firms’ sales and prices are private information. We show that all firms can infer when at least one firm's sales are below some firm‐specific ‘trigger level.’ When firms use this public information to monitor the collusive agreement, price wars may occur on the equilibrium path. Symmetry facilitates collusion but, if price wars are sufficiently long, then the optimal collusive prices of symmetric capacity distributions are lower on average than the competitive prices of asymmetric capacity distributions. We draw conclusions for merger policy.

The Political Economy of Dynamic Elections: Accountability, Commitment, and Responsiveness

We survey the literature on dynamic elections in the traditional settings of spatial preferences and rent seeking under perfect and imperfect monitoring of politicians. We define stationary electoral equilibrium, which encompasses notions used by Barro (1973), Ferejohn (1986), Banks and Sundaram (1998), and others. We show that repeated elections mitigate the commitment problems of politicians and voters, and that a responsive democracy result holds under general conditions. Term limits, however, attenuate the responsiveness finding. We also touch on related applied work, and we point to areas for fruitful future research, including the connection between dynamic models of politics and economics. ( JEL D72, D82, D83)

Jammer-Type Estimation in LTE With a Smart Jammer Repeated Game

Long-term evolution (LTE)/LTE-Advanced (LTE-A) networks are known to be vulnerable to denial-of-service (DOS) and loss-of-service attacks from smart jammers. The interaction between the network and the smart jammer has been modeled as an infinite-horizon general-sum (nonzero-sum) Bayesian game with asymmetric information, with the network being the uninformed player. Although significant work has been done on optimal strategy computation and control of information revelation of the informed player in repeated asymmetric information games, it has been limited to zero-sum games with perfect monitoring. Recent progress on the strategy computation of the uninformed player is also limited to zero-sum games with perfect monitoring and is focused on expected payoff formulations. Since the proposed formulation is a general-sum game with imperfect monitoring, existing formulations cannot be leveraged for estimating true state of nature (the jammer type). Hence, a threat-based mechanism is proposed for the uninformed player (the network) to estimate the informed player's type (jammer type). The proposed mechanism helps the network resolve uncertainty about the state of nature (jammer type) so that it can compute a repeated-game strategy conditioned on its estimate. The proposed algorithm does not rely on the commonly assumed “full monitoring” premise and uses a combination of threat-based mechanism and nonparametric estimation to estimate the jammer type. In addition, it requires no explicit feedback from the network users, nor does it rely on a specific distribution (e.g., Gaussian) of test statistic. It is shown that the proposed algorithm's estimation performance is quite robust under realistic modeling and observational constraints, despite all the aforementioned challenges.

UI ELIGIBILITY RULE, MORAL HAZARD, AND OPTIMAL UNEMPLOYMENT TRANSFER SCHEME

This paper derives the optimal unemployment insurance (UI) transfer scheme, UI benefits, and UI contribution fees: When a worker has to earn his or her UI eligibility through work, the UI benefits do not last forever, and the UI agency has imperfect monitoring power on the strategic behavior of the worker. We show that the consideration of the UI eligibility rule generates the effective entitlement effect, which serves as an additional incentive device and alters the nature of the optimal UI transfer scheme established in literature. In contrast with previous studies, we find that when the effective entitlement effect is large, it completely removes the moral hazards in job searches, job acceptances, and job quits. As a result, the optimal UI benefits and contribution fees become constant. Calibrated to the data in the United States, the model reproduces some key features of the existing UI system.

CAPITAL DESTRUCTION, JOBLESS RECOVERIES, AND THE DISCIPLINE DEVICE ROLE OF UNEMPLOYMENT

I consider an economy growing along the balanced growth path that is hit by an adverse shock to its capital accumulation process. The model integrates efficiency wages due to imperfect monitoring of the quality of labor in a search and matching framework with methods of dynamic general equilibrium analysis. I show that, depending on the firms' abilities to assess workers' performance, the discipline device role of unemployment may account for sharp declines in employment and jobless recoveries driven by exceptional increases in the work effort of employees. The model also explains why rigid real wages may prevail in equilibrium: the large movements in unemployment are indeed associated with real wage rigidity, which is generated endogenously by efficiency wages.

Two-Sided Learning and the Ratchet Principle

I study a class of continuous-time games of learning and imperfect monitoring. A long-run player and a market share a common prior about the initial value of a Gaussian hidden state, and learn about its subsequent values by observing a noisy public signal. The long-run player can nevertheless control the evolution of this signal, and thus affect the market’s belief. The public signal has an additive structure, and noise is Brownian. I derive conditions for an ordinary differential equation to characterize equilibrium behavior in which the long-run player’s actions depend on the history of the game only through the market’s correct belief. Using these conditions, I demonstrate the existence of pure-strategy equilibria in Markov strategies for settings in which the long-run player’s flow utility is nonlinear. The central finding is a learning-driven ratchet principle affecting incentives. I illustrate the economic implications of this principle in applications to monetary policy, earnings management, and career concerns.

