Equilibria and Convergence in Fire Sale Games
Abstract
The complex interactions between algorithmic trading agents can have a severe influence on the functioning of our economy, as witnessed by recent banking crises and trading anomalies. A common phenomenon in these situations are fire sales, a contagious process of asset sales that trigger further sales. We study the existence and structure of equilibria in a game-theoretic model of fire sales. We prove that for a wide parameter range (e.g., convex price impact functions), equilibria exist and form a complete lattice. This is contrasted with a non-existence result for concave price impact functions. Moreover, we study the convergence of best-response dynamics towards equilibria when they exist. In general, best-response dynamics may cycle. However, in many settings they are guaranteed to converge to the socially optimal equilibrium when starting from a natural initial state. Moreover, we discuss a simplified variant of the dynamics that is less informationally demanding and converges to the same equilibria. We compare the dynamics in terms of convergence speed.
Keywords
Cite
@article{arxiv.2206.14429,
title = {Equilibria and Convergence in Fire Sale Games},
author = {Nils Bertschinger and Martin Hoefer and Simon Krogmann and Pascal Lenzner and Steffen Schuldenzucker and Lisa Wilhelmi},
journal= {arXiv preprint arXiv:2206.14429},
year = {2023}
}
Comments
To appear at the 22nd International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2023), full version