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We develop the fictitious play algorithm in the context of the linearprogramming approach for mean field games of optimal stopping and mean fieldgames with regular control and absorption. This algorithm allows to approximatethe mean field game population dynamics without computing the value function bysolving linear programming problems associated with the distributions of theplayers still in the game and their stopping times/controls. We show theconvergence of the algorithm using the topology of convergence in measure inthe space of subprobability measures, which is needed to deal with the lack ofcontinuity of the flows of measures. Numerical examples are provided toillustrate the convergence of the algorithm.

Linear Programming Fictitious Play algorithm for Mean Field Games with optimal stopping and absorption