Competitive and core allocations in large economies with differential information

Summary. We study the core and competitive allocations in exchange economies with a continuum of traders and differential information. We show that if the economy is “irreducible”, then a competitive equilibrium, in the sense of Radner (1968, 1982), exists. Moreover, the set of competitive equilibrium allocations coincides with the “private core” (Yannelis, 1991). We also show that the “weak fine core” of an economy coincides with the set of competitive allocations of an associated symmetric information economy in which the traders information is the joint information of all the traders in the original economy. Received March 22, 2000; revised version: May 1, 2000     

On bubbling dynamics generated by a stochastic model of herd behavior

This paper suggests a class of stochastic collective learning processes exhibiting very irregular behavior. In particular, there are multimodal long run distributions. Some of these modes may vanish as the population size increases. This may be thought of as “bubbles” persistent for a finite range of population sizes but disappearing in the limit. The limit distribution proves to be a discontinuous function of parameters determining the learning process. This gives rise to another type of “bubbles”: limit outcomes corresponding to small perturbations of parameters are different. Since an agent's decision rule involves imitation of the majority choice in a random sample of other members of the population, the resulting collective dynamics exhibit “herding” or “epidemic” features. RID="*" ID="*" We are grateful to two anonymous referees for the comments and suggestions. Correspondence to: L. Gaio     

Evaluating wind-following and ecosystem services for hydroelectric dams in PJM

Hydropower can provide inexpensive, flexible fill-in power to compensate for intermittent renewable generation. Policies for hydropower dams maintain multiple services beyond electric generation, including environmental protection, flood control and recreation. We model the decision of a hydroelectric generator to shift some of its power production capacity away from the day-ahead energy market into a “wind-following” service to smooth the intermittent production of wind turbines. Offering such a service imposes both private and social opportunity costs. Since fluctuations in wind energy output are not perfectly correlated with day-ahead energy prices, a wind-following service will necessarily affect generator revenues. Seasonal wind patterns produce conflicts with the goal of managing rivers for “ecosystem services”—the maintenance or enhancement of downstream ecosystems. We illustrate our decision model using the Kerr Dam in PJM’s territory in North Carolina. We simulate the operation of Kerr Dam over a three-year period that features hydrologic variability from normal water years to extreme drought conditions. We use an optimization framework to estimate reservation prices for Kerr Dam offering wind-following services in the PJM market. Wind-following may be profitable for Kerr Dam at low capacity levels during some time periods if ecosystems services are neglected and if side payments, or reserves-type payments, are provided. Wind-following with ecosystem services yields revenue losses that typically cannot be recovered with reserves market payments. Water release patterns are inconsistent with ecosystem-services goals when Kerr Dam dedicates significant capacity to wind-following, particularly in drought years.     

Risky procurement with an insider bidder

Procurement auctions carry substantial risk when the value of the project is highly uncertain and known only to insiders. This paper reports the results from a series of experiments comparing the performance of three auction formats in such complex and risky settings. In the experiment, every bidder knows the private value for the project but only a single insider bidder knows the common-value part. In addition to the standard second-price and English auctions we test the “qualifying auction,” a two-stage format commonly used in the sale of complex and risky assets. The qualifying auction has a fully “revealing” equilibrium that implements the revenue-maximizing outcome but it also has an uninformative “babbling” equilibrium in which bidders place arbitrarily high bids in the first stage. In the experiments, the latter equilibrium has more drawing power, which causes the qualifying auction to perform worse than the English auction and only slightly better than a sealed-bid second-price auction. Compared to the two other formats, the English auction is roughly 40% more efficient, yields 50% more revenues, avoids windfall profits for the insider, while protecting uninformed bidders from losses.     

Solving coordination failure with “all-or-none” group-level incentives

Coordinating activity among members is an important problem faced by organizations. When firms, or units within firms, are stuck in bad equilibria, managers may turn to the temporary use of simple incentives—flat punishments or rewards—in an attempt to transition the firm or unit to a more efficient equilibrium. We investigate the use of incentives in the context of the “minimum-effort,” or “weak-link,” coordination game. We allow groups to reach the inefficient equilibrium and then implement temporary, flat, “all-or-none” incentives to encourage coordination on more efficient equilibria. We vary whether incentives are positive (rewards) or negative (penalties), whether they have substantial or nominal monetary value, and whether they are targeted to a specific outcome (the efficient equilibrium) or untargeted (apply to more than one outcome). Overall, incentives of all kinds are effective at improving coordination while they are in place, but there is little long-term persistent benefit of incentives—once incentives are removed, groups tend to return to the inefficient outcome. We find some differences between different kinds of incentives. Finally, we contrast our results to other recent work demonstrating greater long-term effectiveness of temporary incentives.      

