Title: Learning To Acquire Resources in Competition
Primary area: other topics in machine learning (i.e., none of the above)
Keywords: Algorithmic Game Theory, Online Learning, Nash Equilibrium

Abstract: We consider multiple agents competing to acquire stakes in some costly divisible resource (e.g. shares of a financial asset, compute resources, or commodities) over time. We propose a novel game-theoretic model for this problem that generalizes settings studied in diverse literatures, and analyze it under different assumptions on agent information. Given complete-information, we establish the existence and uniqueness of a pure Nash equilibrium (NE) in this generalized setting. This is shown to be efficiently computable but has worst-case unbounded price of anarchy. Alternatively, under partial-information with a common prior, we establish the existence and uniqueness of a Bayesian Nash equilibrium (BNE), which is also efficiently computable. Finally, we propose a more realistic learning setting for the game, where agents have partial information but no common prior. Instead, they must learn how to act given online contextual feedback from interactions in stochastically sampled game instances. We provide sufficient conditions on agents doing simultaneous no-regret learning for convergence to Bayesian coarse-correlated equilibrium (BCCE) or last-iterate convergence to the BNE. In each setting, we provide detailed simulations, which empirically validates our theory and provides new insights into strategic behavior of resource acquisition.

TL;DR: We build a strategic model for multiple agents looking to trade/acquire resources in a competitive setting and explore it's equilibrium and learning properties.