Abstract
The planning problem for the mean field game implies that one tries to transfer the system of infinitely many identical rational agents from the given distribution to the final one using the choice of the terminal payoff. It can be formulated as the mean field game system with the boundary condition only on the distribution. In the paper, we consider the continuous-time finite state mean field game, assuming that the space of actions for each player is compact. It is shown that the planning problem in this case may not admit a solution even if the final distribution is reachable from the initial one. Further, we introduce the concept of generalized solution of the planning problem for the finite state mean field game based on the minimization of regret of a fictitious player. This minimal regret solution always exists. Additionally, the set of minimal regret solution is the closure of the set of classical solution of the planning problem, provided that the latter is nonempty. Finally, we examine the uniqueness of the solution to the planning problem using the Lasry–Lions monotonicity arguments.
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Change history
10 March 2023
A Correction to this paper has been published: https://doi.org/10.1007/s13235-023-00498-8
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Acknowledgements
The authors would like the anonymous reviewers for their valuable comments and suggestions. The work of Yurii Averboukh on this paper was in the framework of a research grant funded by the Ministry of Science and Higher Education of the Russian Federation (Grant ID: 075-15-2022-325).
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Yurii Averboukh and Aleksei Volkov contributed equally to this work.
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Averboukh, Y., Volkov, A. Planning Problem for Continuous-Time Finite State Mean Field Game with Compact Action Space. Dyn Games Appl 14, 285–303 (2024). https://doi.org/10.1007/s13235-023-00492-0
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DOI: https://doi.org/10.1007/s13235-023-00492-0