Optimal Social Policies in Mean Field Games

This paper analyzes problems in which a large benevolent player, controlling a set of policy variables, maximizes aggregate welfare in a continuous-time economy populated by atomistic agents subject to idiosyncratic shocks. We first provide as a benchmark the social optimum solution, in which a plan...

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 76; no. 1; pp. 29 - 57
Main Author Nuño, Galo
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2017
Springer Nature B.V
Subjects
Calculus of Variations and Optimal Control; Optimization
Continuity (mathematics)
Control
Economic models
Games
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimization
Simulation
Social policy
Systems Theory
Theoretical
Time-inconsistency
Mean field games
Stackelberg solution
Gateaux derivative
Mean field control
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Summary:This paper analyzes problems in which a large benevolent player, controlling a set of policy variables, maximizes aggregate welfare in a continuous-time economy populated by atomistic agents subject to idiosyncratic shocks. We first provide as a benchmark the social optimum solution, in which a planner directly determines the individual controls. Then we analyze the optimal design of social policies depending on whether the large player may credibly commit to the future path of policies. On the one hand, we analyze the open-loop Stackelberg solution, in which the optimal policy path is set at time zero and the problem is time-inconsistent. On the other hand we analyze the time-consistent feedback Stackelberg solution.
Bibliography:ObjectType-Article-1
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ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-017-9433-1