  We introduce the Proportional Payoff Allocation Game (PPA-Game) to model how
agents, akin to content creators on platforms like YouTube and TikTok, compete
for divisible resources and consumers' attention. Payoffs are allocated to
agents based on heterogeneous weights, reflecting the diversity in content
quality among creators. Our analysis reveals that although a pure Nash
equilibrium (PNE) is not guaranteed in every scenario, it is commonly observed,
with its absence being rare in our simulations. Beyond analyzing static
payoffs, we further discuss the agents' online learning about resource payoffs
by integrating a multi-player multi-armed bandit framework. We propose an
online algorithm facilitating each agent's maximization of cumulative payoffs
over $T$ rounds. Theoretically, we establish that the regret of any agent is
bounded by $O(\log^{1 + \eta} T)$ for any $\eta > 0$. Empirical results further
validate the effectiveness of our approach.
