A DYNAMIC ENTRY AND PRICE GAME WITH CAPACITY INDIVISIBILITY

Strategic market interaction is here modelled as a two‐stage game in which potential entrants choose capacities and next active firms compete in prices. Due to capital indivisibility, the capacity choice is made from a finite grid and there are economies of scale. In the simplest version of the model with a single production technique, the equilibrium turns out to depend on the ratio between the level of total output at the long‐run competitive equilibrium and the firm's minimum efficient scale: if that ratio is sufficiently large (the market is sufficiently ‘large’), then the competitive price emerges at a subgame‐perfect equilibrium of the capacity and price game; if not, then the firms randomize in prices on the equilibrium path. The role of the market size for the competitive outcome is shown to be even more important if there are several available production techniques.     

The effects of rent asymmetries in experimental auction markets

We report the results of twelve ‘double-auction’ market experiments designed to analyze the effects of asymmetric induced supply and demand configurations on the price convergence path toward a competitive equilibrium. The proposition (convergence bias) that prices tend to approach the competitive equilibrium from above (below) when consumer surplus is greater (less) than producer surplus cannot be rejected. We do, however, reject the proposition (convergence symmetry) that these convergence biases are of equal absolute magnitude. Excesses of producer over consumer surplus are found to have a more pronounced effect on the sequence of contract prices.     

Rationing rule, imperfect information and equilibrium

Summary. The impact of imperfect information on the price setting behaviour of firms is analysed. Specifically, consumers support an information cost to become informed about prices. Firms are endowed with U-shaped average cost curves. If a firm does not supply more than its competitive supply as determined by its marginal cost schedule, then we show that the existence of a pure strategy equilibrium is conditional on the rationing rule employed. If uninformed consumers are served first then the monopoly price is the sole equilibrium whenever consumers' information costs are high enough. Otherwise, a pure strategy equilibrium fails to exist contrary to the results of Salop and Stiglitz (1977) or Braverman (1980) who implicitly suppose that firms supply all the demand at a given price. Received: May 17, 1999; revised version: September 15, 2000     

Coalition-proof supply function equilibria in oligopoly

In an industry where firms compete via supply functions, the set of equilibrium outcomes is large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains large. Specifically, the set of prices that can be sustained by supply function equilibria is the interval between the competitive price and the Cournot price. In sharp contrast, when the number of firms is above a threshold we identify (e.g., three if demand is linear), only the Cournot outcome can be sustained by a coalition-proof supply function equilibrium.     

COMPETITIVE PRICING AND EFFICIENCY IN SEARCH EQUILIBRIUM*

We consolidate and generalize some results on price determination and efficiency in search equilibrium. Extending models by Rubinstein and Wolinsky and by Gale, heterogeneous buyers and sellers meet according to a general matching technology and prices are determined by a general bargaining condition. When the discount rate r and search costs converge to 0, we show that prices in all exchanges are the same and equal the competitive, market clearing, price. Given positive search costs, efficiency obtains iff bargaining satisfies Hosios' condition and r=0. When prices are set by third‐party market makers, however, we show that search equilibrium is necessarily efficient.     

Information acquisition and mutual funds

We study the formation of mutual funds by generalizing the standard competitive noisy rational expectations framework. In our model, informed agents set up mutual funds as a means of selling their private information to uninformed agents. We study the case of imperfect competition among fund managers, where uninformed agents invest simultaneously in multiple mutual funds. The size of the assets under management in the mutual fund industry is determined by endogenizing the agents' information acquisition decisions. Our model yields novel predictions on the informativeness of price, the optimal fees of mutual funds, and the equilibrium risk premium. In particular, we show that a sufficiently competitive mutual fund sector yields more informative prices and a lower equity risk premium.     

