Optimal pollution control with distributed delays

We present a model of optimal stock pollution control with general distributed delays in the stock accumulation dynamics. Using generic functional forms and a distribution structure covering a wide range of distributions, we solve analytically the complex dynamic system that arises from the introduction of these distributed delays. From a theoretical standpoint, our contribution extends the dynamic optimization literature that focused on single discrete delays and develops an original method to address control problems written as mixed type functional differential equations with general kernels. Our results show the qualitative impact of acknowledging these distributed delays on the optimal pollution paths dynamics. We study analytically the properties of the dynamics and we identify the conditions for the occurrence of limit cycles. This theoretical work contributes to the design of efficient environmental policies in the presence of complex delays.     

Robust monetary policy in a small open economy

We study how a central bank in a small open economy should conduct monetary policy if it fears that its model is misspecified. Using a new-Keynesian model of a small open economy, we solve analytically for the optimal robust policy rule and the equilibrium dynamics, and we separately analyze the consequences of central bank robustness against misspecification concerning the determination of inflation, output, and the exchange rate. We show that an increase in the preference for robustness makes the central bank respond more aggressively or more cautiously to shocks, depending on the type of shock and the source of misspecification.     

Alliances and negotiations: an incomplete information example

We study a bargaining game between an individual and an ‘alliance’ in the sense of Manzini and Mariotti (J Econ Theory 121:128–41, 2005), in which the opponent of the alliance is incompletely informed about the relative strengths of its members. The best equilibrium outcome for the alliance under a unanimity rule is not attainable with a non-unanimity rule. However, unlike in the complete information model, less than optimal outcomes and delays may occur with positive probability even under unanimity, depending on the prior beliefs and the preferences of the agents. We are grateful to a careful referee for comments. We wish to thank Clara Ponsati for useful comments.     

Self-isolation

We analyze the spread of an infectious disease in a population when individuals strategically choose how much time to interact with others. Individuals are either of the severe type or of the asymptomatic type. Only severe types have symptoms when they are infected, and the asymptomatic types can be contagious without knowing it. In the absence of any symptoms, individuals do not know their type and continuously tradeoff the costs and benefits of self-isolation on the basis of their belief of being the severe type. We show that all equilibria of the game involve social interaction, and we characterize the unique equilibrium in which individuals partially self-isolate at each date. We calibrate our model to the COVID-19 pandemic and simulate the dynamics of the epidemic to illustrate the impact of some public policies.     

Convergence to Walrasian equilibrium with minimal information

We consider convergence to Walrasian equilibrium in a situation where firms know only market price and their own cost function. We term this a situation of minimal information. We model the problem as a large population game of Cournot competition. The Nash equilibrium of this model is identical to the Walrasian equilibrium. We apply the best response (BR) dynamic as our main evolutionary model. This dynamic can be applied under minimal information as firms need to know only the market price and the their own cost to compute payoffs. We show that the BR dynamic converges globally to Nash equilibrium in an aggregative game like the Cournot model. Hence, it converges globally to the Walrasian equilibrium under minimal information. We extend the result to some other evolutionary dynamics using the method of potential games.

     

Investment in a New Technology as a Signal of Firm Value Under Regulatory Opportunism

We examine the question of whether a regulated firm that makes a long-term investment in infrastructure can credibly signal its private information regarding the future demand for its output to the capital market. We show that necessary conditions for a separating equilibrium in which the magnitude of investment signals high future demand may include a low degree of managerial myopia, large variability of future demand, a lenient regulatory climate, and low sunk cost. Our model suggests that in estimating valuation models of regulated firms it is important to separate firms into two groups: firms for which a separating equilibrium is likely to obtain and firms for which the equilibrium is likely to be pooling. The market value of a firm in the first group is positively correlated with its level of investment, but uncorrelated with the level of actual demand, whereas for the second group the opposite holds.     

Oligopoly models with different learning and production time scales

We propose a modelling approach to study Cournotian oligopolies of boundedly rational firms which continuously update production decisions on the basis of information collected periodically. The model consists of a system of differential equations with piecewise constant arguments, which can be recast into a system of difference equations. Considering different economic settings, we study the local stability of equilibrium, proving the destabilizing role of the time lag between two consecutive learning activities. We investigate some particular families of oligopolies showing the occurrence of both flip and Neimark–Sacker bifurcations, as well as the evidence of multistability with the coexistence between different attractors, occurring when oligopolies consisting of both technologically different and identical firms are studied.     

