Asymmetric duopoly and the core

It has recently been proposed that an exchange economy with “small” and “large” traders be represented by a measure space whose atoms represent the set of large traders and whose atomless part represents the set of small traders. For such mixed markets, the equivalence of the core and the set of competitive allocations, which holds when the set of atoms is of measure zero, no longer holds necessarily when this set has positive measure. However, if this set consists of identical traders, the equivalence is restored. The asymptotic analogs of these propositions are proved here.     

A comparison between the core and the monopoly solutions in a mixed exchange economy

Summary. Using a mixed market model for analyzing imperfectly competitive economies, we maximize the oligopolists' Welfare Function, given individual rationality and feasibility constraints. We prove that solutions belong to the core for a large class of economies. This class includes, in particular, every monopoly having a single type of small traders. Note that all such solutions yield the large trader, utility-wise, strictly more than at any monopoly solution, where the monopolist plays strategically, and the ocean of small traders act as being as price-takers. Received: March 4, 1996; revised version July 7, 1996     

Advantageous monopolies

It is proved that in economies with one atom and one type of small traders, for each core allocation x there is a competitive allocation y whose utility to the monopolist is not greater than that of x, whenever either x is an equal treatment core allocation, or all small traders have the same homogeneous preferences. An example shows that these two requirements are, in general, indispensable for the result to hold.     

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.     

The case against eliminating large denomination bills

When large denomination bills are preferred in illegal activities, what is the optimal policy response? We construct a dual currency model where illegal activity can be reduced by modifying the payment environment. In our model, legal (goods) traders are indifferent between small and large bills, but illegal (goods) traders face a lower transaction cost of using large bills in comparison to small bills because it is easier to conceal. We show that eliminating large bills can reduce illegal trade and its associated social cost. However, this pooling equilibrium is sub-optimal because the government can collect more seigniorage by allowing illegal traders to use large bills with a lower rate of return. When the transaction cost of using small bills for illegal traders is sufficiently large, a separating equilibrium, where legal traders use small bills and illegal traders use large bills, can maximize welfare by making an implicit transfer from the illegal traders to the legal traders.     

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     

Commissions Matter: The Trading Behavior of Institutional and Individual Active Traders

We examine how commissions influence trading behavior by analyzing a unique data set of the equity trades of both individual and institutional active traders. Individual traders pay higher trading costs than institutional traders. As a result, they engage in more risky trading behaviors in order to cover these costs. Individual traders also trade significantly less because of their higher cost of trading. Individual traders tend to trade higher-priced stocks, hold their trades longer, and they experience much larger price swings than institutional traders. This leads individual traders to realize more dramatic gains and losses on their round-trips.     

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.     

Liquidity commonality in order-driven trading: evidence from the Athens Stock Exchange

We examine the presence of liquidity commonality in the order-driven Athens Stock Exchange (ASE). Unlike the majority of liquidity commonality studies that focus on the bid–ask spread, our analysis extends deeper in the Limit Order Book, providing insight on the price impact of both small and large trades. We utilize a 6-month FTSE/ATHEX-20 intraday data set to estimate the liquidity factor model of Chordia et al. (2000). To this end, we conduct single-equation analysis as well as panel data analysis with the use of two-way clustered errors, correcting for simultaneous firm and time correlations. Moreover, we apply standard principal component analysis on stock liquidities to extract the marketwide liquidity component. We find that liquidity commonality is low at the bid–ask spread, whereas it increases deeper in the book; consequently, large traders face liquidity risks associated with both individual stock and marketwide illiquidity. Moreover, our empirical evidence hints that liquidity commonality is asynchronous, suggesting that the ASE trading process includes various levels of information speed. Our analysis contributes to the understanding of liquidity commonality in order-driven trading, especially in emerging markets like the ASE where trading activity is limited and information speed is low.     

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     

Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes

We model an economy with clubs (or jurisdictions) where individuals may belong to multiple clubs and where clubs sizes are arbitrary—clubs may be restricted to consist of only one or two persons, or as large as the entire economy, or anything in-between. Notions of price-taking equilibrium and the core, both with communication costs, are introduced. These notions take into account that there is a small communication cost of deviating from a given outcome. We demonstrate that, given communication costs, for all sufficiently large economies the core is nonempty and the set of price-taking equilibrium outcomes is equivalent to the core.     

A limit theorem for an approximate core of a large but finite economy

We present a formulation of an approximate core that can be sustained as an approximate equilibrium for a ‘large enough’ finite exchange economy whose traders need not have transitive, continuous or convex preferences.     

The Effects of Subject Pool and Design Experience on Rationality in Experimental Asset Markets

Empirical evidence suggests that prices do not always reflect fundamental values and individual behavior is often inconsistent with rational expectations theory. We report the results of fourteen experimental asset markets designed to examine whether the interactive effect of subject pool and design experience (i.e., previous experience in a market under identical conditions) tempers price bubbles and improves forecasting ability. Our main findings are: 1) price run-ups are modest and dissipate quickly when traders are knowledgeable about financial markets and have participated in a previous market under identical conditions; 2) price bubbles moderate quickly when only a subset of traders are knowledgeable and experienced; 3) the heterogeneity of expectations about price changes is smaller in markets with knowledgeable and experienced traders, even if such traders only represent a subset of the market; and 4) individual forecasts of prices are not consistent with the predictions of the rational expectations model in any market, although absolute forecast errors are smaller for subjects who are knowledgeable of financial markets and for those subjects who have participated in a previous market. In sum, our findings suggest that markets populated by at least a subset of knowledgeable and experienced traders behave rationally, even though average individual behavior can be characterized as irrational.     

