Oligopolistic competition under knightian uncertainty

This artic/e applies a theorem of Nash equilibrium under uncertainty (Dow & Werlang, 1994) to the classic Coumot model of oligopolistic competition. It shows, in particular, how one can map all Coumot equilibrium (which includes the monopoly and the null solutions) with only a function of uncertainty aversion coefficients of producers. The effect of variations in these parameters over the equilibrium quantities are studied, also assuming exogenous increases in the number of matching firms in the game. The Cournot solutions under uncertainty are compared with the monopolistic one. It shows principally that there is an uncertainty aversion level in the industry such that every aversion coefficient beyond it induces firms to produce an aggregate output smaller than the monopoly output. At the end of the artic/e equilibrium solutions are specialized for Linear Demand and for Coumot duopoly. Equilibrium analysis in the symmetric case allows to identify the uncertainty aversion coefficient for the whole industry as a proportional lack of information cost which would be conveyed by market price in the perfect competition case (Lerner Index).

Nash equilibrium under knightian uncertainty: breaking down backward induction (extensively revised version)

We define Nash equilibrium for two-person normal form games in the presence of uncertainty, in the sense of Knight(1921). We use the fonna1iution of uncertainty due to Schmeidler and Gilboa. We show tbat there exist Nash equilibria for any degree of uncertainty, as measured by the uncertainty aversion (Dow anel Wer1ang(l992a». We show by example tbat prudent behaviour (maxmin) can be obtained as an outcome even when it is not rationaliuble in the usual sense. Next, we break down backward industion in the twice repeated prisoner's dilemma. We link these results with those on cooperation in the finitely repeated prisoner's dilemma obtained by Kreps-Milgrom-Roberts-Wdson(1982), and withthe 1iterature on epistemological conditions underlying Nash equilibrium. The knowledge notion implicit in this mode1 of equilibrium does not display logical omniscience.

Nash equilibrium under knightian uncertainty: breaking-down backward induction

We present two alternative definitions of Nash equilibrium for two person games in the presence af uncertainty, in the sense of Knight. We use the formalization of uncertainty due to Schmeidler and Gilboa. We show that, with one of the definitions, prudent behaviour (maxmin) can be obtained as an outcome even when it is not rationalizable in the usual sense. Most striking is that with the Same definition we break down backward induction in the twice repeated prisoner's dilemma. We also link these results with the Kreps-Milgrom-Roberts-Wilson explanation of cooperation in the finitely repeated prisoner's dilemma.

A notion of subgame perfect Nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game.

A notion of subgame perfect nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game .

The role of consumer's risk aversion on price rigidity

This paper aims at contributing to the research agenda on the sources of price stickiness, showing that the adoption of nominal price rigidity may be an optimal firms' reaction to the consumers' behavior, even if firms have no adjustment costs. With regular broadly accepted assumptions on economic agents behavior, we show that firms' competition can lead to the adoption of sticky prices as an (sub-game perfect) equilibrium strategy. We introduce the concept of a consumption centers model economy in which there are several complete markets. Moreover, we weaken some traditional assumptions used in standard monetary policy models, by assuming that households have imperfect information about the ineflicient time-varying cost shocks faced by the firms, e.g. the ones regarding to inefficient equilibrium output leveIs under fiexible prices. Moreover, the timing of events are assumed in such a way that, at every period, consumers have access to the actual prices prevailing in the market only after choosing a particular consumption center. Since such choices under uncertainty may decrease the expected utilities of risk averse consumers, competitive firms adopt some degree of price stickiness in order to minimize the price uncertainty and fi attract more customers fi.'

Common agency with informed principals

We analyze a common agency game under asymmetric information on the preferences of the non-cooperating principals in a public good context. Asymmetric information introduces incentive compatibility constraints which rationalize the requirement of truthfulness made in the earlier literature on common agency games under complete information. There exists a large class of differentiable equilibria which are ex post inefficient and exhibit free-riding. We then characterize some interim efficient equilibria. Finally, there exists also a unique equilibrium allocation which is robust to random perturbations. This focal equilibrium is characterized for any distribution of types.

Bubbles, collateral and monetary equilibrium

Consider an economy where infinite-lived agents trade assets collateralized by durable goods. We obtain results that rule out bubbles when the additional endowments of durable goods are uniformly bounded away from zero, regardless of whether the asset’s net supply is positive or zero. However, bubbles may occur, even for state-price processes that generate finite present value of aggregate wealth. First, under complete markets, if the net supply is being endogenously reduced to zero as a result of collateral repossession. Secondly, under incomplete markets, for a persistent positive net supply, under the general conditions guaranteeing existence of equilibrium. Examples of monetary equilibria are provided.

