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Some Remarks on the Asymptotic Behavior of Mean Field Games of Controls
Abstract
We analyze the asymptotic behavior of several mean field games of controls. First, in the time-dependent case, we examine the behavior of solutions to discounted mean field games of controls as the discount factor λ tends to infinity. Next, we study three stationary models of mean field games of controls, finding that solutions to the first-order discounted problem and the second-order ergodic problem can be obtained from solutions to the second-order discounted problem by taking ν→ 0 and λ→ 0, respectively. Finally, we investigate the long-time average behavior of solutions to the time-dependent system with no discount, finding that solutions converge to the solution to the second-order ergodic problem as T → ∞.
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BibTeX
@misc{graber2026some,
title = {{Some Remarks on the Asymptotic Behavior of Mean Field Games of Controls}},
author = {Jameson Graber and Elizabeth Matter and Kyle Rosengartner},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00490},
eprint = {2611.00490},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00490},
}
RIS
TY - UNPB
TI - Some Remarks on the Asymptotic Behavior of Mean Field Games of Controls
AU - Jameson Graber
AU - Elizabeth Matter
AU - Kyle Rosengartner
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00490
UR - https://arxiv.org/abs/2611.00490
AB - We analyze the asymptotic behavior of several mean field games of controls. First, in the time-dependent case, we examine the behavior of solutions to discounted mean field games of controls as the discount factor λ tends to infinity. Next, we study three stationary models of mean field games of controls, finding that solutions to the first-order discounted problem and the second-order ergodic problem can be obtained from solutions to the second-order discounted problem by taking ν→ 0 and λ→ 0, respectively. Finally, we investigate the long-time average behavior of solutions to the time-dependent system with no discount, finding that solutions converge to the solution to the second-order ergodic problem as T → ∞.
ER -