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Hamilton-Jacobi Equations with Semilinear Costs and State Constraints, with Applications to Large Deviations in Games

Author

Listed:
  • William H. Sandholm

    (Department of Economics, University of Wisconsin, Madison, Wisconsin 53706)

  • Hung V. Tran

    (Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706)

  • Srinivas Arigapudi

    (Department of Economics, University of Wisconsin, Madison, Wisconsin 53706)

Abstract

We characterize solutions of a class of time-homogeneous optimal control problems with semilinear running costs and state constraints as maximal viscosity subsolutions to Hamilton-Jacobi equations and show that optimal solutions to these problems can be constructed explicitly. We present applications to large deviations problems arising in evolutionary game theory.

Suggested Citation

  • William H. Sandholm & Hung V. Tran & Srinivas Arigapudi, 2022. "Hamilton-Jacobi Equations with Semilinear Costs and State Constraints, with Applications to Large Deviations in Games," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 72-99, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:72-99
    DOI: 10.1287/moor.2020.1114
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    References listed on IDEAS

    as
    1. Arigapudi, Srinivas, 2020. "Transitions between equilibria in bilingual games under logit choice," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 24-34.
    2. Sandholm, William H. & Staudigl, Mathias, 2016. "Large deviations and stochastic stability in the small noise double limit," Theoretical Economics, Econometric Society, vol. 11(1), January.
    3. Dokumacı, Emin & Sandholm, William H., 2011. "Large deviations and multinomial probit choice," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2151-2158.
    4. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    5. Sandholm, William H., 2010. "Decompositions and potentials for normal form games," Games and Economic Behavior, Elsevier, vol. 70(2), pages 446-456, November.
    6. Sandholm, William H. & Staudigl, Mathias, 2016. "Large Deviations and Stochastic Stability in the Small Noise Double Limit, I: Theory," Center for Mathematical Economics Working Papers 505, Center for Mathematical Economics, Bielefeld University.
    7. Myatt, David P. & Wallace, Chris, 2003. "A multinomial probit model of stochastic evolution," Journal of Economic Theory, Elsevier, vol. 113(2), pages 286-301, December.
    8. Arigapudi, Srinivas, 2020. "Exit from equilibrium in coordination games under probit choice," Games and Economic Behavior, Elsevier, vol. 122(C), pages 168-202.
    9. Sandholm, William H. & Staudigl, Mathias, 2016. "Large Deviations and Stochastic Stability in the Small Noise Double Limit, II: The Logit Model," Center for Mathematical Economics Working Papers 506, Center for Mathematical Economics, Bielefeld University.
    10. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    11. Michihiro, Kandori & Rob, Rafael, 1998. "Bandwagon Effects and Long Run Technology Choice," Games and Economic Behavior, Elsevier, vol. 22(1), pages 30-60, January.
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    Cited by:

    1. Arigapudi, Srinivas, 2024. "Transitions between equilibria in Bilingual Games under Probit Choice," Journal of Mathematical Economics, Elsevier, vol. 111(C).

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