Effort Expenditure for Cash Flow in a Mean-Field Equilibrium

International Journal of Theoretical & Applied Finance, 2019

22 Pages Posted: 29 Aug 2018 Last revised: 23 Feb 2019

See all articles by Ryan Francis Donnelly

Ryan Francis Donnelly

University of Washington - Department of Applied Mathematics

Tim Leung

University of Washington - Department of Applied Math

Date Written: August 20, 2018

Abstract

We study a mean-field game framework in which agents expend costly efforts 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 algorithm fails to converge to an equilibrium.

Keywords: real options, mean field games, equilibrium, optimal control

JEL Classification: C61, C73, G11

Suggested Citation

Donnelly, Ryan Francis and Leung, Tim, Effort Expenditure for Cash Flow in a Mean-Field Equilibrium (August 20, 2018). International Journal of Theoretical & Applied Finance, 2019. Available at SSRN: https://ssrn.com/abstract=3235553 or http://dx.doi.org/10.2139/ssrn.3235553

Ryan Francis Donnelly (Contact Author)

University of Washington - Department of Applied Mathematics ( email )

Box 352420
Seattle, WA 98195-2420
United States

Tim Leung

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States
9253381749 (Phone)

HOME PAGE: http://faculty.washington.edu/timleung/

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