Multiple equilibria in mean-field game models of firm competition with strategic complementarities

Jodi Dianetti, Salvatore Federico, Giorgio Ferrari and Giuseppe Floccari

Quantitative Finance, 2025, vol. 25, issue 3, 343-357

Abstract: We consider continuous-time mean-field stochastic games with strategic complementarities. The interaction between the representative productive firm and the population of rivals comes through the price at which the produced good is sold. Existence of minimal and maximal equilibria is shown via lattice-theoretical arguments, and sufficient conditions for deriving comparative statics of the equilibria are presented. A detailed numerical study, based on iterative schemes converging to the maximal and minimal equilibria, allows us to analyze in relevant financial examples of how the emergence of multiple equilibria is related to the intensity of strategic interactions.

Date: 2025
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DOI: 10.1080/14697688.2024.2438217

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