Non-smooth dynamics and multiple equilibria in a Cournot–Ramsey model with endogenous markups

We consider a Ramsey model with a continuum of Cournotian industries where free entry generates an endogenous markup. The model produces two different regimes, monopolistic and Cournotian monopolistic competition, resulting in non-smooth dynamics. We analyze the global dynamics of the model, demonstrating it may exhibit heteroclinic orbits connecting multiple equilibria. Small transitory changes in parameters can lead to large permanent effects and there can be a poverty trap separating a low-capital and high-markup equilibrium from a high-capital low-markup equilibrium. We apply results from the mathematics of non-smooth dynamic systems, which provide a more general framework for understanding regime switching.     

Learning and coordination with dispersed information

We analyse adaptive learning in a model of incomplete and dispersed information, with externalities and strategic interactions. We build on the framework proposed by Angeletos and Pavan (2007a) and extend it to a dynamic multi-period setting where agents need to learn to coordinate. We derive conditions under which adaptive learning obtains in such setting and show that, when actions are strategic substitutes, the information structure affects the speed of convergence: while more precise private information is beneficial, better public information has negative effects. We also show that adaptive learning dynamics converge to the Bayesian Nash equilibrium, which means that agents can learn to act strategically by relying only on observable (exogenous) information.     

Cournot oligopoly models with time delays

In this paper a system of competing firms is considered in which adjustments of output are subject to delays. Under the Cournot strategy, stability of the oligopoly problem is considered. If each firm calculates its optimal output based on a knowledge of its own production at that time, and of its competitor's outputs at a previous time, stability is not affected by the information delays. However, if all the information available to each firm is subject to a delay, then stability is affected, and the likelihood of stability increases with decreasing delays.     

Competitive market equilibrium under asymmetric information

This paper studies the existence of a competitive market equilibrium under asymmetric information. There are two agents involved in the trading of the risky assets: an “informed” trader and an “ordinary” trader. The market is competitive and the ordinary agent can infer the insider information from the price dynamics of the risky assets. The insider information is considered to be the total supply of the risky assets. The definition of market equilibrium is based on the law of supply-demand as described by a rational expectations equilibrium of the Grossman and Stiglitz (Am Econ Rev 70:393–408, 1980) model. We show that equilibrium can be attained by linear dynamics of an admissible price process of the risky assets for a given linear supply dynamics.      

Labor market search and capital accumulation: Some analytical results

This paper integrates labor market search into an intertemporal utility maximization framework and analytically solves for equilibrium dynamics. The integrated model improves upon a neoclassical model by generating the realistic hump-shaped response of output to a productivity shock and the counterclockwise dynamics of job vacancies and unemployment around the Beveridge curve. In contrast to a standard search model, our model endogenizes agents' reservation wage as the marginal rate of substitution between leisure and consumption, through which agents' intertemporal consumption decision directly affects the labor market behavior. As a result, even a permanent productivity shock generates non-monotonic dynamics in employment.     

Foreclosure with Incomplete Information

We investigate the robustness of the new foreclosure doctrine and its associated welfare implications to the introduction of incomplete information. In particular, we let the upstream firm's marginal cost be private information, unknown to the downstream firms. The previous literature has argued that vertical integration is harmful because it allows an upstream monopolist to limit output to monopoly levels, whereas a disintegrated structure will "over-sell," producing more in equilibrium. By contrast, we find that with incomplete information, high-cost firms will often "under-sell" in equilibrium, that is, supply less than their monopoly output. Low-cost firms continue to over-sell, so all types of firms have a reason to integrate downstream, but this is socially harmful only for low-cost types. For high-cost firms vertical integration can be Pareto-improving, resulting in higher output, profits, and consumer surplus.     

Adaptive learning,endogenous uncertainty,and asymmetric dynamics

I present a simple model where forecasting confidence affects aggregate demand. It is shown that this model has similar stability properties, under statistical and evolutionary learning, as a model without a confidence affect. From this setup, I introduce “Expectational Business Cycles” where output fluctuates due to learning, heterogeneous forecasting models and random changes in the efficient forecasting model. Agents use one of two forecasting models to forecast future variables while heterogeneity is dictated via an evolutionary process. Increased uncertainty, due to a shock to the structure of the economy, may result in a sudden decrease in output. As agents learn the equilibrium, output slowly increases to its equilibrium value. Expectational business cycles tend to arrive faster, last longer and are more severe as agents possess less information.     