Unfair contests

Real-world contests are often “unfair” in the sense that outperforming all rivals may not be enough to be the winner, because some contestants are favored by the allocation rule, while others are handicapped. This paper analyzes an unfair, two-player discriminatory contest (all-pay auction) with private values. We characterize equilibrium strategies, provide closed form solutions, and illustrate additional strategic issues arising in such unfair contests.     

Cheap home goods and persistent inequality

There exists a large literature which shows that public education is favorable for growth because it increases the level of human capital and at the same time it tends to produce a more even income distribution. More egalitarian societies are also associated with less social conflicts, and individuals have a lower tendency to report themselves happy when inequality is high. Therefore, it is important to study the reasons why the elite opposes the development of a strong public education system. It might be that education is related to social status and a strong public education system might threaten the elite’s political power. We show that one aspect of social status is the specialization of skilled workers in high-paid jobs and the abundance of unskilled workers in the production of cheap “home goods” in the market, such as painting and cleaning a house, babysitting, and/or cooking. We emphasize the role of general equilibrium price adjustments to show that depending on the level of inequality, the elite might prefer an economy with a positive and “high” cost of education than an economy where skills are freely provided. We show that this result goes through even if the skilled wage is not directly affected by the ratio of skilled to unskilled workers. We also provide empirical evidence consistent with our theory.     

On the growth and welfare effects of monopolistic distortions

The most fundamental proposition about growth and competition is that there is a tradeoff between static welfare and long-term growth. This paper reconsiders this basic proposition in an expanding variety endogenous growth model with competitive markets for “old” innovative products and for a traditional good. We shed light on some implications of monopolistic distortions which tend to be ignored by standard models. First, no growth may be better than some growth, since modest positive growth potentially requires sizeable static welfare losses. Second, the economy may converge to a steady state with zero growth, even though a locally saddle-point stable steady state with positive growth exists if the initial share of “cheap” competitive markets is sufficiently high, as this implies a relatively low demand for “expensive” innovative goods. Third, such a “no-growth trap” may happen in a world economy made up of several countries engaged in free trade with each other. The policy implications are that growth-enhancing policies may be misguided and that quick deregulation as well as quick trade liberalization can lead to stagnation in the long term.      

Computing equilibria: a computational complexity perspective

Computational complexity is the subfield of computer science that rigorously studies the intrinsic difficulty of computational problems. This survey explains how complexity theory defines “hard problems”; applies these concepts to several equilibrium computation problems; and discusses implications for computation, games, and behavior. We assume minimal prior background in computer science.     

The Arrow-Debreu model: How math can hide a fatal conceptual error

I argue that math, like love, can cover a multitude of sins, and I use the neoclassical object of adoration, the Arrow-Debreu model, as the case in point. It is commonplace that the Arrow-Debreu (AD) model of general equilibrium does not describe the real world, but it is equally commonplace to accept it as representing the pure logic of the competitive capitalist economy in an idealized world free of transactions costs. I show that the AD model fails even as an idealized model; it actually mistakes the logic of pure capitalism. Unlike McKenzie’s model of idealized general equilibrium under constant returns to scale, Arrow and Debreu claim to have shown the existence of competitive equilibrium under decreasing returns to scale and positive pure profits. The AD model (again unlike the McKinzie model) needs to assign the profits to individuals and this is done using the notion of “ownership of the production set.” But this notion suffers from a fatal ambiguity. If Arrow and Debreu interpret it to mean “ownership of a corporation” then a simple argument in the form “labor can hire capital or capital can hire labor” defeats the alleged necessity of assigning residual claimancy to the corporation. A given corporation may or may not end up exploiting a set of production opportunities (represented by a production set) depending on whether it hires in labor and undertakes production or hires out its capital to others (all by assumption at the parametrically given prices). In the latter case, residual claimancy is elsewhere. There is no such property right as “ownership of a production set” in a private property market economy. The legal party which purchases or already owns all the inputs used up in production has the defensible legal claim on the outputs: there is no need to also “purchase the production set.” At any set of prices that allow positive pure profits, anyone in the idealized AD model could bid up the price of the inputs and thus try to reap a smaller but still positive profit. Therefore,pace Arrow and Debreu, there could be no equilibrium with positive pure profits. In the Appendix, the property rights fallacy that afflicts the AD model is shown to also afflict orthodox capital theory and corporate finance theory. World Bank The findings, interpretations and conclusions expressed in this paper are entirely those of the author and should not be attributed in any manner to the World Bank, to its affiliated organizations or to the members of its Board of Directors or the countries they represent.     

