A comment on "Rational learning lead to nash equilibrium" by professors Ehud Kalai and Ehud Lehrer

Kalai and Lebrer (93a, b) have recently show that for the case of infinitely repeated games, a coordination assumption on beliefs and optimal strategies ensures convergence to Nash equilibrium. In this paper, we show that for the case of repeated games with long (but finite) horizon, their condition does not imply approximate Nash equilibrium play. Recently Kalai and Lehrer (93a, b) proved that a coordination assumption on beliefs and optimal strategies, ensures that pIayers of an infinitely repeated game eventually pIay 'E-close" to an E-Nash equilibrium. Their coordination assumption requires that if players believes that certain set of outcomes have positive probability then it must be the case that this set of outcomes have, in fact, positive probability. This coordination assumption is called absolute continuity. For the case of finitely repeated games, the absolute continuity assumption is a quite innocuous assumption that just ensures that pIayers' can revise their priors by Bayes' Law. However, for the case of infinitely repeated games, the absolute continuity assumption is a stronger requirement because it also refers to events that can never be observed in finite time.

Learning from Shocks and the Decision to Open

Two claims pervade the literature on the political economy of market reforms: that economic crises cause reforms; and that crises matter because they bring into question the validity of the economic model held to be responsible for them. Economic crises are said to spur a process of learning that is conducive to the abandonment of failing models and to the adoption of successful models. But although these claims have become the conventional wisdom, they have been hardly tested empirically due to the lack of agreement on what constitutes a crisis and to difficulties in measuring learning from them. I propose a model of rational learning from experience and apply it to the decision to open the economy. Using data from 1964 through 1990, I show that learning from the 1982 debt crisis was relevant to the first wave of adoption of an export promotion strategy, but learning was conditional on the high variability of economic outcomes in countries that opened up to trade. Learning was also symbolic in that the sheer number of other countries that liberalized was a more important driver of others’ decisions to follow suit.

Recurrent hyperinflations and learning

This paper uses a model of boundedly rational learning to accountfor the observations of recurrent hyperinflations in the lastdecade. We study a standard monetary model where the fullyrational expectations assumption is replaced by a formaldefinition of quasi-rational learning. The model under learningis able to match remarkably well some crucial stylized factsobserved during the recurrent hyperinflations experienced byseveral countries in the 80's. We argue that, despite being asmall departure from rational expectations, quasi-rationallearning does not preclude falsifiability of the model and itdoes not violate reasonable rationality requirements.

'Biased' Risk Perceptions of Longevity and Disability in Old Age

Rational learning theories postulate that information channels and cognitive biases such as individual optimism may influence an individual¿s assessment of the risk of undesired events, especially with regard to those that have a cumulative nature. This is the case with disability in old age, which may take place upon survival to an advanced age, and such factors have been regarded as responsible for certain individual behaviours (for example, the limited incidence of insurance purchase). This paper examines the determinants of individual perceptions with regard to disability in old age and longevity. The cumulative nature of such perceptions of risk is tested, and potential biases are identified, including `optimism¿ and a set of information determinants. Empirical evidence from a representative survey of Catalonia is presented to illustrate these effects. The findings from this research suggest a significant overestimation of disability in old age, yet this is not the case with longevity. Furthermore, individual perceptions with regard to disability in old age, unlike those with regard to longevity, exhibit on aggregate an `optimistic bias¿ and, are perceived as `cumulative risks¿. Gender influences the perceived risk of disability in old age at a population level but not at the individual level, and the opposite holds true for age. Finally, self-reported health status is the main variable behind risk perceptions at both the individual and population level.

'Biased' Risk Perceptions of Longevity and Disability in Old Age

Rational learning theories postulate that information channels and cognitive biases such as individual optimism may influence an individual¿s assessment of the risk of undesired events, especially with regard to those that have a cumulative nature. This is the case with disability in old age, which may take place upon survival to an advanced age, and such factors have been regarded as responsible for certain individual behaviours (for example, the limited incidence of insurance purchase). This paper examines the determinants of individual perceptions with regard to disability in old age and longevity. The cumulative nature of such perceptions of risk is tested, and potential biases are identified, including `optimism¿ and a set of information determinants. Empirical evidence from a representative survey of Catalonia is presented to illustrate these effects. The findings from this research suggest a significant overestimation of disability in old age, yet this is not the case with longevity. Furthermore, individual perceptions with regard to disability in old age, unlike those with regard to longevity, exhibit on aggregate an `optimistic bias¿ and, are perceived as `cumulative risks¿. Gender influences the perceived risk of disability in old age at a population level but not at the individual level, and the opposite holds true for age. Finally, self-reported health status is the main variable behind risk perceptions at both the individual and population level.

