Star-shapedness of Richter-Aumann integral on a measure space with atoms: theory and economic applications

This paper provides sufficient (as well as necessary) conditions for the integral of a correspondence defined on a measure space with atoms to exhibit star-shaped values. This result is used to analyze the existence of a Nash equilibrium in games with a measure space of agents with atoms and of a competitive equilibrium in economies with mixed markets. In either case it is shown that an exact equilibrium exists whenever atoms are “small enough”.     

Competitive behavior in market games: Evidence and theory

We explore whether competitive outcomes arise in an experimental implementation of a market game, introduced by Shubik (1973) [21]. Market games obtain Pareto inferior (strict) Nash equilibria, in which some or possibly all markets are closed. We find that subjects do not coordinate on autarkic Nash equilibria, but favor more efficient Nash equilibria in which all markets are open. As the number of subjects participating in the market game increases, the Nash equilibrium they achieve approximates the associated competitive equilibrium of the underlying economy. Motivated by these findings, we provide a theoretical argument for why evolutionary forces can lead to competitive outcomes in market games.     

Equilibrium portfolios in the neoclassical growth model

This paper studies equilibrium portfolios in the standard neoclassical growth model under uncertainty with heterogeneous agents and dynamically complete markets. Preferences are purposely restricted to be quasi-homothetic. The main source of heterogeneity across agents is due to different endowments of shares of the representative firm at date 0. Fixing portfolios is the optimal equilibrium strategy in stationary endowment economies with dynamically complete markets. However, when the environment displays changing degrees of heterogeneity across agents, the trading strategy of fixed portfolios cannot be optimal in equilibrium. Very importantly, our framework can generate changing heterogeneity if and only if either minimum consumption requirements are not zero or labor income is not zero and the value of human and non-human wealth are linearly independent.     

Connecting the cooperative and competitive structures of the multiple-partners assignment game

Multiple-partners assignment game is the name used by Sotomayor [The multiple partners game, in: M. Majumdar (Ed.), Equilibrium and Dynamics: Essays in Honor of David Gale, The Macmillan Press Ltd., New York, 1992; The lattice structure of the set of stable outcomes of the multiple partners assignment game, Int. J. Game Theory 28 (1999) 567-583] to describe the cooperative structure of the many-to-many matching market with additively separable utilities. Stability concept is proved to be different from the core concept. An economic structure is proposed where the concept of competitive equilibrium payoff is introduced in connection to the equilibrium concept from standard microeconomic theory. The paper examines how this equilibrium concept compares with the cooperative equilibrium concept. Properties of interest to the cooperative and competitive markets are derived.     

Constrained suboptimality in incomplete markets: a general approach and two applications

Summary. In this paper we re-examine generic constrained suboptimality of equilibrium allocations with incomplete numeraire asset markets. We provide a general framework which is capable of resolving some issues left open by the previous literature, and encompasses many kinds of intervention in partially controlled market economies. In particular, we establish generic constrained suboptimality, as studied by Geanakoplos and Polemarchakis, even without an upper bound on the number of households. Moreover, we consider the case where asset markets are left open, and the planner can make lump-sum transfers in a limited number of goods. We show that such a perfectly anticipated wealth redistribution policy, though consistent with the assumed incomplete financial structure, is typically effective. Received: August 14, 1995; revised version: April 11, 1997     

Consumption choice and asset pricing with a non-price-taking agent

Summary. This paper develops a pure-exchange model to study the consumption-portfolio problem of an agent who acts as a non-price-taker, and to analyze the implications of his behavior on equilibrium security prices. The non-price-taker is modeled as a price leader in all markets; his price impact is then recast as a dependence of the Arrow-Debreu prices on his consumption, allowing a tractable formulation. Besides the aggregate consumption, the endowment of the non-price-taker appears as an additional factor in driving equilibrium allocations and prices. Comparisons of equilibria between a price-taking and a non-price-taking economy are carried out. Received: March 29, 1996; revised version October 29, 1996     

Anonymity and individual risk

Adverse selection economies with private information are generally studied under the assumption that contracts are exclusive. That is, retrading is prohibited. An alternative market mechanism, the anonymous mechanism, is studied here. Risk averse agents trade contingent claims directly and side markets are in equilibrium. The result is the anonymous equilibrium. The anonymous equilibrium results in a set of endogenous transfers and subsidies.     

Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually—so either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.     

Exchange in a general market with indivisible goods

We show how to restrict trades in exchange markets with heterogeneous indivisible goods so that the resulting restricted exchange markets, the fixed deal exchange markets, have a unique core allocation. Our results on fixed deal exchange markets generalize classical results on the Shapley-Scarf housing market, in which each agent owns one good only. Furthermore, we define the class of fixed deal exchange rules for general exchange markets, and prove that these are the only exchange rules that satisfy strategyproofness, individual rationality, and a weak form of efficiency.     

Multiplicity in general financial equilibrium with portfolio constraints

This paper explores the role of portfolio constraints in generating multiplicity of equilibrium. We present a simple financial market economy with two goods and two households, households who face constraints on their ability to take unbounded positions in risky stocks. Absent such constraints, equilibrium allocation is unique and is Pareto efficient. With one portfolio constraint in place, the efficient equilibrium is still possible; however, additional inefficient equilibria in which the constraint is binding may emerge. We show further that with portfolio constraints cum incomplete markets, there may be a continuum of equilibria; adding incomplete markets may lead to real indeterminacy.     

Fundamentals, information, and international capital flows: A welfare analysis

In the recent discussion surrounding the design of a new international financial architecture, enhancing transparency has widely been proposed as a policy essential for increasing the efficiency of international capital markets. This paper uses a simple two-country (two-agent) general equilibrium model with incomplete markets and production to explore the welfare consequences of an increase in public information about country-specific fundamentals (increase in transparency). An improvement in the quality of information has two effects on the ex ante welfare of individual countries: A direct effect that increases the efficiency of global capital allocation and welfare, and an indirect general equilibrium effect that increases asset price volatility and may decrease welfare. When the degree of risk-aversion is low, at least one country will gain from an increase in information quality. If the degree of risk-aversion is high, then there are robust examples of economies for which an increase in information hurts all countries. The paper also discusses how certain institutional arrangements (international derivative markets, international agency) could ensure that all countries gain from better information by providing insurance against information-induced asset price risk.     

Incomplete information and singleton cores in matching markets

We study ordinal Bayesian Nash equilibria of stable mechanisms in centralized matching markets under incomplete information. We show that truth-telling is an ordinal Bayesian Nash equilibrium of the revelation game induced by a common belief and a stable mechanism if and only if all the profiles in the support of the common belief have singleton cores. Our result matches the observations of Roth and Peranson [The redesign of the matching market for American physicians: some engineering aspects of economic design, Amer. Econ. Rev. 89 (1999) 748-780] in the National Resident Matching Program (NRMP) in the United States: (i) the cores of the profiles submitted to the clearinghouse are small and (ii) while truth-telling is not a dominant strategy most participants in the NRMP truthfully reveal their preferences.     

Distribution of wealth and incomplete markets: Theory and empirical evidence

This paper analyses the equilibrium distribution of wealth in an economy where firms’ productivities are subject to idiosyncratic shocks, returns on factors are determined in competitive markets, households have linear consumption functions and government imposes taxes on capital and labour incomes and equally redistributes the collected resources to households. The equilibrium distribution of wealth is explicitly calculated and its shape crucially depends on market incompleteness. With incomplete markets it follows a Paretian law in the top tail and the Pareto exponent depends on the saving rate, on the net return on capital, on the growth rate of population, and on portfolio diversification. The characteristics of the labour market crucially affects the bottom tail, but not the upper tail of the distribution of wealth in the case of completely decentralized labour market. The analysis also suggests a positive relationship between growth and wealth inequality. The theoretical predictions find a corroboration in the empirical evidence of United States in the period 1989-2004.     

