Related papers: Parameter sensitivity analysis for mean field game…
Variational inequalities are modelling tools used to capture a variety of decision-making problems arising in mathematical optimization, operations research, game theory. The scenario approach is a set of techniques developed to tackle…
Motivated by a product pricing problem, a linear-quadratic Stackelberg differential game for a regime switching system involving one leader and two followers is studied. The two followers engage in a zero-sum differential game, and both the…
We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…
Even when confronted with the same data, agents often disagree on a model of the real-world. Here, we address the question of how interacting heterogenous agents, who disagree on what model the real-world follows, optimize their trading…
Mean field games are studied by means of the weak formulation of stochastic optimal control. This approach allows the mean field interactions to enter through both state and control processes and take a form which is general enough to…
This paper investigates the so-called asymptotic solvability problem in linear quadratic (LQ) mean field games. The model has asymptotic solvability if for all sufficiently large population sizes, the corresponding game has a set of…
We develop the counterpart of weak KAM theory for potential mean field games. This allows to describe the long time behavior of time-dependent potential mean field game systems. Our main result is the existence of a limit, as time tends to…
We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in Bayraktar, Budhiraja, and Cohen (2017). The MFG is formulated in terms of a…
We analyze a fractional mean field game of controls system, showing existence of solutions when the order of the fractional Laplacian is $s\in(\frac{1}{2},1)$. Here the running cost depends on the distribution $\mu$ of not only the states…
This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced by Carmona and Lacker (2015). Under similar assumptions as in the finite horizon game, we prove…
In this work, we present an application of the probabilistic weak formulation of mean field games (MFG) for modeling liquidity pools in a constant product automated market maker (AMM) protocol in the context of decentralized finance. Our…
We provide a novel method for sensitivity analysis of parametric robust Markov chains. These models incorporate parameters and sets of probability distributions to alleviate the often unrealistic assumption that precise probabilities are…
We examine the sensitivity at the origin of the distributional robust optimization problem in the context of a model generated by a mean field stochastic differential equation. We adapt the finite dimensional argument developed by Bartl,…
We study strategic interaction in data-driven games where players face uncertainty about payoff distributions inferred from finite samples. To model calibrated attitudes toward such uncertainty, we formulate distributionally robust games…
This paper considers mean field games in a multi-agent Markov decision process (MDP) framework. Each player has a continuum state and binary action, and benefits from the improvement of the condition of the overall population. Based on an…
This paper studies mean field games for multi-agent systems with control-dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal…
A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem…
We study the forward-backward system of stochastic partial differential equations describing a mean field game for a large population of small players subject to both idiosyncratic and common noise. The unique feature of the problem is that…
We present an efficient finite difference method for the computation of parameter sensitivities that is applicable to a wide class of continuous time Markov chain models. The estimator for the method is constructed by coupling the perturbed…
We establish the convergence of the deep actor-critic reinforcement learning algorithm presented in [Angiuli et al., 2023a] in the setting of continuous state and action spaces with an infinite discrete-time horizon. This algorithm provides…