Carbon sequestration and permit trading on the competitive fringe

This paper makes two contributions to the carbon-sequestration policy literature. First and foremost, we develop a theoretical framework in which sequestration and permit-trading markets are analyzed jointly in the context of a competitive fringe model. Our framework formalizes the linkage between regulatory policy changes (as they manifest themselves in the permit market) and subsequent equilibrium allocations in the sequestration market. Second, we perform a numerical analysis demonstrating the role market structure, or market power, might play in the determination of the equilibrium sequestration allocation and carbon price. Both our analytical and numerical results demonstrate the importance of incorporating into empirical supply-side models demand-side information that is reflective of an underlying market structure.     

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.     

Risky arbitrage,asset prices,and externalities

We introduce a no-risky-arbitrage price condition (NRAP) for asset market models allowing both unbounded short sales and externalities such as trading volume. We then demonstrate that NRAP is sufficient for the existence of competitive equilibrium in the presence of externalities. Moreover, we show that if all risky arbitrages are utility increasing, then NRAP characterizes competitive equilibrium in the presence of externalities. We are indebted to an anonymous referee for helpful comments on an earlier version of this paper. Page and Wooders are especially grateful to CERMSEM and EUREQua for their support and hospitality which made possible our collaboration.     

Robust monopoly pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the pricing policies under two distinct decision criteria with multiple priors: (i) maximin utility and (ii) minimax regret. The equilibrium price under either criterion is lower then in the absence of uncertainty. The concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty.     

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.     

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.     

The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labor union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences and on the distribution of bargaining power over the input price. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function.     

Retrading in market games

When agents are not price takers, they typically cannot obtain an efficient real location of resources in one round of trade. This paper presents a non-cooperative model of imperfect competition where agents can retrade allocations, consistent with Edgeworth's idea of recontracting. We show (a) there are Pareto optimal allocations, including competitive equilibrium allocations, that can be approximated arbitrarily closely when trade is myopic, i.e., when agents play a static Nash equilibrium at every round of retrading; (b) any converging sequence of allocations generated by myopic retrading can be supported along some retrade-proof subgame perfect equilibrium path when traders anticipate future rounds of trading.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

Softening competition through forward trading

In the history of alleged manipulations on forward markets, it has been observed that high prices resulted from a cartel's long positions. The present paper addresses this issue in a simple model of price setting duopolists. We show that forward trading results in producers buying forward their own production, so that equilibrium prices are increased compared to the case without forward trading. This result contrasts with the social desirability of forward markets emphasized by the academic literature.     

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.     

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.     

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.     

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.     

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.     

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.     

Rock around the clock: An agent-based model of low- and high-frequency trading

We build an agent-based model to study how the interplay between low- and high-frequency trading affects asset price dynamics. Our main goal is to investigate whether high-frequency trading exacerbates market volatility and generates flash crashes. In the model, low-frequency agents adopt trading rules based on chronological time and can switch between fundamentalist and chartist strategies. By contrast, high-frequency traders activation is event-driven and depends on price fluctuations. High-frequency traders use directional strategies to exploit market information produced by low-frequency traders. Monte-Carlo simulations reveal that the model replicates the main stylized facts of financial markets. Furthermore, we find that the presence of high-frequency traders increases market volatility and plays a fundamental role in the generation of flash crashes. The emergence of flash crashes is explained by two salient characteristics of high-frequency traders, i.e., their ability to i. generate high bid-ask spreads and ii. synchronize on the sell side of the limit order book. Finally, we find that higher rates of order cancellation by high-frequency traders increase the incidence of flash crashes but reduce their duration.     

The existence of fully rational expectations approximate equilibria with noisy price observations

Nonrevealing fully rational expectations approximate equilibria exist in microeconomic pure exchange economies in which uninformed agents have suitably dispersed noisy price observations. Such traders maximize a state-dependent expected utility conditional on the price vector they observe, the distributions of noisy price observations, and the correct equilibrium relationship between states of the world and prices. In equilibrium, aggregate excess demand is small with high probability in every state of the world (and its expectation is also small); this magnitude diminishes as the noisy price observations become more accurate. Equilibria are obtained by applying a fixed point argument to state-dependent excess demand functions which are smooth because of the noisy price observations.     

Trading mechanism selection with directed search when buyers are risk averse

We endogenize the trading mechanism selection in a model of directed search with risk averse buyers and show that the unique symmetric equilibrium entails all sellers using fixed price trading. Mechanisms that prescribe the sale price as a function of the realized demand (auctions, bargaining, discount pricing, etc.) expose buyers to the “price risk”, the uncertainty of not knowing how much to pay in advance. Fixed price trading eliminates the price risk, which is why risk averse customers accept paying more to shop at such stores.     

Biology as a Source of Non-convexities in Ecological Production Functions

Generating ecological production functions, including harvest yield functions, is a high priority research area. Most yield functions used in economics and ecology rely on convexity properties of species growth functions, but convexity is shown here to depend on whether realistic biology is incorporated. Optimizing behavior by individual organisms is connected with species population dynamics in order to derive growth functions in a general equilibrium ecosystem model. Non convexities are shown to be an inherent property of the growth functions owing to familiar biological processes including predator-prey and competitive relations, predator satiation and prey substitution. The growth functions generate yield functions that are problematic for management, because they exhibit kinked average revenue curves, discontinuous marginal revenue curves, and knife edge optimum effort levels where a small increase above the optimum effort can rapidly deplete the stock. These phenomena can be explained entirely by the underlying biological processes.