A mean field search game
Résumé
We consider a symmetric search game with the following features: 1) each player chooses a searching area, 2) any player's search can be successful at only one location and 3) successively the reward (yield) at any location is assigned at random to one of the players searching at this location. We derive the mean-field version of the game by letting the number of players tend to infinity and obtain a concise characterization of equilibrium strategies. Based on this we provide sufficient conditions on the reward function for the existence and uniqueness of equilibria. We illustrate with an example that the equilibrium may not be Pareto optimal, suggesting that the intervention of a central planner could improve outcomes for all players.
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