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Effort Expenditure For Cash Flow In A Mean-Field Equilibrium

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Michael Ludkovski & Xuwei Yang, 2017. "Mean Field Game Approach to Production and Exploration of Exhaustible Commodities," Papers 1710.05131, arXiv.org.
    5. 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.
    6. Guillermo Gallego & Ming Hu, 2014. "Dynamic Pricing of Perishable Assets Under Competition," Management Science, INFORMS, vol. 60(5), pages 1241-1259, May.
    7. 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.
    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. 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.
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    Cited by:

    1. Ryan Donnelly & Zi Li, 2022. "Dynamic Inventory Management with Mean-Field Competition," Papers 2210.17208, arXiv.org.

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