Environment,Directed Technical Change and Economic Policy

We study the effects of an economic policy in an endogenous growth general equilibrium framework where production of consumption goods requires two resource inputs: a polluting non-renewable resource and a non-polluting labour resource. The use of the former contributes to the accumulation of pollution in the atmosphere, which affects welfare. There is a specific research sector associated with each of those resources. We provide a full welfare analysis, and we describe the equilibrium paths in a decentralized economy. We go on to study the effects of three associated economic policy tools: a tax on the polluting resource, and two research subsidies. We show that the optimal environmental policy has two main effects; it delays the extraction of the resource and with it the level of polluting emissions and it reallocates research efforts, decreasing the amount put into “grey” research to the benefit of “green” research. We also show that the environmental policy is grey-biased in the short-term, and green-biased in the long-term. Finally, we compute the optimal values for these tools.      

Do brain drain and poverty result from coordination failures?

The bidirectional causal links between high-skilled emigration and poverty can give rise to multiple equilibria and coordination failures. Two countries sharing identical characteristics may end up in either a “low poverty-low brain drain” equilibrium or in a “high poverty-high brain drain” equilibrium. In this paper, we build a model which endogenizes high-skilled emigration and economic performances in order to derive the conditions under which multiplicity occurs. After identifying country-specific parameters, we find that in the majority of developing countries, the best equilibrium is selected and that the observed brain drain is inevitable. In 22 small developing countries however, the worse equilibrium prevails, implying that poverty and brain drain are increased by coordination failure. These countries require appropriate development policies, such as a temporary subsidization of the repatriation of their high-skilled expatriates. Our results are robust to the inclusion of a brain gain mechanism.     

An experimental analysis of the bandit problem

Summary.  We investigate, in an experimental setting, the behavior of single decision makers who at discrete time intervals over an “infinite” horizon may choose one action from a set of possible actions where this set is constant over time, i.e. a bandit problem. Two bandit environments are examined, one in which the predicted behavior should always be myopic (the two-armed bandit) and the other in which the predicted behavior should never be myopic (the one-armed bandit). We also investigate the comparative static predictions as the underlying parameters of the bandit environments are changed. The aggregate results show that the behavior in the two bandit environments are quantitatively different and in the direction of the theoretical predictions. Received: October, 27, 1994; revised version February 27, 1996     

Coping with Preference Anomalies in Cost–Benefit Analysis: A Market-Simulation Approach

This paper proposes a methodological strategy for cost–benefit analysis (CBA) which does not require the assumption that individuals’ preferences satisfy standard coherence conditions, and so renders CBA immune to the problems generated by preference anomalies. The proposal treats CBA as an exercise in market simulation, based on the measurement of surplus. Anomalies occur when surplus measurements vary according to the hypothetical payment mechanism used. In such cases, the mechanism that is the “closest market analogue” should be used. This approach is used to resolve problems associated with some familiar anomalies, including inconsistencies between “citizen” and “consumer” valuations, and endowment effects. JEL classifications: D61, D63, Q51     

The bargaining set of a large economy with differential information

Summary. We study the Mas-Colell bargaining set of an exchange economy with differential information and a continuum of traders. We established the equivalence of the private bargaining set and the set of Radner competitive equilibrium allocations. As for the weak fine bargaining set, we show that it contains the set of competitive equilibrium allocations of an associated symmetric information economy in which each trader has the “joint information” of all the traders in the original economy, but unlike the weak fine core and the set of fine value allocations, it may also contain allocations which are not competitive in the associated economy. Received: February 15, 1999; revised version: August 9, 1999     

Detrimental externalities, pollution rights, and the “Coase theorem”

