Computing And Learning Stationary Mean Field Equilibria With Scalar Interactions: Algorithms And Applications

Abstract

Mean field equilibrium (MFE) has emerged as a computationally tractable solution concept for large dynamic games. However, computing MFE remains challenging due to nonlinearities and the absence of contraction properties, limiting its reliability for counterfactual analysis and comparative statics. This paper focuses on MFE in dynamic models where agents interact through a scalar function of the population distribution, referred to as the scalar interaction function. Such models naturally arise in a wide range of applications involving market dynamics and strategic competition. The main contribution of this paper is to introduce iterative algorithms that leverage the scalar interaction structure and are guaranteed to converge to the MFE under mild assumptions. Leveraging this structure, we also establish an MFE existence result for non-compact state spaces and analytical comparative statics. To the best of our knowledge, these are the first algorithms with global convergence guarantees

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