Monotonicity and Rationalizability in a Large First Price Auction

This paper proves that the monotonicity of bidding strategies together with the rationality of bidders implies that the winning bid in a first price auction converges to the competitive equilibrium price as the number of bidders increases ( Wilson, 1977 ). Instead of analysing the symmetric Nash equilibrium, we examine rationalizable strategies ( Bernheim (1984) , Pearce (1984) ) among the set of monotonic bidding strategies to prove that any monotonic rationalizable bidding strategy must be within a small neighbourhood of the „truthful” valuation of the object, conditioned on the signal received by the bidder. We obtain an information aggregation result similar to that of Wilson (1977) , while dispensing with almost all symmetric assumptions and using a milder solution concept than the Nash equilibrium. In particular, if every bidder is ex ante identical, then any rationalizable bidding strategy must be within a small neighbourhood of the symmetric Nash equilibrium. In a symmetric first price auction, the symmetry of outcomes is implied rather than assumed.     

Information and behavior in experimental markets

This paper reports the results of a block of experiments designed to analyze the effects of information on market performance in experimental competitive markets. Variations in institutional structure are utilized to affect the kind and amount of information subjects could gather about prices and supply and demand conditions. More information is associated with more rapid convergence, smaller variances, and closer convergence while efficiency and mean transactions prices are unaffected.     

Asymmetries in price and quantity adjustments by the competitive firm

Focusing on the crucial role of inventory carry-overs in the production and sales decision, we describe the profit maximizing behavior of a dynamic competitive firm facing random prices. Each firm's behavior is incorporated into a stochastic equilibrium model of the competitive industry with uncertain demand. The industry model exhibits asymmetric cyclical fluctuations of the “Keynesian” sort: when demand is weak, output contracts while price holds at a fixed floor; when demand is strong, price increases as output is constrained by a ceiling. Even in a pure world of constant returns, without increasing costs, the inability to instantaneously coordinate production and sales along with the existence of inventories is sufficient to yield a “backward L” shaped supply curve for the short run.     

Bertrand vs. Cournot equilibrium with risk averse firms and cost uncertainty

Summary. In an oligopoly game with cost uncertainty and risk averse firms, we show that Bertrand and Cournot equilibrium have different convergence properties when the market is replicated. The Cournot equilibrium price converges to the competitive price. Under very typical and somewhat general conditions, the highest Bertrand equilibrium price converges to one higher than the competitive equilibrium. We also give examples to show how to compute the limit of the highest Bertrand equilibrium prices and illustrate the ideas of the proof. We explore conditions under which the supply curve is upward sloping, a useful condition for our results. Received: April 20, 2000; revised version: May 10, 2001     

Two-period trading sentiment asset pricing model with information

We present a dynamic asset pricing model with investor sentiment and information, which shows that the investor sentiment plays a systematic and important role in the asset prices and the information is gradually incorporated into prices. The model has an analytical solution to the sentiment equilibrium price. We find that sentiment trading quantity not only increases the market liquidity, but also causes the asset prices' overreaction if the intensity of sentiment demand is more than a constant value. Therefore, the continuing overreactions result in a short-term momentum and a long-term reversal. The model could offer a partial explanation to some financial anomalies such as price bubbles, high volatility, asset prices' overreaction and so on.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

The efficiency of competitive mechanisms under private information

We consider the efficiency properties of exchange economies where privately informed traders behave strategically. Specifically, a competitive mechanism is any mapping of traders’ reports about their types to an equilibrium price vector and allocation of the reported economy. In our model, some traders may have non-vanishing impact on prices and allocations regardless of the size of the economy. Although truthful reporting by all traders cannot be achieved, we show that, given any desired level of approximation, there is such that any Bayesian-Nash equilibrium of any competitive mechanism of any private information economy with or more traders leads, with high probability, to prices and allocations that are close to a competitive equilibrium of the true economy. In particular, allocations are approximately efficient. A key assumption is that there is small probability that traders behave non-strategically.     

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.     

Dynamic Optimal Taxation with Private Information

We study dynamic optimal taxation in a class of economies with private information. Optimal allocations in these environments are complicated and history-dependent. Yet, we show that they can be implemented as competitive equilibria in market economies supplemented with simple tax systems. The market structure in these economies is similar to that in Bewley (1986) ; agents supply labour and trade risk-free claims to future consumption, subject to a budget constraint and a debt limit. Optimal taxes are conditioned only on two observable characteristics—an agent's accumulated stock of claims, or wealth, and her current labour income. We show that optimal taxes are generally non-linear and non-separable in these variables and relate the structure of marginal wealth and income taxation to the properties of agent preferences.     

