Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies the connections beten mean-field games and the social lfare optimization problems.  consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean field term that depends on the mean of the population states.  show that under some mild conditions any ∊-Nash equilibrium of the mean field game coincides with the optimal solution to a convex social lfare optimization problem. The results are proved based on a general formulation in the functional spaces and can be applied to a variety of mean field games studied in the literature. Our result also implies that the computation of the mean field equilibrium can be cast as a convex optimization problem, which can be efficiently solved by a decentralized primal dual algorithm.
['Sen Li', 'Wei Zhang', 'Lin Zhao', 'Jianming Lian', 'Karanjit Kalsi']
I am writing a research paper on a idea On social optima of non-cooperative mean field games
[{"from": "human", "value": "I am writing a research paper on a idea On social optima of non-cooperative mean field games"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  studies the connections beten mean-field games and the social lfare optimization problems.  consider a mean field game in functional spaces with a large population of agents, each of which seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean field term that depends on the mean of the population states.  show that under some mild conditions any \u220a-Nash equilibrium of the mean field game coincides with the optimal solution to a convex social lfare optimization problem. The results are proved based on a general formulation in the functional spaces and can be applied to a variety of mean field games studied in the literature. Our result also implies that the computation of the mean field equilibrium can be cast as a convex optimization problem, which can be efficiently solved by a decentralized primal dual algorithm."}]