Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model

P.V. Reddy, J.M. Schumacher, J.C. Engwerda

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Abstract

Abstract: In this article we analyze how the presence of thresholds influences multi agent decision making situations. We introduce a class of discounted autonomous optimal control problems with threshold effects and discuss tools to analyze these problems. Later, using these results we investigate two types of threshold effects; namely, simple and hysteresis switching, in the canonical model of the shallow lake. We solve the optimal management and open loop Nash equilibrium solutions for the shallow lake model with threshold effects. We establish a bifurcation analysis of the optimal vector field. Further, we observe that modeling with threshold effects simplifies this analysis. To be precise, the bifurcation scenarios rely on simple rules (inequalities) which can be verified easily. However, the qualitative behavior of the switching vector field is similar to the smooth case.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages28
Volume2012-001
Publication statusPublished - 2012

Publication series

NameCentER Discussion Paper
Volume2012-001

Keywords

  • Optimal control
  • Differential games
  • Threshold effects
  • Discontinuous dynamics
  • Shallow lake

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