Title
Wellposedness and quantitative convergence for distributed equilibria of displacement monotone N-player games with interaction through controls
Abstract
In this talk we will study the wellposedness of distributed equilibria of
N-player games under displacement semi-monotonicity and convexity assump
tions, in which the running cost of a player depends also on the controls used
by other players. We consider running costs that are not necessarily separable,
resulting in a set of consistency/fixed point relations on infinite dimensional
spaces. We will also talk about quantitative convergence results (both for op
timal trajectories/control and value functions) for the N-player games to the
corresponding Mean Field Games of Controls (MFGC). Our approach works
for both stochastic and deterministic cases but in this talk we will focus on
the deterministic case (distributed equilibria coincides with open-loop equilib
ria in this case), where further quantitative convergence results can be proved
for the gradients of value functions. This talk is based on joint work with Alpár Mészáros (Durham University).
N-player games under displacement semi-monotonicity and convexity assump
tions, in which the running cost of a player depends also on the controls used
by other players. We consider running costs that are not necessarily separable,
resulting in a set of consistency/fixed point relations on infinite dimensional
spaces. We will also talk about quantitative convergence results (both for op
timal trajectories/control and value functions) for the N-player games to the
corresponding Mean Field Games of Controls (MFGC). Our approach works
for both stochastic and deterministic cases but in this talk we will focus on
the deterministic case (distributed equilibria coincides with open-loop equilib
ria in this case), where further quantitative convergence results can be proved
for the gradients of value functions. This talk is based on joint work with Alpár Mészáros (Durham University).
Please note that the seminar will take place in person in room 144 of Huxley Building.