Optimal Execution among $N$ Traders with Transient Price Impact

Bibliographic Details
Title: Optimal Execution among $N$ Traders with Transient Price Impact
Authors: Campbell, Steven, Nutz, Marcel
Publication Year: 2025
Collection: Quantitative Finance
Subject Terms: Quantitative Finance - Trading and Market Microstructure, Quantitative Finance - Mathematical Finance, 91A06, 91A15, 91G10
More Details: We study $N$-player optimal execution games in an Obizhaeva--Wang model of transient price impact. When the game is regularized by an instantaneous cost on the trading rate, a unique equilibrium exists and we derive its closed form. Whereas without regularization, there is no equilibrium. We prove that existence is restored if (and only if) a very particular, time-dependent cost on block trades is added to the model. In that case, the equilibrium is particularly tractable. We show that this equilibrium is the limit of the regularized equilibria as the instantaneous cost parameter $\varepsilon$ tends to zero. Moreover, we explain the seemingly ad-hoc block cost as the limit of the equilibrium instantaneous costs. Notably, in contrast to the single-player problem, the optimal instantaneous costs do not vanish in the limit $\varepsilon\to0$. We use this tractable equilibrium to study the cost of liquidating in the presence of predators and the cost of anarchy. Our results also give a new interpretation to the erratic behaviors previously observed in discrete-time trading games with transient price impact.
Comment: 63 pages, 4 figures, 1 table
Document Type: Working Paper
Access URL: http://arxiv.org/abs/2501.09638
Accession Number: edsarx.2501.09638
Database: arXiv
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