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 \emph{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:算法贸易代理商之间的复杂互动,如最近的银行危机和贸易异常现象所见证的那样,可以对我们经济的运作产生严重影响。这些情况中的一种常见现象是:\emph{fire sail},这是资产销售的传染性过程,触发进一步销售。我们研究在火灾销售的游戏理论模型中平衡的存在和结构。我们证明,对于广泛的参数范围(例如,convex价格影响功能)来说,平衡的存在和形成一个完整的平衡。这与价格影响不变的不共存结果形成对照。此外,我们研究最佳反应动态在存在时与平衡的趋同。一般而言,最佳反应动态可以循环。然而,在许多环境中,从自然的初始状态开始,保证它们会与社会最佳平衡趋于一致。此外,我们讨论一种简化的动态变式,即信息要求较低,与同一平衡的趋同。我们比较了趋同速度的动态。