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.

翻译：算法交易代理间的复杂相互作用可能对经济运行产生严重影响，近期银行业危机和交易异常现象即为明证。此类情形中的常见现象是"抛售潮"——即资产抛售引发连锁反应的传染过程。本文研究了抛售潮博弈论模型中均衡的存在性与结构特征。我们证明，在广泛参数范围内（如凸性价格影响函数），均衡存在且构成完备格。这与凹性价格影响函数下不存在均衡的结果形成对比。此外，我们研究了最佳响应动态在均衡存在时的收敛性。一般而言，最佳响应动态可能出现循环。但在多种情境下，从自然初始状态出发时，该动态可保证收敛至社会最优均衡。同时，我们讨论了一种简化动态变体，该变体对信息需求较低且收敛至相同均衡。最后，我们对不同动态的收敛速度进行了比较分析。