Correlation and unmediated cheap talk in repeated games with imperfect monitoring

This paper studies n-player \((n\ge 3)\) undiscounted repeated games with imperfect monitoring. We prove that all uniform communication equilibrium payoffs of a repeated game can be obtained as Nash equilibrium payoffs of the game extended by unmediated cheap talk. We also show that all uniform communication equilibrium payoffs of a repeated game can be reached as Nash equilibrium payoffs of the game extended by a pre-play correlation device and a cheap-talk procedure that only involves public messages; furthermore, in the case of imperfect public and deterministic signals, no cheap talk is conducted on the equilibrium path.

Macro-Environmental Forces that Drive Carmakers to Misconduct: Intense Competition and Stringent Standards

This paper investigates how tightening standards can result in greater non-compliance, especially when the market and regulatory interests are misaligned. We confirm a causal relationship that explains the highly publicized auto industry non-compliance phenomenon where on-road NOx emissions exceeded standards. Based on a 15-year on-road vehicle emissions dataset covering 148,837 vehicles from 42 automakers in the EU, we use Regression Discontinuity to identify the causal impact of standards tightening on non-compliance by controlling other confounding factors. Our results suggest that in the absence of effective monitoring, tightening standards directly drives up automakers’ non-compliance. Furthermore, we find that automakers facing more intense substitution pressure from competitors or with less advanced emissions control technology have a higher non-compliance rate. Our findings speak to both policymakers as well as managers in the private sector. When setting limit-based performance goals in situations with conflicting interests and imperfect monitoring, they should anticipate non-compliance from the regulated parties. Our results suggest that tightening standards in such situations should be accompanied by stricter monitoring or other actions that discourage non-compliance.

Economic analysis of e-waste market

Despite international regulations that prohibit the trans-boundary movement of electronic and electric waste (e-waste), non-reusable e-waste is often illegally mixed with reusable e-waste and results in being sent to developing countries. As developing countries are not well prepared to properly manage e-waste, this illegal trade has important negative externalities and creates ‘environmental injustice’. The two main information problems on the e-waste market are imperfect monitoring and imperfect information on the so-called ‘degree of purity’ of the e-waste. In this paper, we use a simple bilateral North–South trade model and show that there exists an alternative e-waste market that is better than the standard e-waste market for developing countries. This alternative e-waste market is a joint trade in reusable and non-reusable e-waste. In both cases, we consider demand and supply sides, plus the equilibrium of the e-waste market to show that the alternative market that we propose is better for developing countries.

Better stuck together or free to go? Of the stability of cooperation when individuals have outside options

How do outside options affect cooperation? We examine the stability of cooperation and the reasons for exit in public projects with stochastic outcomes, imperfect monitoring and an exit option. We find that treatments with high barriers to exit generate higher welfare overall as they foster stability and prevent inefficient separation of pairs. There is excessive exit in treatments with low barriers to exit, driven in part by an overestimate of the likelihood that the peer will leave and a desire not to be left alone in the public project. We contrast long-term “strategic” and short-term “egoistic” drivers of exit and find that short-term cost-benefit considerations play a more important role in treatments with lower barriers to exit.

Imperfect Monitoring of Job Search: Structural Estimation and Policy Design

We build and estimate a nonstationary structural job search model that incorporates the main stylized features of a typical job search monitoring scheme in unemployment insurance (UI) and acknowledges that search effort and requirements are measured imperfectly. On the basis of Belgian data, monitoring is found to affect search behavior only weakly because assessments were scheduled late and infrequently, the monitoring technology was not sufficiently precise, and lenient Belgian UI results in caseloads that are less responsive to incentives than elsewhere. Simulations show how changing the aforementioned design features can enhance effectiveness and that precise monitoring is key in this.

Imperfect Monitoring of Job Search: Structural Estimation and Policy Design

We build and estimate a non-stationary structural job search model that incorporates the main stylized features of a typical job search monitoring scheme in unemployment insurance (UI) and acknowledges that search effort and requirements are measured imperfectly. Based on Belgian data, monitoring is found to affect search behavior only weakly, because (i) assessments were scheduled late and infrequently; (ii) the monitoring technology was not sufficiently precise, (iii) lenient Belgian UI results in caseloads that are less responsive to incentives than elsewhere. Simulations show how changing the aforementioned design features can enhance effectiveness and that precise monitoring is key in this.

Imperfect Monitoring of Job Search: Structural Estimation and Policy Design

Imperfect Monitoring of Job Search: Structural Estimation and Policy Design

An Antifolk Theorem for Large Repeated Games

In this article, we study infinitely repeated games in settings of imperfect monitoring. We first prove a family of theorems showing that when the signals observed by the players satisfy a condition known as (ϵ, γ)-differential privacy, the folk theorem has little bite: for values of ϵ and γ sufficiently small, for a fixed discount factor, any equilibrium of the repeated game involves players playing approximate equilibria of the stage game in every period. Next we argue that in large games ( n player games in which unilateral deviations by single players have only a small impact on the utility of other players), many monitoring settings naturally lead to signals that satisfy (ϵ, γ)-differential privacy for ϵ and γ tending to zero as the number of players n grows large. We conclude that in such settings, the set of equilibria of the repeated game collapses to the set of equilibria of the stage game. Our results nest and generalize previous results of Green [1980] and Sabourian [1990], suggesting that differential privacy is a natural measure of the “largeness” of a game. Further, techniques from the literature on differential privacy allow us to prove quantitative bounds, where the existing literature focuses on limiting results.

