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arXiv · 2206.14429

Equilibria and Convergence in Fire Sale Games

Nils Bertschinger·Martin Hoefer·Simon Krogmann·Pascal Lenzner·Steffen Schuldenzucker·Lisa Wilhelmi
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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.

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Nils Bertschinger, Martin Hoefer, Simon Krogmann, Pascal Lenzner, Steffen Schuldenzucker, Lisa Wilhelmi. 2022-06-29. Equilibria and Convergence in Fire Sale Games. https://arxiv.org/abs/2206.14429

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