Cournot Oligopoly and the Theory of Supermodular Games

We reconsider the Cournot oligopoly problem in light of the theory of supermodular games. Invoking the recent ordinal version of this theory proposed by Milgrom and Shannon, we generalize Novshek's existence result, derive the associated uniqueness result, give an extension of a classical existence result under symmetry, and provide conditions making a Cournot oligopoly into a log-supermodular game (with the natural order on the action sets). We also provide extensive and precise insight as to why decreasing best-responses are widely regarded as being “typical” for the Cournot model with production costs. Several illustrative examples are provided.Journal of Economic LiteratureClassification Numbers: C72, L10, L13.     

The existence of core allocations in a one sector model of capital accumulation

The existence of core allocations in a one sector model of capital accumulation with heterogeneous households is demonstrated. The result follows as an application of Scarf's Theorem on the core of a balanced game.     

Understanding some recent existence results for discontinuous games

We introduce a new condition, weak better-reply security, and show that every compact, locally convex, metric, quasiconcave and weakly better-reply secure game has a Nash equilibrium. This result is established using simple generalizations of classical ideas. Furthermore, we show that, when players’ action spaces are metric and locally convex, it implies the existence results of Reny (Econometrica 67:1029–1056, 1999) and Carmona (J Econ Theory 144:1333–1340, 2009) and that it is equivalent to a recent result of Barelli and Soza (On the Existence of Nash Equilibria in Discontinuous and Qualitative Games, University of Rochester, Rochester, 2009). Our general existence result also implies a new existence result for weakly upper reciprocally semicontinuous and weakly payoff secure games that satisfy a strong quasiconcavity property.     

A Simple Extension of the Dasgupta–Maskin Theorem,with an Application

This paper generalizes the classical existence results for games with discontinuous payoffs, developed by Dasgupta and Maskin in 1986. This new existence result is then applied to a simple duopoly model with quantity precommitment and Bertrand competition.     

On the long-run wealth distribution in a simple Ramsey model with heterogeneous households

This paper analyzes the long-run wealth distribution in a Ramsey model where individuals have a common rate of time preference but different intertemporal elasticities of substitution. As a result, it is shown that heterogeneity among households in intertemporal substitution is sufficient for the existence of a non-degenerate long-run wealth distribution. We also investigate the properties of the long-run wealth distribution and the transition of capital and consumption using the phase diagram.     

汇率制度、金融加速器和经济波动

本文建立一个小型开放经济模型,目的之一是探究中国开放经济中金融加速器的存在性;二是针对中国1997—2008年间宏观经济波动特征分析不同汇率制度下金融加速器效应的差异,以验证相对浮动汇率来说,固定汇率是否会加大经济波动。通过使用中国数据和ML方法估计含和不含金融加速器的DSGE模型发现,似然率检验接受前者而拒绝后者。模拟结果显示含金融加速器模型模拟数据与实际数据特征更接近,再次验证了开放经济中金融加速器的存在。固定汇率下金融加速器效应强于浮动汇率,部分解释了1997—2008年间中国经济在不同汇率制度下宏观变量波动的差异。金融加速器主要传播和放大投资效率和货币政策冲击对经济的影响,对货币需求和国外冲击也有一定的放大作用,但对技术和偏好冲击的放大作用不明显。     

A Sufficient Condition for Topological Chaos with an Application to a Model of Endogenous Growth

This paper provides an easily verifiable sufficient condition for topological chaos for unimodal maps which can be satisfied when the well-known Li–Yorke condition is not satisfied. It then shows how this result can be applied to a model of endogenous growth with externalities to establish the existence of chaotic equilibrium growth paths in that framework. Journal of Economic Literature Classification Numbers: C61, D90, O41.     

Seasonality,price discrimination,and welfare

We discuss a potential limitation to a widely accepted result, namely that an output increase is a necessary condition for welfare to increase with price discrimination. We use a theoretical model to show that the existence of seasonal demand fluctuations may allow for a simultaneous reduction in average output and increase in average welfare. We also discuss a number of extensions of our basic model.     

On the existence of equilibria in economies with infinitely many commodities and without ordered preferences

The present paper deals with the existence of equilibria in economies whose commodity space is L_∞(M, M, μ) and where the agents' preferences need not be complete or transitive. Applying a fixed point theorem of Browder, an equilibrium existence theorem for abstract economies (generalized qualitative games) is proven where each agent's choice set is contained in an arbitrary topological vector space. With the help of this theorem the existence of Walrasian general equilibrium for a suitably specified economic model is obtained. The final result is a generalization of T. F. Bewley's (J. Econ. Theory4 (1972), 514–540) equilibrium existence theorem to the case of non-ordered preferences.     

Foundations of Bayesian theory

This paper states necessary and sufficient conditions for the existence, uniqueness, and updating according to Bayes’ rule, of subjective probabilities representing individuals’ beliefs. The approach is preference based, and the result is an axiomatic subjective expected utility model of Bayesian decision making under uncertainty with state-dependent preferences. The theory provides foundations for the existence of prior probabilities representing decision makers’ beliefs about the likely realization of events and for the updating of these probabilities according to Bayes’ rule.     

Learning towards system innovation: Evaluating a systemic instrument

In this paper we develop an analytical framework for studying learning processes in the context of efforts to bring about system innovation by building new networks of actors who are willing to work on a change towards sustainable development. We then use it to evaluate two specific intervention programmes carried out by a self-proclaimed ‘system instrument’. The framework integrates elements from the Innovation Systems approach with a social learning perspective. The integrated model proposes essentially that these kinds of systemic instruments can serve to enhance conditions for social learning and that such processes may result in learning effects that contribute to system innovation by combating system imperfections. The empirical findings confirm the assumption that differences in learning can be explained by the existence or absence of conditions for learning. Similarly, the existence or creation of conducive conditions could be linked to the nature and quality of the interventions of the systemic instrument. We conclude that the investigated part of the hypothesised model has not been refuted and seems to have explanatory power. At the same time we propose that further research is needed among others on the relation between learning, challenging system imperfections and system innovation.     

