Competing Mechanisms in a Common Value Environment

Abstract

Consider strategic risk-neutral traders competing in schedules to supply liquidity to a risk-averse agent who is privately informed about the value of the asset and his hedging needs. Imperfect competition in this common¨alue en¨ironment is analyzed as a multiprincipal game in which liquidity suppliers offer trading mechanisms in a decentralized way. Each liquidity supplier behaves as a monopolist facing a residual demand curve resulting from the maximizing behavior of the informed agent and the trading mechanisms offered by his competitors. There exists a unique equilibrium in convex schedules. It is symmetric and differentiable and exhibits typical features of market-power: Equilibrium trading volume is lower than ex ante efficiency would require. Liquidity suppliers charge positive mark-ups and make positive expected profits, but these profits decrease with the Ž . number of competitors. In the limit, as this number goes to infinity, ask resp. bid prices Ž . Ž . converge towards the upper resp. lower tail expectations obtained in Glosten 1994 and expected profits are zero.

Competitive rational expectations equilibria without apology

“…Indeed, the naive idea that with risk-neutral traders Bertrand competition would push the strategic and competitive regimes closer together does not hold. This is consistent with the results in Biais et al (2000) according to which adverse selection softens supply schedule competition among risk-neutral market makers in a common value environment.…”

“…We find that the asymptotic variance of the price difference between the strategic and the competitive regime in a finite economy is small, and the approximation of the strategic equilibrium by the competitive equilibrium is good, when the prior volatility of the asset is low, noise trading is large in relation to the risk bearing capacity of the informed traders, or the signals are very noisy. 2 We confirm, therefore, the idea that the competitive approximation works, even in a moderately sized market, basically when competitive traders have incentives to be restrained in their trading. As traders become less and less risk averse, the asymptotic 1 The latter paper extends the work on independent and identically distributed (i.i.d.)…”

Optimal Bunching without Optimal Control

“…Baron and Myerson [1]; see also Laffont and Tirole [11]). It also holds in models of (monopoly) market making, as in Biais, Martimort and Rochet [2] (see also Glosten [6,7]), in which 0 ∈ (x, x) corresponds to the no-trade outcome satisfying u(0, θ) = 0 for all θ. 7 Assumption 1 also holds in models with countervailing incentives in which the agent's reservation utility profile is concave (cf.…”

Aggressive and Defensive High-Frequency Trading and its Impact on Liquidity of German Stock Market

“…First papers that focused on the related topics are studies concerning the liquidity providers (companies submitting limit orders) and liquidity takers. They have assumed either liquidity suppliers are perfectly competitive (Glosten, 1994) or that their commissions are declining with the number of liquidity suppliers (Biais, 2000). The provision given to the liquidity providers in market making position, who are obliged to take a position in trade have been priced as an option (Copeland, 1983) and these option costs have been optimized by effective market monitoring (Foucault, 2003).…”