Desenho de um sistema de metas sociais

Este trabalho discute a racionalidade econômica para o desenvolvimento de um sistema de metas sociais como forma de o governo federal aumentar a eficiência na utilização dos recursos sociais transferidos para os municípios. O trabalho desenvolve algumas extensões do modelo de agente-principal incluindo abordagens estáticas com e sem informação imperfeita e abordagens dinâmicas com contratos perfeitos e imperfeitos. Os resultados dos modelos estáticos indicam que o uso de critérios usuais de focalização onde localidades mais pobres recebem mais recursos pode levar a incentivos adversos para a erradicação da pobreza. Nós também mostramos que transferências incondicionais do governo federal deslocam gastos sociais locais. O trabalho argumenta em favor do uso de contratos onde quanto maior for a melhora no indicador social escolhido, mais recursos o município receberia. A introdução de informação imperfeita neste modelo basicamente gera uma penalidade aos segmentos pobres de áreas onde os governos demonstram ser menos avessos a pobreza. O trabalho também aborda o problema de favoritismo político onde determinados grupos sociais têm maior, ou menor, atenção por parte de governos locais. O resultado é que as políticas sociais acabam privilegiando determinados setores em detrimento de outros. Com o estabelecimento de metas sociais é possível, se não eliminar o problema, ao menos criar incentivos corretos para que os gastos sociais sejam distribuídos de forma mais equânime. Também desenvolvemos modelos dinâmicos com diferentes possibilidades de renegociação ao longo do tempo. Demonstramos que a melhor forma de aumentar a eficiência alocativa dos fundos seria criar mecanismos institucionais garantindo a impossibilidade de renegociações bilaterais. Esse contrato ótimo reproduz a seqüência de metas e transferências de vários períodos encontrada na solução do modelo estático. Entretanto, esse resultado- desaparece quando incorporamos contratos incompletos. Nesse caso, as ineficiências ex-ante criadas pela possibilidade de renegociação devem ser comparadas com as ineficiências ex-post criadas por não se usar a informação nova revelada ao longo do processo. Finalmente, introduzimos a possibilidade do resultado social observado depender não só do investimento realizado, mas também da presença de choques. Nesse caso, tanto o governo quanto o município aumentam as suas metas de investimento na área social. Contratos lineares na presença de choques negativos fazem com que os municípios recebem menos recursos justamente em situações adversas. Para contornar esse problema, mostramos a importância da utilização de contratos com comparação de performance.

Fiscal multipliers in an incomplete markets economy

This paper studies the behavior of fiscal multipliers in two different economic environments: complete markets and incomplete markets. Based on steady state analysis, output multipliers are found within a range between 0.49 and 0.66, when the markets are complete. Under incomplete markets, output multiplier was found in an interval between 0.75 and 0.94. These results indicates that the market structure, which reflects the degree of risk sharing and the intensity of the precautionary motive faced by individuals, plays a key role in determining the fiscal multipliers. In the second part of the paper, was performed an exercise to analyze the dynamic response of macroeconomic aggregates to an exogenous and unexpected rise in government spending financed by lump-sum taxes. In this case, impact output multipliers varies in a range between 0.64 and 0.68, under complete markets, and within 1.05 and 1.20 when markets are incomplete. The results found under incomplete markets are very close to that found on related literature which usually uses an econometric approach or calibrated/estimated New Keynesian models. These results shows that taking into account the deficiencies in the insurance mechanisms can be an interesting way to reconcile theoretical models with the results found on related current literature, without the need of ad-hoc assumptions relative to price stickness.

Common agency with informed principals

We analyze a common agency game under asymmetric information on the preferences of the non-cooperating principals. Asymmetric information introduces incentive compatibility constraints which rationalize the requirement of truthfulness made in the earlier literature on common agency games under complete information. There exists a large class of differentiable equilibria which are ex post inefficient and exhibit free-riding. We then characterize some interim efficient equilibria. Finally, there exists also a unique equilibrium allocation which is robust to random perturbations. This focal equilibrium is characterized for any distribution of types.

Robustness and stabilization properties of monetary policy rules in Brazil

Based on three versions of a small macroeconomic model for Brazil, this paper presents empirical evidence on the effects of parameter uncertainty on monetary policy rules and on the robustness of optimal and simple rules over different model specifications. By comparing the optimal policy rule under parameter uncertainty with the rule calculated under purely additive uncertainty, we find that parameter uncertainty should make policymakers react less aggressively to the economy's state variables, as suggested by Brainard's "conservatism principIe", although this effect seems to be relatively small. We then informally investigate each rule's robustness by analyzing the performance of policy rules derived from each model under each one of the alternative models. We find that optimal rules derived from each model perform very poorly under alternative models, whereas a simple Taylor rule is relatively robusto We also fmd that even within a specific model, the Taylor rule may perform better than the optimal rule under particularly unfavorable realizations from the policymaker' s loss distribution function.

Normality under uncertainty

Consider the demand for a good whose consumption be chosen prior to the resolution of uncertainty regarding income. How do changes in the distribution of income affect the demand for this good? In this paper we show that normality, is sufficient to guarantee that consumption increases of the Radon-Nikodym derivative of the new distribution with respect to the old is non-decreasing in the whole domain. However, if only first order stochastic dominance is assumed more structure must be imposed on preferences to guanantee the validity of the result. Finally a converse of the first result also obtains. If the change in measure is characterized by non-decreasing Radon-Nicodyn derivative, consumption of such a good will always increase if and only if the good is normal.

Uncertainty aversion and the optmal choice of portfolio

In this paper we apply the theory of declsion making with expected utility and non-additive priors to the choice of optimal portfolio. This theory describes the behavior of a rational agent who i5 averse to pure 'uncertainty' (as well as, possibly, to 'risk'). We study the agent's optimal allocation of wealth between a safe and an uncertain asset. We show that there is a range of prices at which the agent neither buys not sells short the uncertain asset. In contrast the standard theory of expected utility predicts that there is exactly one such price. We also provide a definition of an increase in uncertainty aversion and show that it causes the range of prices to increase.