Existence and uniqueness for mean field games with state constraints
P Cannarsa, R Capuani - PDE models for multi-agent phenomena, 2018 - Springer
P Cannarsa, R Capuani
PDE models for multi-agent phenomena, 2018•SpringerIn this paper, we study deterministic mean field games for agents who operate in a bounded
domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as
for unrestricted state space because, for a large set of initial conditions, the uniqueness of
the solution to the associated minimization problem is no longer guaranteed. We attack the
problem by interpreting equilibria as measures in a space of arcs. In such a relaxed
environment the existence of solutions follows by set-valued fixed point arguments. Then …
domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as
for unrestricted state space because, for a large set of initial conditions, the uniqueness of
the solution to the associated minimization problem is no longer guaranteed. We attack the
problem by interpreting equilibria as measures in a space of arcs. In such a relaxed
environment the existence of solutions follows by set-valued fixed point arguments. Then …
Abstract
In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of initial conditions, the uniqueness of the solution to the associated minimization problem is no longer guaranteed. We attack the problem by interpreting equilibria as measures in a space of arcs. In such a relaxed environment the existence of solutions follows by set-valued fixed point arguments. Then, we give a uniqueness result for such equilibria under a classical monotonicity assumption.
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