Abstracts of Talks 

Mete Soner

Title: Synchronization games, Markov Perfect Equilibria and time discretization

Abstract: Building on Winfree's work, the Kuramoto model (1975) has become the corner stone of mathematical models of collective synchronization, and has received attention in all natural sciences, engineering, and mathematics. While the classical model postulates the dynamics of each oscillator in the form of a system of nonlinear ordinary differential equations, one may design games mimicking similar behavior: the system is unsynchronized when the coupling is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to synchronization above a critical value of the interaction parameter.  In this talk, I describe the general problem and then specialize to simple two-state model with a remarkably rich structure.  Through this example, I introduce the discrete time, finite player games with a finite state-space, and discuss the corresponding  Markov Perfect Equilibria (MPE).  In particular, MPE are always unique in continuous time and iterative schemes converge exponentially.  Interestingly, in discrete time these properties hold only when the time step is sufficiently small.

This talk is based on joint works with Rene Carmona, Felix Hoefer, and Qinxin Yan of Princeton, Quentin Cormier of INRIA, Mathieu Lauriere of NYU-Shanghai, and Atilla Yilmaz of Temple.

Xin Zhang

Title: TBA

Abstract: TBA

Jiamin Jian

Title: Turnpike properties in linear quadratic Gaussian N-player differential games

Abstract: We consider the long-time behavior of equilibrium strategies and state trajectories in a linear quadratic N-player game with Gaussian initial data. By analyzing convergence toward the corresponding ergodic game, we establish exponential convergence estimates between the solutions of the finite-horizon Riccati system and the associated algebraic Riccati system arising in the ergodic setting. Building on these results, we prove the convergence of the time-averaged value function and derive a turnpike property for the equilibrium pairs of each player. Importantly, our approach avoids reliance on the mean field game limiting model, allowing for a fully uniform analysis with respect to the number of players N. As a result, we further establish a uniform turnpike property for the equilibrium pairs between the finite-horizon and ergodic games with N players.

Xiaofei Shi

Title: TBA

Abstract: TBA

Fang Rui Lim

Title: TBA

Abstract: TBA

Daniel Lacker

Title: TBA

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Sebastian Jaimungal

Title: TBA

Abstract: TBA

Max Reppen

Title: TBA

Abstract: TBA

Silvana Pesenti

Title: TBA

Abstract: TBA

Yuqiong Wang

Title: TBA

Abstract: TBA

Valentin Tissot-Daguette

Title: TBA

Abstract: TBA

Ali Kara

Title: TBA

Abstract: TBA

Ioannis Karatzas

Title: Degenerate Competing Three-Particle Systems

Abstract: We study the process of gaps in a degenerate system of three particles interacting through their ranks, and obtain the Laplace transform of its invariant measure as well as an explicit expression for the corresponding invariant density. We start from the basic adjoint relationship characterizing the invariant measure, then apply a combination of two approaches: the invariance methodology of W. Tutte, thanks to which we compute the Laplace transform in closed form; and a recursive compensation approach which leads to the density of the invariant measure in the form of an infinite sum of exponentials. As in the case of Brownian motion with reflection or killing at the endpoints of an interval, certain Jacobi theta-type functions play a crucial role in our computations. (Joint work with Sandro Franceschi, Tomoyuki Ichiba and Killian Rachel.)