INCENTIVE EFFICIENT PRICE SYSTEMS IN LARGE INSURANCE ECONOMIES WITH ADVERSE SELECTION

We decentralize incentive efficient allocations in large adverse selection economies by introducing a competitive market for mechanisms, that is, for menus of contracts. Facing a budget constraint, informed individuals purchase (lottery) tickets to enter mechanisms, whereas firms sell tickets and supply slots at mechanisms at given prices. Beyond optimization, market clearing, and rational expectations, an equilibrium requires that firms cannot favorably change, or cut, prices. An equilibrium exists and is incentive efficient. An equilibrium can be computed as the solution to a programming problem that selects the incentive efficient outcome preferred by the highest type within an appropriately defined set. For two‐types economies, this is the only equilibrium outcome.     

Fixed price plus rationing: an experiment

This paper theoretically and experimentally explores a fixed price mechanism in which, if aggregate demand exceeds supply, bidders are proportionally rationed. If demand is uncertain, in equilibrium bidders overstate their true demand in order to alleviate the effects of being rationed. This effect is the more intense the lower the price, and bids reach their upper limit for sufficiently low prices. In the experiment we observe a significant proportion of equilibrium play. However, subjects tend to overbid the equilibrium strategy when prices are high and underbid when prices are low. We explain the experimental evidence by a simple model in which the probability of a deviation is decreasing in the expected loss associated with it.

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Trade prices and supply in the UK economy

Current account imbalances are a major source of instability in the world monetary and trading system. Measures to correct these imbalances have largely involved adjustments to exchange rates. In the international trade literature, when the current account is in deficit, the Marshall-Lerner condition is sufficient for a successful devaluation. However, this partial equilibrium condition — apart from being based on the assumption that supply elasticities are infinite — abstracts from how the domestic economy responds to the change in relative prices. In this paper we develop a model of price and output determination in an open economy with imperpectly competitive markets, and draw a distinction between goods which are exported and those which are supplied to the domestic market. This means that we have to determine jointly both export prices and the domestic price of house sales. We show that as long as there is no money illusion in the labour market a fall in the nominal exchange rate raises domestic and export prices proportionally and leaves trade volumes unaffected. However, shifts in domestic absorption relative to overseas demand — by changing relative prices — cause shifts in the relative supply of exports and domestically sold goods and affect the trade balance. Thus fiscal and monetary measures directed towards reducing domestic absorption are more likely to be successful in correcting current account imbalances than exchange rate depreciation.     

Competition and confidentiality: Signaling quality in a duopoly when there is universal private information

We model non-cooperative signaling by two firms that compete over a continuum of consumers, assuming each consumer has private information about the intensity of her preferences for the firms' respective products and each firm has private information about its own product's quality. We characterize a symmetric separating equilibrium in which each firm's price reveals its respective product quality. We show that the equilibrium prices, the difference between those prices, the associated outputs, and profits are all increasing functions of the ex ante probability of high safety. If horizontal product differentiation is sufficiently great then equilibrium prices and profits are higher under incomplete information about quality than if quality were commonly known. Thus, while signaling imposes a distortionary loss on a monopolist using price to signal quality, duopolists may benefit from the distortion as it can reduce competition. Finally, average quality is lower since signaling quality redistributes demand towards low-quality firms.     

Long-run industry equilibrium with uncertainty

In this paper we consider the effects of uncertainty on industry equilibrium when firms must commit themselves to production before prices are revealed. We show that (a) an increase in demand uncertainty will (i) not affect the equilibrium number and size of firms if they are risk neutral, (ii) reduce the equilibrium number of firms if they are risk averse, but will have an ambiguous effect on their size. (b) In equilibrium, firms operate at capacity if they are risk neutral, but at excess capacity if they are risk averse.