Convergence of the Aumann–Davis–Maschler and Geanakoplos bargaining sets

Summary. Geanakoplos [17] defined a notion of bargaining set, and proved that his bargaining set is approximately competitive in large finite transferable utility (TU) exchange economies with smooth preferences. Shapley and Shubik [26] showed that the Aumann–Davis–Maschler bargaining set is approximately competitive in replica sequences of TU exchange economies with smooth preferences. We extend Geanakoplos result to nontransferable utility (NTU) exchange economies without smooth preferences, and we extend the Shapley and Shubik result to non-replica sequences of NTU exchange economies with smooth preferences.Received: November 11, 1996This revised version was published online in February 2005 with corrections to the cover date.     

“Very Nice” trivial equilibria in strategic market games

Following Shapley [Theory of Measurement of Economic Externalities, Academic Press, New York, 1976], we study the problem of the existence of a Nash Equilibrium (NE) in which each trading post is either active or “legitimately” inactive, and we call it a Shapley NE. We consider an example of an exchange economy, borrowed from Cordella and Gabszewicz [Games Econ. Behav. 22 (1998) 162–169], which satisfies the assumptions of Dubey and Shubik [J. Econ. Theory 17 (1978) 1–20], and we show that the trivial equilibrium, the unique NE of the associated strategic market game, is not “very nice,” in the sense that it is not “legitimately” trivial. This result has the more general implication that, under the Dubey and Shubik's assumptions, a Shapley NE may fail to exist.     

The nonatomic assignment model

Summary We formulate a model with a continuum of individuals to be assigned to a continuum of different positions which is an extension of the finite housing market version due to Shapley and Shubik. We show that optimal solutions to such a model exist and have properties similar to those established for finite models, namely, an equivalence among the following: (i) optimal solutions to the linear programming problem (and its dual) associated with the assignment model; (ii) the core of the associated market game; (iii) the Walrasian equilibria of the associated market economy.     

Evolution of Walrasian equilibrium in an exchange economy

We study the stochastic stability of a dynamic trading process in an exchange economy. We use a simplified version of a trading model à la Shapley and Shubik (J Polit Econ 85:937–968, 1977). Two types of agents equipped with Leontief preferences trade goods in markets by offering endowments, and actual trades occur at market clearing prices. Better behavior tends to spread through the same type of agents by imitation, and agents also make mistakes occasionally. We provide a sufficient condition for the perturbed dynamic process to have a unique stochastically stable state that is a Walrasian equilibrium allocation. In this sense, we give a rationale for Walrasian behavior.     

Market Games in Large Economies with a Finite Number of Types

We study market games derived from an exchange economy with a continuum of agents, each having one of finitely many possible types. The type of agent determines his initial endowment and utility function. It is shown that, unlike the well-known Shapley–Shubik theorem on market games (Shapley and Shubik in J Econ Theory 1:9–25, 1969), there might be a (fuzzy) game in which each of its sub-games has a non-empty core and, nevertheless, it is not a market game. It turns out that, in order to be a market game, a game needs also to be homogeneous. We also study investment games – which are fuzzy games obtained from an economy with a finite number of agents cooperating in one or more joint projects. It is argued that the usual definition of the core is inappropriate for such a model. We therefore introduce and analyze the new notion of comprehensive core. This solution concept seems to be more suitable for such a scenario. We finally refer to the notion of feasibility of an allocation in games with a large number of players. Some of the results in this paper appear in a previous draft distributed by the name “Cooperative investment games or Population games”. An anonymous referee of Economic Theory is acknowledged for his/her comments     

Multiple equilibria and hysteresis in simple exchange models

This paper presents a simple two-good general equilibrium model of exchange in which demands are linear functions of relative prices. The solution of the model is represented by a cubic equation which can have either a single root which corresponds to a unique equilibrium price or three roots corresponding to multiple equilibria. The major properties of the model are that the relative price can make large discrete jumps in response to small parameter changes, and can display hysteresis. The paper shows how recent developments in non-linear methods can be used to examine the equilibrium properties of the model and establish conditions under which multiple equilibria can arise. The model is compared with that used by Shapley and Shubik.     

