Existence and Uniqueness Result for Mean Field Games with Congestion Effect on Graphs

Some Characterization, Uniqueness and Existence Results for Euclidean Graphs of Constant Mean Curvature with Planar Boundary

We establish the existence and uniqueness of solutions to the Dirichlet problem for the cmc surface equation, including the minimal one, for zero boundary data, in certain domains of the plane. We obtain results that characterize the sphere and cmc graphs among compact embedded cmc surfaces with planar boundary satisfying certain geometric conditions. We also find conditions that imply that a c...

Prescribing Mean Curvature: Existence and Uniqueness Problems

The results in this paper are part of a program to understand to what extent one can use mean curvature data to determine the shape of a surface in R. The first section of the paper presents some new results on a uniqueness problem suggested by Bonnet. A generic immersion is uniquely determined up to a rigid motion by its first fundamental form and its mean curvature function, but there are som...

An existence result for discontinuous games

We introduce a notion of upper semicontinuity, weak upper semicontinuity, and show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. We show that our result generalizes the pure strategy existence theorem of Dasgupta and Maskin [3] and that it is neither implied nor does it imply the existen...

Equilibrium existence and uniqueness in network games with additive preferences

Mean field type control with congestion

We analyze some systems of partial differential equations arising in the theory of mean field type control with congestion effects. We look for weak solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as the optima of two optimal control problems in duality.