Stationary Mean-Field Games of Singular Control under Knightian Uncertainty

Giorgio Ferrari and Ioannis Tzouanas
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Giorgio Ferrari: Center for Mathematical Economics, Bielefeld University
Ioannis Tzouanas: Center for Mathematical Economics, Bielefeld University

No 706, Center for Mathematical Economics Working Papers from Center for Mathematical Economics, Bielefeld University

Abstract: In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an Itô-diffusion via onesided singular stochastic control, aiming to maximize a long-term average expected profit criterion. The mean-field interaction is of scalar type through the stationary distribution of the population. Due to the presence of uncertainty, the problem involves the study of a stochastic (zero-sum) game, where the decision maker chooses the ‘best’ singular control policy, while the adversarial player selects the ‘worst’ probability measure. Using a constructive approach, we prove existence and uniqueness of a stationary mean-field equilibrium. Finally, we present an example of mean-field optimal extraction of natural resources under uncertainty and we analyze the impact of uncertainty on the mean-field equilibrium.

Keywords: stationary mean-field games; singular control; model uncertainty; ergodic criterion; freeboundary problem; shooting method (search for similar items in EconPapers)
Pages: 32
Date: 2025-05-21
New Economics Papers: this item is included in nep-gth
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Persistent link: https://EconPapers.repec.org/RePEc:bie:wpaper:706

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