IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2201.05959.html
   My bibliography  Save this paper

Master Equation for Discrete-Time Stackelberg Mean Field Games with single leader

Author

Listed:
  • Deepanshu Vasal
  • Randall Berry

Abstract

In this paper, we consider a discrete-time Stackelberg mean field game with a leader and an infinite number of followers. The leader and the followers each observe types privately that evolve as conditionally independent controlled Markov processes. The leader commits to a dynamic policy and the followers best respond to that policy and each other. Knowing that the followers would play a mean field game based on her policy, the leader chooses a policy that maximizes her reward. We refer to the resulting outcome as a Stackelberg mean field equilibrium (SMFE). In this paper, we provide a master equation of this game that allows one to compute all SMFE. Based on our framework, we consider two numerical examples. First, we consider an epidemic model where the followers get infected based on the mean field population. The leader chooses subsidies for a vaccine to maximize social welfare and minimize vaccination costs. In the second example, we consider a technology adoption game where the followers decide to adopt a technology or a product and the leader decides the cost of one product that maximizes his returns, which are proportional to the people adopting that technology

Suggested Citation

  • Deepanshu Vasal & Randall Berry, 2022. "Master Equation for Discrete-Time Stackelberg Mean Field Games with single leader," Papers 2201.05959, arXiv.org.
    • Handle: RePEc:arx:papers:2201.05959
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2201.05959
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dirk Bergemann & Maher Said, 2010. "Dynamic Auctions: A Survey," Cowles Foundation Discussion Papers 1757, Cowles Foundation for Research in Economics, Yale University.
    2. S. Rasoul Etesami & Tamer Başar, 2019. "Dynamic Games in Cyber-Physical Security: An Overview," Dynamic Games and Applications, Springer, vol. 9(4), pages 884-913, December.
    3. Boonen, Tim J. & Pantelous, Athanasios A. & Wu, Renchao, 2018. "Non-cooperative dynamic games for general insurance markets," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 123-135.
    4. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    5. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Deepanshu Vasal, 2022. "Master equation of discrete-time Stackelberg mean field games with multiple leaders," Papers 2209.03186, arXiv.org.
    2. Sina Sanjari & Subhonmesh Bose & Tamer Başar, 2025. "Incentive Designs for Stackelberg Games with a Large Number of Followers and their Mean-Field Limits," Dynamic Games and Applications, Springer, vol. 15(1), pages 238-278, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Deepanshu Vasal, 2022. "Master equation of discrete-time Stackelberg mean field games with multiple leaders," Papers 2209.03186, arXiv.org.
    2. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    3. Cao, Yiyin & Dang, Chuangyin & Xiao, Zhongdong, 2022. "A differentiable path-following method to compute subgame perfect equilibria in stationary strategies in robust stochastic games and its applications," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1032-1050.
    4. Peixuan Li & Chuangyin Dang, 2020. "An Arbitrary Starting Tracing Procedure for Computing Subgame Perfect Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 667-687, August.
    5. Wei He, 2022. "Discontinuous stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(4), pages 827-858, June.
    6. Kalai, Ehud & Shmaya, Eran, 2018. "Large strategic dynamic interactions," Journal of Economic Theory, Elsevier, vol. 178(C), pages 59-81.
    7. Deepanshu Vasal, 2024. "Sequential Decomposition of Discrete-Time Mean-Field Games," Dynamic Games and Applications, Springer, vol. 14(3), pages 697-715, July.
    8. Hoang, Nam H. & Vu, Hai L. & Lo, Hong K., 2018. "An informed user equilibrium dynamic traffic assignment problem in a multiple origin-destination stochastic network," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 207-230.
    9. Tobias Salz & Emanuel Vespa, 2020. "Estimating dynamic games of oligopolistic competition: an experimental investigation," RAND Journal of Economics, RAND Corporation, vol. 51(2), pages 447-469, June.
    10. Adam, Klaus & Billi, Roberto M., 2014. "Distortionary fiscal policy and monetary policy goals," Economics Letters, Elsevier, vol. 122(1), pages 1-6.
    11. Bonetto, Federico & Iacopetta, Maurizio, 2019. "A dynamic analysis of nash equilibria in search models with fiat money," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 207-224.
    12. Abito, Jose Miguel & Chen, Cuicui, 2023. "A partial identification framework for dynamic games," International Journal of Industrial Organization, Elsevier, vol. 87(C).
    13. Deepanshu Vasal & Achilleas Anastasopoulos, 2016. "Decentralized Bayesian learning in dynamic games: A framework for studying informational cascades," Papers 1607.06847, arXiv.org, revised Apr 2018.
    14. Martin, Fernando M., 2015. "Debt, inflation and central bank independence," European Economic Review, Elsevier, vol. 79(C), pages 129-150.
    15. Nakamura, Emi & Steinsson, Jón, 2011. "Price setting in forward-looking customer markets," Journal of Monetary Economics, Elsevier, vol. 58(3), pages 220-233.
    16. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    17. Miguel Villas-Boas, J., 2015. "A short survey on switching costs and dynamic competition," International Journal of Research in Marketing, Elsevier, vol. 32(2), pages 219-222.
    18. James J. Anton & Gary Biglaiser, 2010. "Quality, Upgrades, and Equilibrium in a Dynamic Monopoly Model," Working Papers 10-36, Duke University, Department of Economics.
    19. , & ,, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    20. Daron Acemoglu & Asuman Ozdaglar, 2005. "Competition and Efficiency in Congested Markets," NBER Working Papers 11201, National Bureau of Economic Research, Inc.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2201.05959. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.