Related papers: Large-scale games in large-scale systems
We consider Mean Field Games without idiosyncratic but with Brownian type common noise. We introduce a notion of solutions of the associated backward-forward system of stochastic partial differential equations. We show that the solution…
This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initial guess. Starting from an approximate solution at the…
In this paper we study stochastic dynamic games with many players; these are a fundamental model for a wide range of economic applications. The standard solution concept for such games is Markov perfect equilibrium (MPE), but it is well…
Finite mixture models are an important tool in the statistical analysis of data, for example in data clustering. The optimal parameters of a mixture model are usually computed by maximizing the log-likelihood functional via the…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for…
We study mean field games with scalar It{\^o}-type dynamics and costs that are submodular with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences.…
This paper investigates a linear-quadratic mean field games problem with common noise, where the drift term and diffusion term of individual state equations are coupled with both the state, control, and mean field terms of the state, and we…
We explore a class of stochastic multiplayer games where each player in the game aims to optimize its objective under uncertainty and adheres to some expectation constraints. The study employs an offline learning paradigm, leveraging a…
Population games model the evolution of strategic interactions among a large number of uniform agents. Due to the agents' uniformity and quantity, their aggregate strategic choices can be approximated by the solutions of a class of ordinary…
We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…
Stochastic games generalize Markov decision processes (MDPs) to a multiagent setting by allowing the state transitions to depend jointly on all player actions, and having rewards determined by multiplayer matrix games at each state. We…
This paper studies relative arbitrage opportunities in a market with competitive investors through stochastic differential games in the limit as the number of players tends to infinity. With common noises introduced by the stock…
Mean field games and controls involve guiding the behavior of large populations of interacting agents, where each individual's influence on the group is negligible but collectively impacts overall dynamics. Hybrid systems integrate…
In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the…
The statement of the mean field approximation theorem in the mean field theory of Markov processes particularly targets the behaviour of population processes with an unbounded number of agents. However, in most real-world engineering…
We consider a class of fully stochastic and fully distributed algorithms, that we prove to learn equilibria in games. Indeed, we consider a family of stochastic distributed dynamics that we prove to converge weakly (in the sense of weak…
Evolutionary game dynamics with two 2-strategy games in a finite population has been investigated in this study. Traditionally, frequency-dependent evolutionary dynamics are modeled by deterministic replicator dynamics under the assumption…
We study minority games in efficient regime. By incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of state of the game. Using this approach, the game can be…
We study the existence of strong solutions for mean-field forward-backward stochastic differential equations (FBSDEs) with measurable coefficients and their implication on the Nash equilibrium of a multi-population mean-field game. More…