Heterogeneous beliefs with herding behaviors and asset pricing in two goods world

We construct a incomplete information equilibrium model with heterogeneous beliefs and herding behaviors to identify their joint effects on the dynamics of asset prices. Herding behaviors make investors revise some of their estimations about expected growth rates of goods streams toward to the other one’s by a manner of weighted average of their own forecast and the other’s. As we expected, herding behaviors generate influences on the Radon Nikodym derivative, that is so-called “sentiment” as in Dumas et al. (2009), and in turn not only impact the dynamics of asset prices but also generate influences on investors’ survivals. We also show that introducing heterogeneous beliefs with herding behaviors permits to explain both the Backus–Smith puzzle and the mixed results about the influences of herding behaviors on asset prices. Moreover, we uncover that herding behaviors have positive influences on stocks’ risk premiums.     

Information or Opinion? Media Bias as Product Differentiation

Two aspects of media bias are important empirically. First, bias is persistent: it does not seem to disappear even when the media is under scrutiny. Second, bias is conflicting: different people often perceive bias in the same media outlet to be of opposite signs. We build a model in which both empirical characteristics of bias are observed in equilibrium. The key assumptions are that the information contained in the facts about a news event may not always be fully verifiable, and consumers have heterogeneous prior views ("ideologies") about the news event. Based on these ingredients of the model, we build a location model with entry to characterize firms' reports in equilibrium, and the nature of bias. When a news item comprises only fully verifiable facts, firms report these as such, so that there is no bias and the market looks like any market for information . When a news item comprises information that is mostly nonverifiable, however, then consumers may care both about opinion and editorials, and a firm's report will contain both these aspects—in which case the market resembles any differentiated product market . Thus, the appearance of bias is a result of equilibrium product differentiation when some facts are nonverifiable. We use the model to address several questions, including the impact of competition on bias, the incentives to report unpopular news, and the impact of owner ideology on bias. In general, competition does not lead to a reduction in bias unless this is accompanied by an increase in verifiability or a smaller dispersion of prior beliefs.     

Multiple equilibria model with intrafirm bargaining and matching frictions

In this paper, we combine a matching model derived from Pissarides (2000) in the case of large firms with monopolistic competition on the product market and the model of intrafirm bargaining à la Stole and Zwiebel (1996). Moreover, we allow for increasing returns to scale in the aggregate production function leading to multiple equilibria. We study the dynamics of such a framework and propose numerical simulations. We show that labour market regulation can make unlikely the occurrence of the Pareto inferior equilibrium and that product market deregulation can have an effect on employment contrary to the expected result when the economy stands at this equilibrium. We give also some policy recommendations to reach the Pareto superior equilibrium when multiple equilibria exist.     

An experiment of social learning with endogenous timing

In this paper, we experimentally investigate a social learning model with endogenous timing. Specifically, we focus on a model, in which two subjects are supposed to make a binary decision. One alternative is a safe action with a fixed payoff, while the other alternative is a risky action. The subjects can make their decisions in three stages. The safe action is reversible, but the risky action is not. A subject who delays his decision can observe the decision of the other subject in the earlier stages, and as a result, acquire more information. We show that players do delay their decisions in order to obtain more information. Furthermore, they delay especially when their private information does not particularly support the risky action. We also find evidence which suggests that risk aversion plays an important role in timing decisions, often leading to ex post inefficient outcomes.     

Technology choice in an evolutionary oligopoly game

In this paper, we propose and analyze a two-stage oligopoly game in which firms first simultaneously choose production technologies and in the second stage simultaneously choose production quantities. After characterizing the Nash equilibrium of the game, we cast our static model in a dynamic setting exploring the stability properties of the market equilibrium in two different cases: (i) exogenously distributed technologies and Cournot adjustments and (ii) endogenously distributed technologies in an infinite population game with Cournot–Nash equilibrium outputs. The main aim of the paper is that of extending the results about Cournot oligopoly stability in an evolutionary setting of heterogeneous decreasing returns-to-scale technologies. We show how the interplay between production decisions and R&D decisions can generate endogenous market fluctuations leading to complex dynamic phenomena.