Abstract
We study the existence of relaxed equilibria for finite-horizon deterministic mean-field games. These relaxed equilibria are probability measures on trajectories. Closed-graph properties play a major role in proving their existence. Two cases are discussed : in the first case, agents control their acceleration and are constrained to stay in a fixed region of the space; in the second case, agents control their speed and evolve on a network with discontinuous costs when crossing network nodes. Regularity results are presented.