This paper, which builds on Chipman (The economist’s vision. Essays in modern economic perspectives, 131–162, 1998), analyzes a simple model formulated by Hurwicz (Jpn World Econ 7:49–74, 1995) of two agents—a polluter and a pollutee—and two commodities: “money” (standing for an exchangeable private good desired by both agents) and “pollution” (a public commodity desired by the polluter but undesired by the pollutee). There is also a government that issues legal rights to the two agents to emit a certain amount of pollution, which can be bought and sold with money. It is assumed that both agents act as price-takers in the market for pollution rights, so that competitive equilibrium is possible. The “Coase theorem” (so-called by Stigler (The theory of price, 1966) asserts that the equilibrium amount of pollution is independent of the allocation of pollution rights. A sufficient condition for this was (in another context) obtained by Edgeworth (Giorn Econ 2:233–245, 1891), namely that preferences of the two agents be “parallel” in the money commodity, whose marginal utility is constant. Hurwicz (Jpn World Econ 7:49–74, 1995) argued that this parallelism is also necessary. This paper, which provides an exposition of the problem, raises some questions about this result and provides an alternative necessary and sufficient condition.     

Winner-take-all price competition

Summary. We analyze an oligopoly model of homogeneous product price competition that allows for discontinuities in demand and/or costs. Conditions under which only zero profit equilibrium outcomes obtain in such settings are provided. We then illustrate through a series of examples that the conditions provided are “tight” in the sense that their relaxation leads to positive profit outcomes. Received: April 7, 2000; revised version: September 14, 2000     

Norms as emergent properties of adaptive learning: The case of economic routines

Interaction among autonomous decision-makers is usually modelled in economics in game-theoretic terms or within the framework of General Equilibrium. Game-theoretic and General Equilibrium models deal almost exclusively with the existence of equilibria and do not analyse the processes which might lead to them. Even when existence proofs can be given, two questions are still open. The first concerns the possibility of multiple equilibria, which game theory has shown to be the case even in very simple models and which makes the outcome of interaction unpredictable. The second relates to the computability and complexity of the decision procedures which agents should adopt and questions the possibility of reaching an equilibrium by means of an algorithmically implementable strategy. Some theorems have recently proved that in many economically relevant problems equilibria are not computable. A different approach to the problem of strategic interaction is a “constructivist” one. Such a perspective, instead of being based upon an axiomatic view of human behaviour grounded on the principle of optimisation, focuses on algorithmically implementable “satisfycing” decision procedures. Once the axiomatic approach has been abandoned, decision procedures cannot be deduced from rationality assumptions, but must be the evolving outcome of a process of learning and adaptation to the particular environment in which the decision must be made. This paper considers one of the most recently proposed adaptive learning models: Genetic Programming and applies it to one the mostly studied and still controversial economic interaction environment, that of oligopolistic markets. Genetic Programming evolves decision procedures, represented by elements in the space of functions, balancing the exploitation of knowledge previously obtained with the search of more productive procedures. The results obtained are consistent with the evidence from the observation of the behaviour of real economic agents.     

In or out: efficient inclusion of installations in an emissions trading scheme?

Regulators around the world are currently considering national emissions trading schemes (ETS) as cost-effective instruments to reduce greenhouse gas emissions. In the process, they are confronted with numerous design issues. The coverage of installations in an ETS is one such issue. While “blanket coverage” that includes all industrial emitters of greenhouse gases in an economy has some intuitive appeal, and seems equitable, it does not take into full account all the costs related to the extent of coverage. This paper shows that an alternative approach of “partial coverage” based on benefit–cost analysis can achieve the same emission reduction outcome at lower social cost. The approach is based on maximizing the benefits from inclusion of installations in an ETS at the same time as taking all relevant transaction costs into account. A broad definition of transaction costs is used, which covers the regulatory costs to the government as well as regulatory costs imposed on covered installations. We find that particularly for relatively modest emissions reduction targets the cost savings of a “partial coverage” compared to “blanket coverage” are significant.     

Walras and pareto on the meaning of the solution concept in general equilibrium theory

The notion of solution plays a crucial role in the conceptual system of Léon Walras, the founder of the General Equilibrium Theory (GET). In this paper, after introducing the two solution concepts employed by Walras in the development of his version of GET, respectively called the “theoretical” and the “practical” solution, we discuss the problems such peculiar conception gives rise to, as well as the attempts Walras makes to dodge them. Then we explain why and to what extent Pareto, Walras’ immediate successor and co-founder of GET, departs from Walras’ original conception, progressively developing an independent viewpoint on the issue of equilibrium computability in GET. (JEL:B13, B21, B31, B41, C62, C68, D50)