King's College London

Research portal

EFFORT EXPENDITURE FOR CASH FLOW IN A MEAN-FIELD EQUILIBRIUM

Research output: Contribution to journalArticle

Original languageEnglish
Article number1950014
JournalInternational Journal of Theoretical and Applied Finance
Volume22
Issue number4
DOIs
Accepted/In press19 Feb 2019
Published1 Jun 2019

King's Authors

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.

View graph of relations

© 2020 King's College London | Strand | London WC2R 2LS | England | United Kingdom | Tel +44 (0)20 7836 5454