An advantage of the bargaining set over the core

An example of a market game is described for which the bargaining set seems to be intuitively more acceptable than the (nonempty) core. It also yields more insight into the nature of the competition that may exist among the traders.     

Competition and collusion in bilateral markets

In this paper, the core of a market game which constitutes the set of equilibria in the process of competitive contracting and recontracting is criticized as a solution concept for not being immune against theory absorption in the sense that knowledge of the core on part of the traders may result in a collusive stabilization of some dominated imputation. It is pointed out that a stable set (or, von Neumann-Morgenstern) solution does not suffer from this deficiency. Moreover, it is argued that stable set solutions provide an adequate analytical framework for the study of collusion, and are in this respect superior to the approach (relying on the core concept) chosen by Aumann in his work on disadvantageous monopolies. For symmetric bilateral market games — generated by markets involving the exchange of only two commodities, one of which also serves as a means of side payment and utility transfer, among two types of traders — with one seller and one up to three buyers all symmetric solutions are determined. Furthermore, a symmetric solution for markets with equal, but otherwise arbitrary, numbers of sellers and buyers is given. The symmetric stable sets of imputations are interpreted as rational standards of behavior providing the consistent and defensible rules of division necessary to make a cartel agreement viable.This research was partially supported by a grant given to New York University, Department of Economics, by the Office of Naval Research. (# N00014-76-C-0033). A first version of the paper was presented at the Third World Congress of the Eeconomtric Society, Toronto, Aug. 20–26, 1975, under the title Symmetric Solutions of Bilateral Market Games.     

Financial Bubbles: Excess Cash,Momentum, and Incomplete Information

We report on a large number of laboratory market experiments demonstrating that a market bubble can be reduced under the following conditions: 1) a low initial liquidity level, i.e., less total cash than value of total shares, 2) deferred dividends, and 3) a bid-ask book that is open to traders. Conversely, a large bubble arises when the opposite conditions exist. The first part of the article is comprised of twenty-five experiments with varying levels of total cash endowment per share (liquidity level), payment or deferral of dividends and an open or closed bid-ask book. We find that the liquidity level has a very strong influence on the mean and maximum prices during an experiment (P < 1/10,000). These results suggest that within the framework of the classical bubble experiments (dividends distributed after each period and closed book), each dollar per share of additional cash results in a maximum price that is $1 per share higher. There is also limited statistical support for the theory that deferred dividends (which also lower the cash per share during much of the experiment) and an open book lead to a reduced bubble. The three factors taken together show a striking difference in the median magnitude of the bubble ($7.30 versus $0.22 for the maximum deviation from fundamental value). Another set of twelve experiments features a single dividend at the end of fifteen trading periods and establishes a 0.8 correlation between price and liquidity during the early periods of the experiments. As a result, calibration of prices and evolution toward equilibrium price as a function of liquidity are possible.     

Liquid markets and competition

A market is liquid if no individual's actions have a big effect on the prices of goods traded in that market. Perfectly competitive markets are therefore perfectly liquid. It is well known that market liquidity can be achieved by increasing the number of traders so that individual trades are small compared to total trades. We show that even when there are only few traders, market liquidity can be achieved through large short sales in which net trades are small relative to gross trades. In particular, for a natural variant of the market game which permits unlimited short sales, we show that there is always a Nash equilibrium allocation arbitrarily close to a competitive equilibrium allocation. Of course, not all NE are near competitive. Only the large-short-sales NE are nearly liquid and hence close to CE.     

Social choice and electoral competition in the general spatial model

This paper extends the theory of the core, the uncovered set, and the related undominated set to a general set of alternatives and an arbitrary measure space of voters. We investigate the properties of social preferences generated by simple games; we extend results on generic emptiness of the core; we prove the general nonemptiness of the uncovered and undominated sets; and we prove the upper hemicontinuity of these correspondences when the voters’ preferences are such that the core is nonempty and externally stable. Finally, we give conditions under which the undominated set is lower hemicontinuous.     

Price Limits, Information Acquisition, and Bid–ask Spreads: Theory and Evidence

A number of futures markets use price limits which, in effect, preclude trade from occurring at prices outside certain exogenous bounds. Noting that such markets are characterized by heterogeneously informed traders, whereas previous work on price limits assumes symmetrically informed traders, we examine the effects of price limits in a setting where market participants are asymmetrically informed. We find that imposing price limits generally lowers the quality of information acquired in equilibrium, but lowers bid–ask spreads as well. Thus, depending on the relative weights placed by society on liquidity versus price efficiency, there may exist a set of price limits that are most efficient in achieving a trade-off between liquidity and informational efficiency. We perform empirical tests of some implications of the model using cross-sectional data on price limits. We find that price limits are strongly negatively related to both price volatility and trading volume. Though other explanations for our empirical findings cannot be ruled out, these results are not inconsistent with the model's implication that price limits should be tighter for contracts which offer greater profit potential for informed traders.     

Cournot-Walras and Cournot equilibria in mixed markets: A comparison

Summary In this paper, we show that, in markets with a continuum of traders and atoms, the set of Cournot-Walras equilibria and the set of Cournot equilibria may be disjoint. We show also that, when the preferences of the traders are represented by Cobb-Douglas utility functions, the set of Cournot-Walras equilibria and the set of Cournot equilibria have a nonempty intersection.I would like to thank R. Amir, B. de Meyer, J. J. Gabszewicz, J.-F. Mertens, H. Polemarchakis and L. Ventura for some helpful discussions about the questions examined in the present work.