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Partially Observed Discrete-Time Risk-Sensitive Mean Field Games

Author

Listed:
  • Naci Saldi

    (Bilkent University)

  • Tamer Başar

    (University of Illinois)

  • Maxim Raginsky

    (University of Illinois)

Abstract

In this paper, we consider discrete-time partially observed mean-field games with the risk-sensitive optimality criterion. We introduce risk-sensitivity behavior for each agent via an exponential utility function. In the game model, each agent is weakly coupled with the rest of the population through its individual cost and state dynamics via the empirical distribution of states. We establish the mean-field equilibrium in the infinite-population limit using the technique of converting the underlying original partially observed stochastic control problem to a fully observed one on the belief space and the dynamic programming principle. Then, we show that the mean-field equilibrium policy, when adopted by each agent, forms an approximate Nash equilibrium for games with sufficiently many agents. We first consider finite-horizon cost function and then discuss extension of the result to infinite-horizon cost in the next-to-last section of the paper.

Suggested Citation

  • Naci Saldi & Tamer Başar & Maxim Raginsky, 2023. "Partially Observed Discrete-Time Risk-Sensitive Mean Field Games," Dynamic Games and Applications, Springer, vol. 13(3), pages 929-960, September.
    • Handle: RePEc:spr:dyngam:v:13:y:2023:i:3:d:10.1007_s13235-022-00453-z
    DOI: 10.1007/s13235-022-00453-z
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    References listed on IDEAS

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    1. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    2. Nicole Bäuerle & Ulrich Rieder, 2014. "More Risk-Sensitive Markov Decision Processes," Mathematics of Operations Research, INFORMS, vol. 39(1), pages 105-120, February.
    3. Naci Saldi & Tamer Bas¸ ar & Maxim Raginsky, 2020. "Approximate Markov-Nash Equilibria for Discrete-Time Risk-Sensitive Mean-Field Games," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1596-1620, November.
    4. Eugene A. Feinberg & Pavlo O. Kasyanov & Michael Z. Zgurovsky, 2016. "Partially Observable Total-Cost Markov Decision Processes with Weakly Continuous Transition Probabilities," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 656-681, May.
    5. Naci Saldi & Tamer Başar & Maxim Raginsky, 2019. "Approximate Nash Equilibria in Partially Observed Stochastic Games with Mean-Field Interactions," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 1006-1033, August.
    6. Hans-Joachim Langen, 1981. "Convergence of Dynamic Programming Models," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 493-512, November.
    7. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    8. Adlakha, Sachin & Johari, Ramesh & Weintraub, Gabriel Y., 2015. "Equilibria of dynamic games with many players: Existence, approximation, and market structure," Journal of Economic Theory, Elsevier, vol. 156(C), pages 269-316.
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