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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.08317 |
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| _version_ | 1866908361992175616 |
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| author | Ferrari, Giorgio Tzouanas, Ioannis |
| author_facet | Ferrari, Giorgio Tzouanas, Ioannis |
| contents | 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 one-sided 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08317 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stationary Mean-Field Games of Singular Control under Knightian Uncertainty Ferrari, Giorgio Tzouanas, Ioannis Optimization and Control 49L20, 91A07, 91A15, 91A16, 91A26, 9J15, 60J70, 35R35 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 one-sided 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. |
| title | Stationary Mean-Field Games of Singular Control under Knightian Uncertainty |
| topic | Optimization and Control 49L20, 91A07, 91A15, 91A16, 91A26, 9J15, 60J70, 35R35 |
| url | https://arxiv.org/abs/2505.08317 |