IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v22y2019i04ns0219024919500146.html
   My bibliography  Save this article

Effort Expenditure For Cash Flow In A Mean-Field Equilibrium

Author

Listed:
  • RYAN DONNELLY

    (Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA)

  • TIM LEUNG

    (Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA)

Abstract

We study a mean-field game framework in which agents expend costly effort in order to transition into a state where they receive cash flows. As more agents transition into the cash flow receiving state, the magnitude of all remaining cash flows decreases, introducing an element of competition whereby agents are rewarded for transitioning earlier. An equilibrium is reached if the optimal expenditure of effort produces a transition intensity which is equal to the flow rate at which the continuous population enters the receiving state. We give closed-form expressions which yield equilibrium when the cash flow horizon is infinite or exponentially distributed. When the cash flow horizon is finite, we implement an algorithm which yields equilibrium if it converges. We show that in some cases, a higher cost of effort results in the agents placing greater value on the potential cash flows in equilibrium. We also present cases where the algorithm fails to converge to an equilibrium.

Suggested Citation

  • Ryan Donnelly & Tim Leung, 2019. "Effort Expenditure For Cash Flow In A Mean-Field Equilibrium," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-23, June.
  • Handle: RePEc:wsi:ijtafx:v:22:y:2019:i:04:n:s0219024919500146
    DOI: 10.1142/S0219024919500146
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024919500146
    Download Restriction: Access to full text is restricted to subscribers

    File URL: https://libkey.io/10.1142/S0219024919500146?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Helen Weeds, 2002. "Strategic Delay in a Real Options Model of R&D Competition," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(3), pages 729-747.
    2. Sun, Yeneng, 2006. "The exact law of large numbers via Fubini extension and characterization of insurable risks," Journal of Economic Theory, Elsevier, vol. 126(1), pages 31-69, January.
    3. Michael Ludkovski & Xuwei Yang, 2017. "Mean Field Game Approach to Production and Exploration of Exhaustible Commodities," Papers 1710.05131, arXiv.org.
    4. David A. Malueg & Shunichi O. Tsutsui, 1997. "Dynamic R&D Competition with Learning," RAND Journal of Economics, The RAND Corporation, vol. 28(4), pages 751-772, Winter.
    5. Partha Dasgupta & Joseph Stiglitz, 1980. "Uncertainty, Industrial Structure, and the Speed of R&D," Bell Journal of Economics, The RAND Corporation, vol. 11(1), pages 1-28, Spring.
    6. Guillermo Gallego & Ming Hu, 2014. "Dynamic Pricing of Perishable Assets Under Competition," Management Science, INFORMS, vol. 60(5), pages 1241-1259, May.
    7. Grzegorz Pawlina & Peter M. Kort, 2006. "Real Options in an Asymmetric Duopoly: Who Benefits from Your Competitive Disadvantage?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(1), pages 1-35, March.
    8. Chi Man Leung & Yue Kuen Kwok, 2016. "Real options game models of R&D competition between asymmetric firms with spillovers," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 259-291, November.
    9. Ludkovski, Michael & Sircar, Ronnie, 2016. "Technology ladders and R&D in dynamic Cournot markets," Journal of Economic Dynamics and Control, Elsevier, vol. 69(C), pages 127-151.
    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. Ryan Donnelly & Zi Li, 2022. "Dynamic Inventory Management with Mean-Field Competition," Papers 2210.17208, arXiv.org.

    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. Thijssen, J.J.J., 2003. "Investment under uncertainty, market evolution and coalition spillovers in a game theoretic perspective," Other publications TiSEM 672073a6-492e-4621-8d4a-0, Tilburg University, School of Economics and Management.
    2. Colombo, Luca & Labrecciosa, Paola, 2021. "A stochastic differential game of duopolistic competition with sticky prices," Journal of Economic Dynamics and Control, Elsevier, vol. 122(C).
    3. Ryan Donnelly & Zi Li, 2022. "Dynamic Inventory Management with Mean-Field Competition," Papers 2210.17208, arXiv.org.
    4. Atal, Vidya & Bar, Talia & Gordon, Sidartha, 2016. "Project selection: Commitment and competition," Games and Economic Behavior, Elsevier, vol. 96(C), pages 30-48.
    5. Dosis, Anastasios & Muthoo, Abhinay, 2019. "Experimentation in Dynamic R&D Competition," CRETA Online Discussion Paper Series 52, Centre for Research in Economic Theory and its Applications CRETA.
    6. Billette de Villemeur, Etienne & Ruble, Richard & Versaevel, Bruno, 2014. "Innovation and imitation incentives in dynamic duopoly," MPRA Paper 59453, University Library of Munich, Germany.
    7. Jacco J.J. Thijssen, "undated". "Equilibria in Continuous Time Preemption Games with Markovian Payoffs," Discussion Papers 11/17, Department of Economics, University of York.
    8. Femminis, Gianluca & Martini, Gianmaria, 2011. "Irreversible investment and R&D spillovers in a dynamic duopoly," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 1061-1090, July.
    9. Steg, Jan-Henrik, 2018. "Preemptive investment under uncertainty," Games and Economic Behavior, Elsevier, vol. 110(C), pages 90-119.
    10. Sendstad, Lars Hegnes & Chronopoulos, Michail, 2017. "Strategic Technology Switching under Risk Aversion and Uncertainty," Discussion Papers 2017/10, Norwegian School of Economics, Department of Business and Management Science.
    11. Azevedo, Alcino & Paxson, Dean, 2014. "Developing real option game models," European Journal of Operational Research, Elsevier, vol. 237(3), pages 909-920.
    12. Boyarchenko, Svetlana & Levendorskiĭ, Sergei, 2014. "Preemption games under Lévy uncertainty," Games and Economic Behavior, Elsevier, vol. 88(C), pages 354-380.
    13. Ebina, Takeshi & Matsushima, Noriaki & Nishide, Katsumasa, 2022. "Demand uncertainty, product differentiation, and entry timing under spatial competition," European Journal of Operational Research, Elsevier, vol. 303(1), pages 286-297.
    14. Steg, Jan-Henrik & Thijssen, Jacco, 2015. "Quick or Persistent? Strategic Investment Demanding Versatility," Center for Mathematical Economics Working Papers 541, Center for Mathematical Economics, Bielefeld University.
    15. Thijssen, Jacco J.J. & Huisman, Kuno J.M. & Kort, Peter M., 2012. "Symmetric equilibrium strategies in game theoretic real option models," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 219-225.
    16. Michi Nishihara, 2018. "Valuation of an R&D project with three types of uncertainty," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 93-113, June.
    17. Diana Terrazas‐Santamaria, 2021. "Strategic introduction of a new product under uncertainty: A duopoly case," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(4), pages 796-807, June.
    18. Ohyama, Atsuyuki & Tsujimura, Motoh, 2008. "Induced effects and technological innovation with strategic environmental policy," European Journal of Operational Research, Elsevier, vol. 190(3), pages 834-854, November.
    19. Mason, Robin & Weeds, Helen, 2010. "Investment, uncertainty and pre-emption," International Journal of Industrial Organization, Elsevier, vol. 28(3), pages 278-287, May.
    20. Wang, Congcong & Chen, Shanshan & Wang, Yuhan & Pansera, Bruno Antonio & Luckraz, Shravan, 2023. "On the welfare and policy implications of a two-period real option game," Socio-Economic Planning Sciences, Elsevier, vol. 90(C).

    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:wsi:ijtafx:v:22:y:2019:i:04:n:s0219024919500146. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.