Mean field games (MFG) represent mathematical models analyzing strategic decision-making amidst a large number of agents, whose choices are influenced by the average behavior of the crowd.
In Mean Field Games with Optimal Stopping (OSMFG), agents must decide when to stop playing to minimize expected costs, leading to the concept of equilibrium within the game.
Constructing an equilibrium in MFG involves three steps: guessing agent distribution propagation, taking optimal control based on this guess, and verifying consistency with actual propagation.
Solving a Fokker-Planck equation is crucial in determining the actual distribution of the crowd, which directly follows from the optimal controls executed by each agent.
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