Unawareness and bankruptcy: A general equilibrium model

Summary. We present a consistent pure-exchange general equilibrium model where agents may not be able to foresee all possible future contingencies. In this context, even with nominal assets and complete asset markets, an equilibrium may not exist without appropriate assumptions. Specific examples are provided. An existence result is proved under the main assumption that there are sufficiently many states that all the agents foresee. An intrinsic feature of the model is bankruptcy, which agents may involuntarily experience in the unforeseen states. Received: April 23, 1997; revised version: May 19, 1997     

Automobile demand,model cycle and age effects

This paper is aimed at exploring the existence of typical patterns of automobile model life and the formal test for age effects in a discrete-choice demand framework estimated with data on the models sold in the Spanish market. Estimates show that the evolution of market shares entails and quantifies age effects resulting from consumer demand. These effects are clearly distinguishable from the impacts generated by changes in attributes and firm pricing. They carry an exogenous factor that is full of implications for firm behaviour over the life of a model: the modification of demand price sensitivities. As a result, for example, equilibrium own-price elasticities are observed to decrease until the fourth year of a model life, and then to increase again.      

Equilibrium with nonconvex technologies

Summary We provide an elementary proof of the existence of equilibrium in a general equilibrium model allowing for non-convex production sets. It is shown that when firms follow upper hemicontinuous and convex-valued pricing rules with bounded losses, a price vector and an allocation exist, such that all agents are in equilibrium and all markets clear.The existence result presented in this paper is a particular case of that one in Bonnisseau & Cornet (1988, Th. 2.1). In this respect our contribution consists of presenting an alternative proof which turns-out to be simpler and more intuitive.Thanks are due to Carmen Herrero and two anonymous referees for very helpful comments. Financial support from theDirection General de Investigación Cientiflca y Ténica, under project PS89–0066, is gratefully acknowledged.     

Characterizing the sustainability problem in an exhaustible resource model

We provide a general condition under which consumption can be sustained indefinitely bounded away from zero in the continuous time Dasgupta–Heal–Solow–Stiglitz model, by letting augmentable capital substitute for a non-renewable resource. The assumptions made on the production function are mild, thus generalizing previous work. By showing that Hartwick?s rule minimizes the required resource input per unit of capital accumulation, and integrating the required resource input with respect to capital, we obtain a complete technological characterization without reference to the time path. We also use the characterization result to establish general existence of a maximin path.     

Unique stability in simple coalition formation games

We investigate the uniqueness of stable coalition structures in a simple coalition formation model, for which specific coalition formation games, such as the marriage and roommate models, are special cases that are obtained by restricting the coalitions that may form. The main result is a characterization of collections of permissible coalitions which ensure that there is a unique stable coalition structure in the corresponding coalition formation model. In particular, we show that only single-lapping coalition formation models have a unique stable coalition structure for each preference profile, where single-lapping means that two coalitions cannot have more than one member in common, and coalitions do not form cycles. We also give another characterization using a graph representation, explore the implications of our results for matching models, and examine the existence of strategyproof coalition formation rules.     

Premium auctions and risk preferences

In a premium auction, the seller offers some “payback”, called premium, to a set of high bidders at the end of the auction. This paper investigates how the performance of such premium tactics is related to the bidders? risk preferences. We analyze a two-stage English premium auction model with symmetric interdependent values, in which the bidders may be risk averse or risk preferring. Upon establishing the existence and uniqueness of a symmetric equilibrium, we show that the premium causes the expected revenue to increase in the bidders? risk tolerance. A “net-premium effect” is key to this result.     

ENTRANTS' REPUTATION AND INDUSTRY DYNAMICS

This article analyzes entry–exit decisions in a market where reputation determines the price that firms may charge, within a rational‐expectation model of competition in a nonatomic market under heterogeneous reputations. The analysis focuses on the class of name‐switching reputational equilibria, in which a firm discards its name if and only if its reputation falls below the entrants' reputation. The main technical result is the existence of a unique steady‐state equilibrium within this class, in which the entrants' reputation is endogenous. The resulting industry dynamics is largely on agreement with the findings in the empirical literature.     

On the existence of optimal processes in non-stationary environments

We consider an aggregative model of intertemporal allocation under uncertainty, in which the utility and production functions are allowed to be time dependent, the random shocks occurring in each period are entirely arbitrary, and the production functions are permitted to be non-concave. In this framework, we provide a theorem on the existence of infinite-horizon optimal processes. In the course of establishing this result, we obtain the existence of optimal policy functions and we show that they are monotone in the stock levels.This paper has benefitted from the comments of two referees of the journal. Research of the first author was supported by a National Science Foundation Grant.     

Intertemporal substitution and the liquidity effect in a sticky price model

The liquidity effect, defined as a decrease in nominal interest rates in response to a monetary expansion, is a major stylized fact of the business cycle. This paper first confirms that, with separable preferences, a low degree of intertemporal substitution in consumption is a necessary condition for the existence of the liquidity effect. In contrast to this result, in a model with non-separable preferences and capital accumulation it takes an implausibly high elasticity of intertemporal substitution to produce a liquidity effect. The robustness of these results to alternative degrees of nominal rigidities, capital adjustment costs and stochastic monetary processes is also analysed. We conclude that price stickiness, by itself, does not guarantee the existence of a liquidity effect.