In recent years, there has been a significant increase in attention towards designing incentive mechanisms for federated learning (FL). Tremendous existing studies attempt to design the solutions using various approaches (e.g., game theory, reinforcement learning) under different settings. Yet the design of incentive mechanism could be significantly biased in that clients' performance in many applications is stochastic and hard to estimate. Properly handling this stochasticity motivates this research, as it is not well addressed in pioneering literature. In this paper, we focus on cross-device FL and propose a multi-level FL architecture under the real scenarios. Considering the two properties of clients' situations: uncertainty, correlation, we propose FL Incentive Mechanism based on Portfolio theory (FL-IMP). As far as we are aware, this is the pioneering application of portfolio theory to incentive mechanism design aimed at resolving FL resource allocation problem. In order to more accurately reflect practical FL scenarios, we introduce the Federated Learning Agent-Based Model (FL-ABM) as a means of simulating autonomous clients. FL-ABM enables us to gain a deeper understanding of the factors that influence the system's outcomes. Experimental evaluations of our approach have extensively validated its effectiveness and superior performance in comparison to the benchmark methods.

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