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Self-consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games

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Listed:
  • Alberto Bressan

    (Penn State University)

  • Yilun Jiang

    (Penn State University)

Abstract

The paper introduces a concept of “self consistent” Stackelberg equilibria for stochastic games in infinite time horizon, where the two players adopt feedback strategies and have exponentially discounted costs. The analysis is focused on games in continuous time, described by a controlled Markov process with finite state space. Results on the existence and uniqueness of such solutions are provided. As an intermediate step, a detailed description of the structure of the best reply map is achieved, in a “generic” setting. Namely: for all games where the cost functions and the transition coefficients of the Markov chain lie in open dense subset of a suitable space $$\mathcal{C}^k$$Ck. Under generic assumptions, we prove that a self-consistent Stackelberg equilibrium exists, provided that either (i) the leader is far-sighted, i.e., his exponential discount factor is sufficiently small, or (ii) the follower is narrow-sighted, i.e., his discount factor is large enough.

Suggested Citation

  • Alberto Bressan & Yilun Jiang, 2020. "Self-consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 328-360, June.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:2:d:10.1007_s13235-019-00329-9
    DOI: 10.1007/s13235-019-00329-9
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    References listed on IDEAS

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    1. Alberto Bressan & Yilun Jiang, 2019. "On the Generic Structure and Stability of Stackelberg Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 840-880, December.
    2. Alberto Bressan & Deling Wei, 2013. "Stackelberg Solutions of Feedback Type for Differential Games with Random Initial Data," Dynamic Games and Applications, Springer, vol. 3(3), pages 341-358, September.
    3. Alain Bensoussan & Shaokuan Chen & Suresh P. Sethi, 2014. "Feedback Stackelberg Solutions of Infinite-Horizon Stochastic Differential Games," International Series in Operations Research & Management Science, in: Fouad El Ouardighi & Konstantin Kogan (ed.), Models and Methods in Economics and Management Science, edition 127, pages 3-15, Springer.
    4. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, September.
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    Cited by:

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    2. Guerrazzi, Marco & Candido, Giuseppe, 2023. "The determination of the price of capital goods: A differential game approach," MPRA Paper 119118, University Library of Munich, Germany.

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