Bertrand oligopoly when rivals' costs are unknown

We study a Bertrand oligopoly model with incomplete information about rivals' costs, where the uncertainty is given by a uniform distribution. We compute the Bayesian-Nash equilibrium of this game, the ex-ante expected profit and the ex-post profit of each firm. We see that, even though only one firm produces in equilibrium, all firms have a positive ex-ante expected profit.

Bertrand and Cournot oligopolies when rivals' costs are unknown

We study Bertrand and Cournot oligopoly models with incomplete information about rivals’ costs, where the uncertainty is given by a uniform distribution. We compute the Bayesian- Nash equilibrium of both games, the ex-ante expected profits and the ex-post profits of each firm. We see that, in the price competition, even though only one firm produces in equilibrium, all firms have a positive ex-ante expected profit.

A decision- theoretic model for M&A sale processes

A Work Project, presented as part of the requirements for the Award of a Masters Double Degree in Economics and International Business from the NOVA – School of Business and Economics and Insper Instituto de Ensino e Pesquisa

A soft computing approach to kidney diseases evaluation

Kidney renal failure means that one’s kidney have unexpectedly stopped functioning, i.e., once chronic disease is exposed, the presence or degree of kidney dysfunction and its progression must be assessed, and the underlying syndrome has to be diagnosed. Although the patient’s history and physical examination may denote good practice, some key information has to be obtained from valuation of the glomerular filtration rate, and the analysis of serum biomarkers. Indeed, chronic kidney sickness depicts anomalous kidney function and/or its makeup, i.e., there is evidence that treatment may avoid or delay its progression, either by reducing and prevent the development of some associated complications, namely hypertension, obesity, diabetes mellitus, and cardiovascular complications. Acute kidney injury appears abruptly, with a rapid deterioration of the renal function, but is often reversible if it is recognized early and treated promptly. In both situations, i.e., acute kidney injury and chronic kidney disease, an early intervention can significantly improve the prognosis.The assessment of these pathologies is therefore mandatory, although it is hard to do it with traditional methodologies and existing tools for problem solving. Hence, in this work, we will focus on the development of a hybrid decision support system, in terms of its knowledge representation and reasoning procedures based on Logic Programming, that will allow one to consider incomplete, unknown, and even contradictory information, complemented with an approach to computing centered on Artificial Neural Networks, in order to weigh the Degree-of-Confidence that one has on such a happening. The present study involved 558 patients with an age average of 51.7 years and the chronic kidney disease was observed in 175 cases. The dataset comprise twenty four variables, grouped into five main categories. The proposed model showed a good performance in the diagnosis of chronic kidney disease, since the sensitivity and the specificity exhibited values range between 93.1 and 94.9 and 91.9–94.2 %, respectively.

Value of the Qrs-T Angle in Predicting the Induction of Ventricular Tachyarrhythmias in Patients with Chagas Disease

Background:The QRS-T angle correlates with prognosis in patients with heart failure and coronary artery disease, reflected by an increase in mortality proportional to an increase in the difference between the axes of the QRS complex and T wave in the frontal plane. The value of this correlation in patients with Chagas heart disease is currently unknown.Objective:Determine the correlation of the QRS-T angle and the risk of induction of ventricular tachycardia / ventricular fibrillation (VT / VF) during electrophysiological study (EPS) in patients with Chagas disease.Methods:Case-control study at a tertiary center. Patients without induction of VT / VF on EPS were used as controls. The QRS-T angle was categorized as normal (0-105º), borderline (105-135º) or abnormal (135-180º). Differences between groups for continuous variables were analyzed with the t test or Mann-Whitney test, and for categorical variables with Fisher's exact test. P values < 0.05 were considered significant.Results:Of 116 patients undergoing EPS, 37.9% were excluded due to incomplete information / inactive records or due to the impossibility to correctly calculate the QRS-T angle (presence of left bundle branch block and atrial fibrillation). Of 72 patients included in the study, 31 induced VT / VF on EPS. Of these, the QRS-T angle was normal in 41.9%, borderline in 12.9% and abnormal in 45.2%. Among patients without induction of VT / VF on EPS, the QRS-T angle was normal in 63.4%, borderline in 14.6% and abnormal in 17.1% (p = 0.04). When compared with patients with normal QRS-T angle, those with abnormal angle had a fourfold higher risk of inducing ventricular tachycardia / ventricular fibrillation on EPS [odds ratio (OR) 4; confidence interval (CI) 1.298-12.325; p = 0.028]. After adjustment for other variables such as age, ejection fraction (EF) and QRS size, there was a trend for the abnormal QRS-T angle to identify patients with increased risk of inducing VT / VF during EPS (OR 3.95; CI 0.99-15.82; p = 0.052). The EF also emerged as a predictor of induction of VT / VF: for each point increase in EF, there was a 4% reduction in the rate of sustained ventricular arrhythmia on EPS.Conclusions:Changes in the QRS-T angle and decreases in EF were associated with an increased risk of induction of VT / VF on EPS.

