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.     

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.     

Herding effects in order driven markets: The rise and fall of gurus

We introduce an order driver market model with heterogeneous traders that imitate each other on a dynamic network structure. The communication structure evolves endogenously via a fitness mechanism based on agents performance. We assess under which assumptions imitation, among noise traders, can give rise to the emergence of gurus and their rise and fall in popularity over time. We study the wealth distribution of gurus, followers and non followers and show that traders have an incentive to imitate and a desire to be imitated since herding turns out to be profitable. The model is then used to study the effect that different competitive strategies (i.e. chartist & fundamentalist) have on agents performance. Our findings show that positive intelligence agents cannot invade a market populated by noise traders when herding is high.     

Strategic noise traders and liquidity pressure with a physically deliverable futures contract

Do physically deliverable futures contracts induce liquidity pressure in the underlying spot market? The answer is believed to be no since the asset is delivered sometimes after the expiration of the contract so that the futures trader's payoff does not clearly depend on the price of the underlying stock at expiration. We construct a rational expectations equilibrium model in which a strategic uninformed trader induces liquidity pressure in the underlying spot market at the expiration of a physically deliverable futures contract. Liquidity pressure is the result of a pure informational advantage: if it is known that futures traders hedge their position in the spot market then a strategic trader with no information about the fundamental value of the underlying has an incentive to create noise in the futures market in order to gain information on the composition of the spot order flow at future auctions. We show that informed traders benefit from this form of strategic noise and that the efficiency of the prices remains unaffected.     

Strategic Bargaining and Competitive Bidding in a Dynamic Market Equilibrium

This paper extends the bargaining and matching literature, such as Rubinstein and Wolinsky (1985), by considering a new matching process. We assume that a central information agency exists, such as real estate agencies in the housing market and employment agencies (or newspapers) in the labour market, which puts traders into direct contact with each other. With heterogeneity of trader preferences, equilibrium trade is characterized by existing traders on each side of the market trying to match with the flow of new traders on the other side (since existing traders have already sampled and rejected each other). Two procedures of trade co-exist, namely a strategic bilateral bargaining process and a competitive bidding process, depending on the number of potential matches a new trader obtains. We characterize the unique symmetric Markov perfect equilibrium to this stochastic trading game.     

Convergence of outcomes and evolution of strategic behavior in double auctions

We study the emergence of strategic behavior in double auctions with an equal number of buyers and sellers, under the distinct assumptions that orders are cleared simultaneously or asynchronously. The evolution of strategic behavior is modeled as a learning process driven by a genetic algorithm. We find that, as the size of the market grows, allocative inefficiency tends to zero and performance converges to the competitive outcome, regardless of the order-clearing rule. The main result concerns the evolution of strategic behavior as the size of the market gets larger. Under simultaneous order-clearing, only marginal traders learn to be price takers and make offers equal to their valuations/costs. Under asynchronous order-clearing, all intramarginal traders learn to be price makers and make offers equal to the competitive equilibrium price. The nature of the order-clearing rule affects in a fundamental way what kind of strategic behavior we should expect to emerge.     

Trading networks with price-setting agents

In a wide range of markets, individual buyers and sellers trade through intermediaries, who determine prices via strategic considerations. Typically, not all buyers and sellers have access to the same intermediaries, and they trade at correspondingly different prices that reflect their relative amounts of power in the market. We model this phenomenon using a game in which buyers, sellers, and traders engage in trade on a graph that represents the access each buyer and seller has to the traders. We show that the resulting game always has a subgame perfect Nash equilibrium, and that all equilibria lead to an efficient allocation of goods. Finally, we analyze trader profits in terms of the graph structure — roughly, a trader can command a positive profit if and only if it has an “essential” connection in the network, thus providing a graph-theoretic basis for quantifying the amount of competition among traders.     

