arXiv subjects

Ioannis Tzouanas

Publications and source records attributed to Ioannis Tzouanas.

3 recordsLinked to original sources

arXiv2026

Stationary Mean-Field Games of Singular Control under Knightian Uncertainty

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 reward 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 provide a stylized numerical benchmark of dirty-capacity reduction under ambiguity and analyze the impact of uncertainty on the mean-field equilibrium.

math.OC↗

arXiv2026

Optimal Coarse Correlated Equilibria in Mean Field Games: Linear Programming and No-Regret Learning

We introduce optimal coarse correlated equilibria for continuous-time mean field games. A coarse correlated equilibrium is a randomized recommendation scheme from which no player can gain by ignoring the recommendation and switching to an alternative strategy. The problem is as follows: a moderator selects, among all mean-field coarse correlated equilibria, one that optimizes a prescribed performance criterion, which may differ from the representative player's objective. After formulating the problem, we develop a linear programming (LP) formulation, prove the existence of optimal LP coarse correlated equilibria, and relate the LP characterization to the original probabilistic setting. Building on this characterization, we design a no-regret primal-dual algorithm, based on an equivalent Lagrangian formulation of the external-regret constraint, for learning such equilibria. We provide explicit convergence rates for the learning algorithm, and numerical examples illustrate the method.

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arXiv2024

Ergodic Mean-Field Games of Singular Control with Regime-Switching (Extended Version)

This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated Itô-diffusion via a two-sided singular stochastic control and faces a long-time-average expected profit criterion. The mean-field interaction is of scalar type and it is given through the stationary distribution of the population. Via a constructive approach, we prove the existence and uniqueness of the stationary mean-field equilibrium. Furthermore, we show that this realizes a symmetric $\varepsilon_N$-Nash equilibrium for a suitable ergodic $N$-player game with singular controls. The proof hinges on the characterization of the optimal solution to the representative player's ergodic singular stochastic control problem with regime switching in terms of an auxiliary Dynkin game, which is of independent interest and appears here for the first time.

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