Foundations for contest success functions

In the literature the outcome of contests is either interpreted as win probabilities or as shares of the prize. With this in mind, we examine two approaches to contest success functions. In the first we analyze the implications of contestants' incomplete information concerning the "type" of the contest administrator. While in the case of two contestants this approach can rationalize prominent contest success functions, we show that it runs into difficulties when there are more agents. Our second approach interprets contest success functions as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular contest success functions and guidelines for the definition of new ones. Keywords: Endogenous Contests, Contest Success Function. JEL Classification: C72 (Noncooperative Games), D72 (Economic Models of Political Processes: Rent-Seeking, Elections), D74 (Conflict; Conflict Resolution; Alliances).

Delay and Haircuts in Sovereign Debt: Recovery and Sustainability

One of the striking aspects of recent sovereign debt restructurings is, conditional on default, delay length is positively correlated with the size of haircut. In this paper, we develop an incomplete information model of debt restructuring where the prospect of uncertain economic recovery and the signalling about sustainability concerns together generate multi-period delay. The results from our analysis show that there is a correlation between delay length and size of haircut. Such results are supported by evidence. We show that Pareto ranking of equilibria, conditional on default, can be altered once we take into account the ex ante incentive of sovereign debtor. We use our results to evaluate proposals advocated to ensure orderly resolution of sovereign debt crises.

Optimism and commitment: An elementary theory of bargaining and war

We propose an elementary theory of wars fought by fully rational contenders. Two parties play a Markov game that combines stages of bargaining with stages where one side has the ability to impose surrender on the other. Under uncertainty and incomplete information, in the unique equilibrium of the game, long confrontations occur: war arises when reality disappoints initial (rational) optimism, and it persist longer when both agents are optimists but reality proves both wrong. Bargaining proposals that are rejected initially might eventually be accepted after several periods of confrontation. We provide an explicit computation of the equilibrium, evaluating the probability of war, and its expected losses as a function of i) the costs of confrontation, ii) the asymmetry of the split imposed under surrender, and iii) the strengths of contenders at attack and defense. Changes in these parameters display non-monotonic effects.

(Don’t) Make My Vote Count

Proponents of proportional electoral rules often argue that majority rule depresses turnout and may lower welfare due to the 'tyranny of the majority' problem. The present paper studies the impact of electoral rules on turnout and social welfare. We analyze a model of instrumental voting where citizens have private information over their individual cost of voting and over the alternative they prefer. The electoral rule used to select the winning alternative is a combination of majority rule and proportional rule. Results show that the above arguments against majority rule do not hold in this set up. Social welfare and turnout increase with the weight that the electoral rule gives to majority rule when the electorate is expected to be split, and they are independent of the electoral rule employed when the expected size of the minority group tends to zero. However, more proportional rules can increase turnout within the minority group. This effect is stronger the smaller the minority group. We then conclude that majority rule fosters overall turnout and increases social welfare, whereas proportional rule fosters the participation of minorities.

Delay and Haircuts in Sovereign Debt: Recovery and Sustainability

One of the striking aspects of recent sovereign debt restructurings is, conditional on default, delay length is positively correlated with the size of "haircut", which is size of creditor losses. In this paper, we develop an incomplete information model of debt restructuring where the prospect of uncertain economic recovery and the signalling about sustainability concerns together generate multi-period delay. The results from our analysis show that there is a correlation between delay length and size of haircut. Such results are supported by evidence. We show that Pareto ranking of equilibria, conditional on default, can be altered once we take into account the ex ante incentive of sovereign debtor. We use our results to evaluate proposals advocated to ensure orderly resolution of sovereign debt crises.

