The investment boundaries defined by Grenadier (2002) for an oligopoly investment game determine equilibria in open-loop strategies. As closed-loop strategies, they are not equilibria, because any firm by investing sooner can preempt the investments of other firms and expropriate the growth options. The perfectly competitive outcome is produced by closed-loop strategies that are mutually best responses. In this equilibrium, the option to delay investment has zero value, and the simple NPV rule is followed by all firms. The Author 2009. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: [email protected]., Oxford University Press.

We characterize and prove the existence of Nash equilibrium in a limit order market with a finite number of risk-neutral liquidity providers. We show that if there is sufficient adverse selection, then pointwise optimization (maximizing in p for each q) in a certain nonlinear pricing game produces a Nash equilibrium in the limit order market. The need for a sufficient degree of adverse selection does not vanish as the number of liquidity providers increases. Our formulation of the nonlinear pricing game encompasses various specifications of informed and liquidity trading, including the case in which nature chooses whether the market-order trader is informed or a liquidity trader. We solve for an equilibrium analytically in various examples and also present examples in which the first-order condition for pointwise optimization does not define an equilibrium, because the amount of adverse selection is insufficient.

This paper analyzes models of securities markets with a single strategic informed trader and competitive market makers. In one version, uninformed trades arrive as a Brownian motion and market makers see only the order imbalance, as in Kyle (1985). In the other version, uninformed trades arrive as a Poisson process and market makers see individual trades. This is similar to the Glosten–Milgrom (1985) model, except that we allow the informed trader to optimize his times of trading. We show there is an equilibrium in the Glosten–Milgrom-type model in which the informed trader plays a mixed strategy (a point process with stochastic intensity). In this equilibrium, informed and uninformed trades arrive probabilistically, as Glosten and Milgrom assume. We study a sequence of such markets in which uninformed trades become smaller and arrive more frequently, approximating a Brownian motion. We show that the equilibria of the Glosten–Milgrom model converge to the equilibrium of the Kyle model.

We compare a sealed-bid uniform-price auction (the Treasury’s experimental format) with a sealed-bid discriminatory auction (the Treasury’s format heretofore), assuming the good is perfectly divisible. We show that the auction theory that prompted the experiment, which assumes single-unit demands, does not adequately describe the bidding game for Treasury securities. Collusive strategies are self-enforcing in uniform-price divisible-good auctions. In these equilibria, the seller’s expected revenue is lower than in equilibria of discriminatory auctions.

We provide a theoretical rationale for dealer objections to ex post transparency in over-the-counter markets. Disclosure of the terms of a transaction conveys information possessed by the dealer about the asset quality and reduces the dealer’s rents when she disposes of the inventory in a second transaction. We show that costly signaling in a transparent market benefits investors through lower spreads and higher volume. Dealers may also gain from transparency despite lower spreads when potential gains from trade are small or adverse selection is high, because in those circumstances higher volume offsets smaller spreads for dealer profits.

ABSTRACT We analyze limit order markets and floor exchanges, assuming an informed trader and discretionary liquidity traders use market orders and can either submit block orders or work their demands as a series of small orders. By working their demands, large market order traders pool with small traders. We show that every equilibrium on a floor exchange must involve at least partial pooling. Moreover, there is always a fully pooling (worked order) equilibrium on a floor exchange that is equivalent to a block order equilibrium in a limit order market.

We analyze competition among informed traders in the continuous‐time Kyle(1985) model, as Foster and Viswanathan (1996) do in discrete time. We explicitly describe the unique linear equilibrium when signals are imperfectly correlated and confirm the conjecture of Holden and Subrahmanyam (1992) that there is no linear equilibrium when signals are perfectly correlated. One result is that at some date, and at all dates thereafter, the market would have been more informationally efficient had there been a monopolist informed trader instead of competing traders. The relatively large amount of private information remaining near the end of trading causes the market to approach complete illiquidity.

We propose and estimate a model of endogenous informed trading that is a hybrid of the PIN and Kyle models. When an informed trader trades optimally, both returns and order flows are needed to identify information asymmetry parameters. Empirical relationships between parameter estimates and price impacts and between parameter estimates and stochastic volatility are consistent with theory. We illustrate how the estimates can be used to detect information events in the time series and to characterize the information content of prices in the cross-section. We also compare the estimates to those from other models on various criteria. Received April 5, 2017; editorial decision September 21, 2017 by Editor Itay Goldstein. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Recent work uses option prices to derive lower bounds for the risk premia of the market portfolio and individual stocks. We test the bounds conditionally. We cannot reject that they are valid, but we do reject that they are tight. Using the market bounds as forecasts appears unreasonable in many cases due to their high slackness. Adding past mean slackness is a potential improvement but is hampered by the brevity of the available data series. The correlation of the stock bounds with subsequent returns stems primarily from the time series rather than the cross section.