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A Maximum Principle approach to deterministic Mean Field Games of Control with Absorption

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  • Paulwin Graewe
  • Ulrich Horst
  • Ronnie Sircar

Abstract

We study a class of deterministic mean field games on finite and infinite time horizons arising in models of optimal exploitation of exhaustible resources. The main characteristic of our game is an absorption constraint on the players' state process. As a result of the state constraint the optimal time of absorption becomes part of the equilibrium. This requires a novel approach when applying Pontyagin's maximum principle. We prove the existence and uniqueness of equilibria and solve the infinite horizon models in closed form. As players may drop out of the game over time, equilibrium production rates need not be monotone nor smooth.

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  • Paulwin Graewe & Ulrich Horst & Ronnie Sircar, 2021. "A Maximum Principle approach to deterministic Mean Field Games of Control with Absorption," Papers 2104.06152, arXiv.org.
    • Handle: RePEc:arx:papers:2104.06152
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    References listed on IDEAS

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    6. Xuancheng Huang & Sebastian Jaimungal & Mojtaba Nourian, 2019. "Mean-Field Game Strategies for Optimal Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(2), pages 153-185, March.
    7. Daskalakis, Constantinos & Papadimitriou, Christos H., 2015. "Approximate Nash equilibria in anonymous games," Journal of Economic Theory, Elsevier, vol. 156(C), pages 207-245.
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