Strategic freedom, constraint, and symmetry in one-period markets with cash and credit payment

Summary. In order to explain in a systematic way why certain combinations of market, financial, and legal structures may be intrinsic to certain capabilities to exchange real goods, we introduce criteria for abstracting the qualitative functions of markets. The criteria involve the number of strategic freedoms the combined institutions, considered as formalized strategic games, present to traders, the constraints they impose, and the symmetry with which those constraints are applied to the traders. We pay particular attention to what is required to make these strategic market games well-defined, and to make various solutions computable by the agents within the bounds on information and control they are assumed to have. As an application of these criteria, we present a complete taxonomy of the minimal one-period exchange economies with symmetric information and inside money. A natural hierarchy of market forms is observed to emerge, in which institutionally simpler markets are often found to be more suitable to fewer and less-diversified traders, while the institutionally richer markets only become functional as the size and diversity of their users gets large.Received: 5 June 2003, Revised: 18 November 2003, JEL Classification Numbers: C7, G10, G20, L10, D40, D50. Correspondence to: Eric SmithEric Smith, Martin Shubik: We are grateful to Lloyd Shapley, Duncan Foley, and Doyne Farmer for discussions in the course of this work.     

Cooperative bargaining foundations of the Shapley–Shubik index

In a recent paper, we provide an interpretation of the Shapley–Shubik index as a measure of the ‘bargaining power’ that a voting rule gives to each member of a committee negotiating in search of consensus. It is assumed that negotiation takes place under the condition that every winning coalition can impose any agreement. In this paper we further investigate the axiomatic foundations of this interpretation of the Shapley–Shubik index. To this end a wider framework admitting random voting rules is considered.     

Information aggregation in financial markets with career concerns

What are the equilibrium features of a dynamic financial market in which traders care about their reputation for ability? We modify a standard sequential trading model to include traders with career concerns. We show that this market cannot be informationally efficient: there is no equilibrium in which prices converge to the true value, even after an infinite sequence of trades. We characterize the most revealing equilibrium of this game and show that an increase in the strength of the traders' reputational concerns has a negative effect on the extent of information that can be revealed in equilibrium but a positive effect on market liquidity.     

Front-running dynamics

We integrate a monopolist dual trader into a dynamic model of speculation. In static settings, [J.-C. Rochet, J.-L. Vila, Insider trading without normality, Rev. Econ. Stud. 61 (1994), 131-152] establish an irrelevance result—expected equilibrium outcomes are the same whether the monopolist speculator sees liquidity trade or not; and Roell [Dual-capacity trading and market quality, J. Finan. Intermediation (1990), 105-124] shows that with multiple speculators, dual trading benefits liquidity traders. In dynamic settings, these results are reversed: a front-running speculator exploits knowledge of future liquidity trade, extracting greater profits by smoothing profit extraction intertemporally. Front running introduces positive serial correlation to order flow. Accordingly, market makers discount past order flow in prices, but prices retain the martingale property.     

Market Games in Successive Oligopolies

This paper introduces a new approach to successive oligopolies. We draw on market games à la Shapley–Shubik to examine how successive oligopolies operate between downstream and upstream markets when the input price is determined by the action of all firms, downstream and upstream both. This approach differs from the classical one as it allows us to consider downstream firms that exercise market power both in both downstream and upstream markets. We perform a comparison of the market outcome with each scenarios as well as a welfare analysis.     

Money in the pure consumption loan model

The purpose of this paper is to show how modern techniques of Temporary competitive equilibrium analysis can be applied to models of the “pure consumption loan model” type. One considers Samuelson's simplest model where traders live two periods and where money is the only store of value. It is proved that a temporary equilibrium exists if price expectations are sufficiently independent of current prices. A stationary market equilibrium is shown to exist if there is a set of traders (i) whose total resources are greater when they are young than when they are old, (ii) who are indifferent between present and future consumption. It is proved that this existence theorem still holds if the economy is sufficiently “close” to an economy which has this property. A stationary market equilibrium is shown to be Pareto optimal if all traders hold positive cash balances. It may be inefficient if this condition is not satisfied, for some traders may then be willing to borrow, which they cannot do in this model.     

