We consider multiple agents competing to acquire some costly divisible resource (e.g. shares of a financial asset, compute resources, etc.) over time. Leveraging a standard model for price dynamics, we propose a novel game-theoretic model for this problem, generalizing settings studied in diverse literatures. Our analysis considers different assumptions on the information available to agents. Under partial-information with a common prior (which subsumes complete information as a special case), we establish the existence, uniqueness, and efficient computability of the Bayesian Nash equilibrium (BNE), and bound the price of anarchy. Next and more generally, we consider agents with no common prior learning to act optimally given realistic market feedback from repeated interactions. We provide sufficient conditions on agents doing simultaneous learning dynamics for last-iterate convergence to the BNE. For all settings, we provide simulations based on real financial data to illustrate our theoretical results and offer new insights on strategic behavior in the context of trading and resource acquisition.

翻译：我们考虑多个智能体随时间竞争获取某种昂贵的可分资源（例如金融资产份额、计算资源等）的问题。利用标准的价格动态模型，我们为此问题提出了一种新颖的博弈论模型，统一了不同文献中研究的多种设定。我们的分析考虑了智能体可获得信息的不同假设。在具有共同先验的部分信息设定下（完整信息是其特例），我们证明了贝叶斯纳什均衡的存在性、唯一性和高效可计算性，并界定了无政府代价。接下来，更一般地，我们考虑没有共同先验的智能体，在重复交互中根据现实市场反馈学习最优行动。我们为智能体采用同步学习动态时最后迭代收敛至贝叶斯纳什均衡提供了充分条件。针对所有设定，我们基于真实金融数据进行了模拟，以说明理论结果，并为交易和资源获取情境下的策略行为提供新见解。