BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Panayotis Mertikopoulos (CNRS / INRIA) DTSTART:20200713T130000Z DTEND:20200713T140000Z DTSTAMP:20260423T021018Z UID:OWOS/7 DESCRIPTION:Title: Gam es\, dynamics and optimization\nby Panayotis Mertikopoulos (CNRS / INR IA) as part of One World Optimization seminar\n\n\nAbstract\nThis talk aim s to survey the triple-point interface between optimization\, game theory\ , and dynamical systems. In the first part of the talk\, we will discuss h ow the ordinary differential equation (ODE) method of stochastic approxima tion can be used to analyze the trajectories of stochastic first-order alg orithms in non-convex programs – both in terms of convergence to the pro blem's critical set as well as the avoidance of non-minimizing critical ma nifolds. Subsequently\, we will examine the behavior of these algorithms i n a game-theoretic context involving \\emph{several} optimizing agents\, e ach with their individual objective. In this multi-agent setting\, the sit uation is considerably more involved: On the one hand\, if the game being played satisfies a monotonicity condition known as "diagonal strict convex ity" (Rosen\, Econometrica\, 1965)\, the induced sequence of play converge s to Nash equilibrium with probability $1$. On the other hand\, in non-mon otone games\, the sequence of play may converge with arbitrarily high prob ability to spurious attractors that are in no way unilaterally stable (or even stationary). "Traps" of this type can arise even in simple two-player zero-sum games with one-dimensional action sets and polynomial payoffs\, a fact which highlights the fundamental gap between min-min and min-max pr oblems.\n\nWe will discuss both classical and recent results – but not t he proofs thereof.\n\n[joint talk with the One World Mathematical Game The ory Seminar]\n\nthe address and password of the zoom room of the seminar a re sent by e-mail on the mailinglist of the seminar one day before each ta lk\n LOCATION:https://researchseminars.org/talk/OWOS/7/ END:VEVENT END:VCALENDAR