ArticleApplied mathematics and optimization2026
From Nash Equilibrium to Social Optimum and Back: A Mean Field Perspective.
Article in Applied mathematics and optimization, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
Mean field games (MFGs) and mean field control (MFC) have been introduced to study large populations of strategic players. They correspond respectively to non-cooperative or cooperative scenarios, where the aim is to find the Nash equilibrium and social optimum. They approximate finite player problems and have many applications in economics, biology, machine learning. This paper studies how players can pass from a non-cooperative to a cooperative regime, and vice-versa. The first direction is reminiscent of mechanism design, in which the game's definition is modified so that non-cooperative players reach an outcome similar to a cooperative scenario. The second direction studies how initially cooperative players gradually deviate from social optimum to reach Nash equilibrium when they optimize their individual cost very much in the spirit of the free-rider phenomenon. To formalize these connections, we introduce and theoretically analyze two new classes of games which lie between MFG and MFC:
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