Limit orders,asymmetric information,and the formation of asset prices with a computerized specialist

We analyze the existence of equilibrium in an asset market under asymmetric information. Price formation is modeled as a bilateral sealed bid auction where uninformed and informed traders submit limit orders to a computerized specialist. The computerized specialist is programmed to sell to the highest bidder and buy from the seller asking the lowest price. We show that this mechanism — which is designed to model the Globex and RAES trading institutions used in Chicago, London, New York, Paris, and Germany — yields an equilibrium in which the bid-ask spread is endogenously random and the passive specialist earns nonnegative profits.     

Informed manipulation

In asymmetric information models of financial markets, prices imperfectly reveal the private information held by traders. Informed insiders thus have an incentive not only to trade less aggressively but also to manipulate the market by trading in the wrong direction and undertaking short-term losses, thereby increasing the noise in the trading process. In this paper we show that when the market faces uncertainty about the existence of the insider in the market and when there is a large number of trading periods before all private information is revealed, long-lived informed traders will manipulate in every equilibrium.     

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.     

Local coordination and market equilibria

We reformulate the local stability analysis of market equilibria in a competitive market as a local coordination problem in a market game, where the map associating market prices to best-responses of all traders is common knowledge and well-defined both in and out of equilibrium. Initial expectations over market variables differ from their equilibrium values and are not common knowledge. This results in a coordination problem as traders use the structure of the market game to converge back to equilibrium. We analyse a simultaneous move and a sequential move version of the market game and explore the link with local rationalizability.     

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.     

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.     

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: The finite state case

This paper is devoted to the question of whether traders can learn rational expectations from repeated observations of market data in a stationary environment with finitely many exogenous states of the world. The learning problem is placed in the context of an iterative adjustment process which achieves equilibrium if traders have rational expectations. The main result is that even if traders begin with no knowledge of their environment, there exists an estimation procedure which converges to rational expectations when the environment satisfies a certain regularity condition. The regularity condition is shown to be generic.     

Increasing risk and equilibrium under uncertainty

The impact of increasing risk on social welfare and resource allocation is analysed in a general equilibrium model with endowment uncertainty. It is shown that the equilibrium allocation of resources is affected only by an increase in those risks which are important for society as a whole. In contrast, increases in purely individual risk do not influence achievable social welfare and have no effect on the utility of traders in a competitive market.     

Dynamic price formation in a futures market via double auctions

Summary We report an exploratory study of the process of price formation in a speculative market in the absence of liquidity traders. Traders exchange a futures contract because they interpret information differently. We formulate trading as a sequence of anonymous double auctions and introduce a notion of bounded rationality in which traders use approximate models of market response in forming their bids. We prove existence of a perfect equilibrium in the sequential anonymous auctions game, and show that the equilibrium has a no-regret property. After learning the market price, a trader regrets neither the bid that he made nor the position that he holds. We show that trading volume is related to changes in the distribution of information in the economy. We also show that volume and expected change in price are related to two different attributes of the pattern of private information flow. Fundamentally, no particular relationship between the time series of these variables is always valid for all futures contracts. This point is emphasized by an example.I am thankful for useful comments made by Avraham Beja, James Gammil, Chi-fu Huang, David Scharfstein and three anonymous referees. Financial support from Stanford Graduate School Faculty Fellowship is gratefully acknowledged.     

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.     

Rational panics and stock market crashes

This paper offers an explanation for stock market crashes which focuses on the role of rational but uninformed traders. We show that uninformed traders can precipitate a price crash because as prices decline, they surmise that informed traders received negative information, which leads them to reduce their demand for assets and drive the price of stocks even lower. The model yields several implications, such as that crashes can occur even when the fundamentals are strong, and that the magnitude of the crash depends on the fraction of uninformed investors and the amount of unsophisticated passive investing present in the market.     

Admissible market data structures: A complete characterization

This paper characterizes the market data which, if observed by traders in a stochastic exchange environment, will permit the general existence of (rational) expectations equilibria. It is proved that if a trader observes and conditions his expectations on some nonconstant market data, he must observe at least the equilibrium price and his own equilibrium trade. Any data which do not satisfy this requirement, such as the price alone, or the price and the volume of trade, will fail to permit the existence of an expectations equilibrium for some otherwise well-behaved stochastic environment.