Multiple equilibria in mean-field game models for large oligopolies with strategic complementarities

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 and the intensity of interaction is measured by a so-called "strenght parameter" $\xi$. Via lattice-theoretic arguments we first prove existence of equilibria and provide comparative statics results when varying $\xi$. A careful numerical study based on iterative schemes converging to suitable maximal and minimal equilibria allows then to study in relevant financial examples how the emergence of multiple equilibria is related to the strenght of the strategic interaction.