Delayed Review in Repeated Relationships

Many theoretical results rely on delayed review of imperfect information for sustaining cooperative outcomes. Using two laboratory experiments, this paper shows that delayed review can hinder cooperation in practice through a mechanism not captured by standard theory. The experiments make use of two different but closely related environments: a repeated prisoner's dilemma game with imperfect monitoring and pre-programmed grim triggers (but flexibility about what action to choose before the trigger is set off), and a decision problem played against a computer with a known strategy. At odds with the theoretical predictions, subjects cooperate less in both experiments when information is delayed. The results can be rationalized by a simple stochastic choice model with a bias toward survival.

How fast do equilibrium payoff sets converge in repeated games?

We provide tight bounds on the rate of convergence of the equilibrium payoff sets for repeated games under both perfect and imperfect public monitoring. The distance between the equilibrium payoff set and its limit vanishes at rate (1−δ)1/2 under perfect monitoring, and at rate (1−δ)1/4 under imperfect monitoring. For strictly individually rational payoff vectors, these rates improve to 0 (i.e., all strictly individually rational payoff vectors are exactly achieved as equilibrium payoffs for δ high enough) and (1−δ)1/2, respectively.

How Fast Do Equilibrium Payoff Sets Converge in Repeated Games?

We provide tight bounds on the rate of convergence of the equilibrium payoff sets for repeated games under both perfect and imperfect public monitoring. The distance between the equilibrium payoff set and its limit vanishes at rate (1 - delta)^{1/2} under perfect monitoring, and at rate (1 - delta)^{1/4} under imperfect monitoring. For strictly individually rational payoff vectors, these rates improve to 0 (i.e., all strictly individually rational payoff vectors are exactly achieved as equilibrium payoffs for delta high enough) and (1 - delta)^{1/2}, respectively.

Sniffer Channel Assignment With Imperfect Monitoring for Cognitive Radio Networks

Sniffer channel assignment (SCA) is a fundamental building block for wireless data capture, which is essential for traffic monitoring and network forensics. Most of the existing SCA approaches for cognitive radio networks (CRNs) adopt optimization-based methods and rely on the prior knowledge of the secondary user (SU) activities. To relax this constraint, learning-based methods have been recently developed; however, there is still insufficient theoretical understanding within the learning framework for SCA. In this paper, we aim to maximize the total amount of the captured SU traffic, and we formulate the SCA problem as a nonstochastic/adversarial multiarmed bandit problem. Moreover, the inherent error in wireless capturing, i.e., imperfect monitoring, is considered in our model. We propose two online learning algorithms for the SCA scenarios with and without channel switching costs, respectively, and their regret performances are proved uniformly sublinear in time and polynomial in the number of channels. The numerical evaluation shows, in addition to their robust regret performances, the proposed algorithms greatly outperform the existing SCA approaches in the amount of effectively captured SU traffic.

The Sorry Clause

When players face uncertainty in choosing actions, undesirable outcomes cannot be avoided. Accidental defections caused by uncertainty, that does not depend on the level of care, require a mechanism to reconcile the players. This paper shows the existence of a perfect sorry equilibrium in a game of imperfect public monitoring. In the sorry equilibrium, costly apology is self-imposed in case of accidental defections, making private information public and allowing cooperation to resume. Cost of the apology required to sustain this equilibrium is calculated, the efficiency characteristics of the equilibrium evaluated and outcomes compared to those from other bilateral social governance mechanisms and formal legal systems. It is argued that with the possibility of accidental defections, other social mechanisms have limitations, while formal legal systems can generate perverse incentives. Therefore, apologies can serve as a useful economic governance institution.

Effect of Ban on Exports Containing Child Labour in a Dynamic Model in Presence of Imperfect Monitoring

We build up a simple overlapping generations’ model where parents derive utility from their children’s education and use this framework to understand and analyze the implications of a ban on exports with child labour content. Since perfect monitoring seems unrealistic, we develop a model with imperfect monitoring. The export industry is competitive and therefore zero-profit condition holds. The country under consideration is assumed to be a small open economy and therefore faces a fairly elastic demand. Then, a ban on child labour imposed by the importing countries will increase the cost of employing child labour and will discourage the producers in that sector to use child labour. The final effect on the incidence of child labour will however depend on whether the aggregate supply of unskilled labour by child workers in the pre-ban equilibrium situation is greater or less than the demand for unskilled labour in the import-competing sector.