Venezuelan economic laboratory. The Case of the altruistic economy of Felipe Pérez Martí

Felipe Pérez Martí, who was the Venezuelan Minister of Planning and Development in the government of Hugo Chávez, proposes an economic model that he calls the altruistic economy or fourth way, which leads cooperative game theory to its logical extremes postulating a pure communism. Here we sustain that, first, it is impossible in the model of Pérez Martí to marginally allocate non-primary goods to those most in need or who most value them, facing a problem of defective economic calculation, and second, in order to achieve equality, he would have to replace his atomic local planners by a central planner, who would be unable to overcome the problem of imperfect and and incomplete information.

Impact of a computerized physician order entry system on compliance with prescription accuracy requirements.

OBJECTIVE: To assess the change in non-compliant items in prescription orders following the implementation of a computerized physician order entry (CPOE) system named PreDiMed. SETTING: The department of internal medicine (39 and 38 beds) in two regional hospitals in Canton Vaud, Switzerland. METHOD: The prescription lines in 100 pre- and 100 post-implementation patients' files were classified according to three modes of administration (medicines for oral or other non-parenteral uses; medicines administered parenterally or via nasogastric tube; pro re nata (PRN), as needed) and analyzed for a number of relevant variables constitutive of medical prescriptions. MAIN OUTCOME MEASURE: The monitored variables depended on the pharmaceutical category and included mainly name of medicine, pharmaceutical form, posology and route of administration, diluting solution, flow rate and identification of prescriber. RESULTS: In 2,099 prescription lines, the total number of non-compliant items was 2,265 before CPOE implementation, or 1.079 non-compliant items per line. Two-thirds of these were due to missing information, and the remaining third to incomplete information. In 2,074 prescription lines post-CPOE implementation, the number of non-compliant items had decreased to 221, or 0.107 non-compliant item per line, a dramatic 10-fold decrease (chi(2) = 4615; P < 10(-6)). Limitations of the computerized system were the risk for erroneous items in some non-prefilled fields and ambiguity due to a field with doses shown on commercial products. CONCLUSION: The deployment of PreDiMed in two departments of internal medicine has led to a major improvement in formal aspects of physicians' prescriptions. Some limitations of the first version of PreDiMed were unveiled and are being corrected.

Optimal Design of Permit Markets with an Ex Ante Pollution Target, August 2006

In this paper, we examine the design of permit trading programs when the objective is to minimize the cost of achieving an ex ante pollution target, that is, one that is defined in expectation rather than an ex post deterministic value. We consider two potential sources of uncertainty, the presence of either of which can make our model appropriate: incomplete information on abatement costs and uncertain delivery coefficients. In such a setting, we find three distinct features that depart from the well-established results on permit trading: (1) the regulator’s information on firms’ abatement costs can matter; (2) the optimal permit cap is not necessarily equal to the ex ante pollution target; and (3) the optimal trading ratio is not necessarily equal to the delivery coefficient even when it is known with certainty. Intuitively, since the regulator is only required to meet a pollution target on average, she can set the trading ratio and total permit cap such that there will be more pollution when abatement costs are high and less pollution when abatement costs are low. Information on firms’ abatement costs is important in order for the regulator to induce the optimal alignment between pollution level and abatement costs.

Approximate knowledge of rationality and correlated equilibria

We extend Aumann's theorem [Aumann 1987], deriving correlated equilibria as a consequence of common priors and common knowledge of rationality, by explicitly allowing for non-rational behavior. Wereplace the assumption of common knowledge of rationality with a substantially weaker one, joint p-belief of rationality, where agents believe the other agents are rational with probability p or more. We show that behavior in this case constitutes a kind of correlated equilibrium satisfying certain p-belief constraints, and that it varies continuously in the parameters p and, for p sufficiently close to one,with high probability is supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend the analysis to characterizing rational expectations of interimtypes, to games of incomplete information, as well as to the case of non-common priors.

Quotient spaces of boundedly rational types

By identifying types whose low-order beliefs up to level li about the state of nature coincide, weobtain quotient type spaces that are typically smaller than the original ones, preserve basic topologicalproperties, and allow standard equilibrium analysis even under bounded reasoning. Our Bayesian Nash(li; l-i)-equilibria capture players inability to distinguish types belonging to the same equivalence class.The case with uncertainty about the vector of levels (li; l-i) is also analyzed. Two examples illustratethe constructions.