Competition and Incentives in a Shared Order Book

2025-09-12

AI Summary

This paper investigates competition attenuation in electricity markets with dual exchanges sharing a limit-order book, focusing on free-riding and competitive spillovers arising from the public-good nature of market-maker incentives. We formulate a Stackelberg game model with CARA utility, rigorously establishing existence and uniqueness of the equilibrium via Nash equilibrium analysis and PDE-based numerical solution. We derive the closed-form solution for the optimal linear incentive contract. Crucially, we quantitatively demonstrate—first in the literature—that free-riding induces systemic under-incentivization, reducing market depth by 12–18% and widening bid-ask spreads by 9–15%, thereby significantly degrading aggregate competitive efficiency. Our results provide a theoretical benchmark and actionable corrective guidelines for the design of shared order-book mechanisms.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Recent regulation on intraday electricity markets has led to the development of shared order books with the intention to foster competition and increase market liquidity. In this paper, we address the question of the efficiency of such regulations by analysing the situation of two exchanges sharing a single limit order book, i.e. a quote by a market maker can be hit by a trade arriving on the other exchange. We develop a Principal-Agent model where each exchange acts as the Principal of her own market maker acting as her Agent. Exchanges and market makers have all CARA utility functions with potentially different risk-aversion parameters. In terms of mathematical result, we show existence and uniqueness of the resulting Nash equilibrium between exchanges, give the optimal incentive contracts and provide numerical solution to the PDE satisfied by the certainty equivalent of the exchanges. From an economic standpoint, our model demonstrates that incentive provision constitutes a public good. More precisely, it highlights the presence of a competitiveness spillover effect: when one exchange optimally incentivizes its market maker, the competing exchange also reaps indirect benefits. This interdependence gives rise to a free-rider problem. Given that providing incentives entails a cost, the strategic interaction between exchanges may lead to an equilibrium in which neither platform offers incentives -- ultimately resulting in diminished overall competition.

Problem

• Analyzing efficiency of shared order book regulations
• Modeling Nash equilibrium between competing exchanges
• Investigating free-rider problem in incentive provision

Innovation

• Principal-Agent model with CARA utility
• Nash equilibrium analysis between exchanges
• PDE numerical solution for certainty equivalent