异质信念、投机均衡与农产品期货定价*

农产品期货市场套利并不充分,交易者也不是完全理性的。本文假设农产品期货市场有限套利、交易者异质信念并遵循“经验法则”预期,构建了农产品期货投机均衡定价模型,并认为集中竞价规则下产生的农产品期货价格是由交易者的预期决定的;前期期货价格水平、现货价格和前期期货价格的变动趋势、不同类型交易者的比例结构及其预期模式共同影响农产品期货价格的形成与波动;基本分析法交易者占主导地位的农产品期货市场具有更高的套期保值与价格发现效率。针对中国七种主要农产品期货的实证结果显示,农产品期货投机均衡定价模型对解释中国农产品期货价格的形成与波动是有效的。这意味着在期货行情系统中实时披露现货价格信息,培育和引导交易者运用基本分析法预测期货价格走势,有助于提升农产品期货市场的效率。     

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.     

Insider trading with public and shared information

We study the impact of public information and shared information on traders' trading behavior in the context of Kyle's (1985) speculative market. We suppose that there are four types of traders in our model: one insider, M outsiders, liquidity traders, and market makers. We explicitly describe the unique linear Nash equilibrium and find that public information harms the insider but benefits the outsiders and noise traders. Also, the market is more efficient because of the existence of public information.     

Product differentiation and competitive pressure

This paper compares the commonly used linear demand model introduced by Bowley (The mathematical groundwork of economics, Oxford University Press, Oxford, 1924) with the specification of Shapley and Shubik (Kyklos 22:30?C44, 1969). The latter has the advantage that aggregate demand does not depend on a parameter that measures the degree of product differentiation. This allows to interpret variations in the degree of product differentiation as changes in competitive pressure because these changes can influence aggregate demand only through changes in equilibrium prices and quantities. The consequences of the alternative specifications are made explicit with two applications. In both cases the different specifications yield substantial changes in important results in industrial economics.     

Efficiency properties of strategies market games: An axiomatic approach

The paper investigates the conditions under which an abstractly given market game will have the property that if there is a continuum of traders then every noncooperative equilibrium is Walrasian. In orther words, we look for a general axiomatization of Cournot's well-known result. Besides some convexity, continuity, and nondegeneracy hypotheses, the crucial axioms are: anonymity (i.e., the names of traders are irrelevant to the market) and aggregation (i.e., the net trade received by a trader depends only on his own action and the mean action of all traders). It is also shown that the same axioms do not guarantee efficiency if there is only a finite number of traders. Some examples are discussed and a notion of strict noncooperative equilibrium for anonymous games is introduced.     

Learning rational expectations in an asset market

Will traders in a risky asset market learn Muthian expectations when they initially lack the necessary information? If some traders learn from their observations, will market dynamics depend only on “fundamentals,” as implied by the Efficient Market Hypothesis? This paper shows that at any finite point in time the answer to these questions is “no”. The context is a constant absolute risk aversion model with two kinds of traders and asymmetric information. The market converges asymptotically to a rational expectations equilibrium where prices depend only on fundamentals and the market is efficient.     

Learning,estimation, and the stability of rational expectations

The stability of the rational expectations equilibrium of a simple asset market model is studied in a situation where a group of traders learn about the relationship between the price and return on the asset using ordinary least squares estimation, and then use their estimates in predicting the return from the price. The model which they estimate is a well-specified model of the rational expectations equilibrium, but a misspecified model of the situation in which the traders are learning. It is shown that for appropriate values of a stability parameter the situation converges almost surely to the rational expectations equilibrium.     

Endogenous market segmentation with heterogeneous agents

Summary. An explanation is provided for the evolution of segmented marketplaces in a pairwise exchange economy. Large traders operating in a pairwise exchange market prefer to meet other similar traders, because this enables them to trade their endowments in a smaller number of encounters. Large and small traders, however, cannot be distinguished a priori, and the existence of the small traders imposes a negative externality on the large traders. We show that, under conditions which are not very restrictive, establishing a separate market (perhaps with an entry fee) designated for the large traders induces the two types of traders to segment themselves. However, this segmentation is not necessarily welfare improving. Received: January 12, 2001; revised version: July 17, 2002 RID="*" ID="*" I wish to thank the participants in the Friday Theory Workshop at the University of Sydney, and the participants at the 17th Australian Theory Workshop at the University of Melbourne for comments and discussion. John Hillas and Stephen King pointed out an omission in an earlier version, and Catherine de Fontenay and Hodaka Morita made extensive comments on earlier drafts. This work was initiated while I was a short-term visitor at the University of Southern California.