We investigate long-time learning in ergodic, potential, monotone mean-field games (MFGs) via a self-fictitious-play (SFP) dynamics coupling an optimally controlled diffusion with a slowly evolving belief. At each time, the state follows the optimal feedback associated with the current belief, while the belief is updated using the player's own empirical occupation measure rather than the population distribution. For ergodic monotone potential MFGs on the torus, we prove that the SFP dynamics is contractive and admits a unique invariant law. Moreover, we show that this invariant law is quantitatively close to the MFG Nash equilibrium, with an error of order equal to the square root of the belief-update rate. The proof combines uniform-in-time regularity estimates for the ergodic Hamilton-Jacobi-Bellman equation with an energy argument based on the Lasry-Lions divergence. The linear-quadratic example shows that this rate is sharp, and the numerical experiments illustrate the predicted scaling.
We study contraction properties of non-stationary continuous-time mean-field games (MFGs) under discounting and entropy regularization. The state of the representative agent evolves according to a controlled continuous-time Markov chain, and both the state and action spaces are finite. In contrast to the undiscounted c...
This work introduces an independently randomized formulation in which each stopping rule is represented by an adapted, nondecreasing cumulative stopping process, and identifies an exact-potential subclass with a closed-form threshold equilibrium.
Mean-field games provide a continuum framework for modeling the dynamics of large, interacting populations of non-cooperative agents. This paper studies symmetry-breaking in a finite-horizon, two-choice min-LQG mean-field game in which identical agents with linear stochastic dynamics choose one of two equally desirable...
We revisit the problem of computing mean-field equilibria (MFEs) in discrete-time, monotone, finite-horizon mean-field games (MFGs). We show that, when the transition kernel is independent of the state-measure term and the reward function satisfies the usual weak monotonicity condition and is Lipschitz continuous, anch...
Metric conditioning can change which equilibrium attracts learning dynamics without moving the equilibria of a differentiable game. We study how to use state-dependent symmetric positive-definite (SPD) metrics to select among known equilibria by keeping a designated equilibrium attracting while making a rival unstable....
Karan Mahesh, R. Zhang, Michael R. Benjamin et al.· 0 citations
This paper studies partially observed mean field games without perfect recall (WPR). The representative agent observes a noisy signal, but the control at time \(t\) uses only \(\mathcal G_t^I=\sigma(y_t)\), a generally non-nested information family. The conditional population law instead uses the observation filtration...
Xuan-Ping Zhang, Xiao Zhang, Wang Yao· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