Elaboração de um curso interativo voltado ao aprendizado de um sistema aplicativo em Odontologia, utilizando a plataforma Moodle

In universities, in any type of faculty or research institute, it is possible to observe innumerable informatics applications: database management, organization of catalogues, expediting diagnoses and many other applications. Within this context, distance learning could facilitate the learning of various professions. Distance education is the process of teaching-learning and the professional has to be prepared to deal with the new tools that are made available, using them to his/her benefit, and consequently in his/her professional capacity, to guarantee greater productivity and interaction with the various spheres in the work field. Methods: The aim of this research is to develop a course on the use of the Dentistry software application EasyDental, using the teaching at a distance methodology by means of the Moodle platform. The proposed course was composed of 14 modules, in order to enable a progressive and a rational learning. Conclusion: It could be concluded that this platform allowed the preparation of the proposed distance course, in a practical and versatile manner, considering the resources and activities it has. However, to use this platform, one must have dominion of the basic concepts of informatics, and the tools of the Moodle platform.

Um estudo dos avanços conceituais dos estudantes sobre calor e temperatura decorrentes da aplicação de uma estratégia de ensino inspirada na teoria de Lakatos

We report here a study about the application of a formal teaching strategy about heat and temperature concepts applied among high school students. The strategy belongs to a research trend which deals with epistemological analogies and has an innovative character related to the students’ preparation for rational debates between conceptions and/or rival theories, using didactical rational reconstruction (DRR) which aims to help scientific concepts rational learning. We investigate the outcomes of this preparation and students’ conceptual development, analyzed through a qualitative-interpretative methodological approach.

Information and communication technologies in education – a web-based intelligent tutoring system on teaching and learning electrical project

Electrical activity is extremely broad and distinct, requiring by one hand, a deep knowledge on rules, regulations, materials, equipments, technical solutions and technologies and assistance in several areas, as electrical equipment, telecommunications, security and efficiency and rational use of energy, on the other hand, also requires other skills, depending on the specific projects to be implemented, being this knowledge a characteristic that belongs to the professionals with relevant experience, in terms of complexity and specific projects that were made.

Learning the ropes and embracing the rules: CFSP institutions as arenas for learning and strategic socialisation

The aim of this article is to analyse those situations in which learning and socialisation take place within the context of the Common Foreign and Security Policy (CFSP), in particular, at the level of experts in the Council Working Groups. Learning can explain the institutional development of CFSP and changes in the foreign policies of the Member States. Some scope conditions for learning and channels of institutionalisation are identified. Socialisation, resulting from learning within a group, is perceived as a strategic action by reflective actors. National diplomats, once they arrive in Brussels, learn the new code of conduct of their Working Groups. They are embedded in two environments and faced with two logics: the European one in the Council and the national one in the Ministries of Foreign Affairs (MFA). The empirical evidence supports the argument that neither rational nor sociological approaches alone can account for these processes.

Expectations, Learning and Monetary Policy: An Overview of Recent Research

Expectations about the future are central for determination of current macroeconomic outcomes and the formulation of monetary policy. Recent literature has explored ways for supplementing the benchmark of rational expectations with explicit models of expectations formation that rely on econometric learning. Some apparently natural policy rules turn out to imply expectational instability of private agents’ learning. We use the standard New Keynesian model to illustrate this problem and survey the key results about interest-rate rules that deliver both uniqueness and stability of equilibrium under econometric learning. We then consider some practical concerns such as measurement errors in private expectations, observability of variables and learning of structural parameters required for policy. We also discuss some recent applications including policy design under perpetual learning, estimated models with learning, recurrent hyperinflations, and macroeconomic policy to combat liquidity traps and deflation.

A Model of Near-Rational Exuberance

We study how the use of judgement or “add-factors” in forecasting may disturb the set of equilibrium outcomes when agents learn using recursive methods. We isolate conditions under which new phenomena, which we call exuberance equilibria, can exist in a standard self-referential environment. Local indeterminacy is not a requirement for existence. We construct a simple asset pricing example and find that exuberance equilibria, when they exist, can be extremely volatile relative to fundamental equilibria.

Does Ricardian Equivalence Hold When Expectations are not Rational?

This paper considers the Ricardian Equivalence proposition when expectations are not rational and are instead formed using adaptive learning rules. We show that Ricardian Equivalence continues to hold provided suitable additional conditions on learning dynamics are satisfied. However, new cases of failure can also emerge under learning. In particular, for Ricardian Equivalence to obtain, agents’ expectations must not depend on government’s financial variables under deficit financing.

Fiscal Policy and Learning

Using the standard real business cycle model with lump-sum taxes, we analyze the impact of fiscal policy when agents form expectations using adaptive learning rather than rational expectations (RE). The output multipliers for government purchases are significantly higher under learning, and fall within empirical bounds reported in the literature (in sharp contrast to the implausibly low values under RE). Effectiveness of fiscal policy is demonstrated during times of economic stress like the recent Great Recession. Finally it is shown how learning can lead to dynamics empirically documented during episodes of 'fiscal consolidations.'

Baysian Model Averaging, Learning and Model Selection

Agents have two forecasting models, one consistent with the unique rational expectations equilibrium, another that assumes a time-varying parameter structure. When agents use Bayesian updating to choose between models in a self-referential system, we find that learning dynamics lead to selection of one of the two models. However, there are parameter regions for which the non-rational forecasting model is selected in the long-run. A key structural parameter governing outcomes measures the degree of expectations feedback in Muth's model of price determination.