Learning to Strategically Acquire Resources in Competition
This work provides a unified framework and theoretical guarantees for strategic resource acquisition in competitive settings, benefiting economists and AI researchers studying multi-agent systems.
The paper proposes a novel game-theoretic model for multiple agents competing to acquire costly divisible resources over time, establishing existence, uniqueness, and efficient computability of Bayesian Nash equilibrium under partial information, and providing convergence guarantees for learning dynamics. Simulations on real financial data validate the theoretical results.
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.