Nonlinear incentive provision in Walrasian markets: a Cournot convergence approach

The paper studies insurance with moral hazard in a system of contingent-claims markets. Insurance buyers are modelled as Cournot monopolists or oligopolists. The other agents condition their expectations on market prices, as in models of rational-expectations equilibrium with asymmetric information. Thereby they correctly anticipate accident probabilities corresponding to effort incentives induced by insurance buyers’ net trades. When there are many agents to share the insurance buyers’ risks, Cournot equilibrium outcomes are close to being second-best. In contrast, if insurance buyers are price takers, equilibria fail to exist or are bounded away from being second-best.     

Matching and bargaining models of markets: approximating small markets by large markets

Summary. We show that the equilibrium of a matching and bargaining model of a market in which there is a finite number of agents at each date need not be near the equilibrium of a market with a continuum of agents, although matching probabilities are the same in both markets. Holding the matching process fixed, as the finite market becomes large its equilibrium approaches the equilibrium of its continuum limit.Received: January 22, 1996; revised version: September 24, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Inducing liquidity in thin financial markets through combined-value trading mechanisms

Asset pricing theory hypothesizes that investors are only interested in portfolios; individual securities are evaluated only in terms of their contribution to portfolio risk and return. Yet, standard financial market design is that of parallel, unconnected markets, whereby investors cannot submit orders in one market conditional on events in others. When markets are thin, this exposes them to substantial execution risk. Fear of ending up with unbalanced portfolios after trading may even keep investors from submitting orders, further eroding liquidity and the ability of markets to equilibrate. The suggested solution is a portfolio trading mechanism referred to as combined-value trading (CVT). Investors are allowed to submit orders for packages of securities and the system matches trades and computes prices by optimally combining portfolio orders in an open book. We study the performance of the CVT mechanism experimentally and compare it to the performance of parallel, unconnected double auctions in experiments with similar parametrization and either a similar number of subjects or substantially thicker markets. We present evidence that our portfolio trading mechanism facilitates equilibration to the extent that the thicker markets do. Inspection of order submission and trade activity reveals that subjects manage to exploit the direct linkages between markets enabled by the CVT system.     

Supply function equilibria: Step functions and continuous representations

In most electricity markets generators must submit step-function offers to a uniform price auction. These markets are often modelled as simpler pure-strategy Supply Function Equilibria (SFE) with continuous supply functions. Critics argue that the discreteness and discontinuity of the required steps drastically change Nash equilibria, invalidating predictions of the SFE model. We prove that there are sufficient conditions, offered quantities can be continuously varied, offered prices are selected from a finite set, and the density of the additive demand shock is not too steep, where the resulting stepped SFE converges to the continuous SFE as the number of steps increases, reconciling the apparently very disparate approaches to modelling electricity markets.     

Matching through position auctions

Using a mechanism design framework, we characterize how a profit-maximizing intermediary can design matching markets when each agent is privately informed about his quality as a partner. Sufficient conditions are provided that ensure a version of positive assortative matching (what we call truncated positive assortative matching) maximizes profits. Under these conditions, all-pay position auctions always implement the profit-maximizing allocation. Winners-pay position auctions, however, only do so in sufficiently large markets.     

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     

Network effects, market structure and industry performance

This paper analyzes oligopolistic markets with network externalities. Exploiting a minimal complementarity structure on the model primitives that allows for pure network goods, we prove existence of non-trivial fulfilled-expectations equilibrium. We formalize the concept of industry viability, investigate its determinants, and show that it improves with more firms in the market and/or by technological progress. These results enlighten some well-known conclusions from case studies in the management strategy literature. We also characterize the effects of market structure on industry performance, which depart substantially from ordinary markets. The approach relies on lattice-theoretic methods, supplemented with basic insights from nonsmooth analysis.