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

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

Research output: Working paperDiscussion paperOther research output

280 Downloads (Pure)

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

Fingerprint

Lakes
Hysteresis
Decision making

Keywords

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

Cite this

Reddy, P. V., Schumacher, J. M., & Engwerda, J. C. (2012). Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model. (CentER Discussion Paper; Vol. 2012-001). Tilburg: Econometrics.
Reddy, P.V. ; Schumacher, J.M. ; Engwerda, J.C. / Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model. Tilburg : Econometrics, 2012. (CentER Discussion Paper).
@techreport{d0dda6e4ecbd4999a1f3251063aed9c5,
title = "Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model",
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.",
keywords = "Optimal control, Differential games, Threshold effects, Discontinuous dynamics, Shallow lake",
author = "P.V. Reddy and J.M. Schumacher and J.C. Engwerda",
note = "Pagination: 28",
year = "2012",
language = "English",
volume = "2012-001",
series = "CentER Discussion Paper",
publisher = "Econometrics",
type = "WorkingPaper",
institution = "Econometrics",

}

Reddy, PV, Schumacher, JM & Engwerda, JC 2012 'Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model' CentER Discussion Paper, vol. 2012-001, Econometrics, Tilburg.

Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model. / Reddy, P.V.; Schumacher, J.M.; Engwerda, J.C.

Tilburg : Econometrics, 2012. (CentER Discussion Paper; Vol. 2012-001).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model

AU - Reddy, P.V.

AU - Schumacher, J.M.

AU - Engwerda, J.C.

N1 - Pagination: 28

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Optimal control

KW - Differential games

KW - Threshold effects

KW - Discontinuous dynamics

KW - Shallow lake

M3 - Discussion paper

VL - 2012-001

T3 - CentER Discussion Paper

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

PB - Econometrics

CY - Tilburg

ER -

Reddy PV, Schumacher JM, Engwerda JC. Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model. Tilburg: Econometrics. 2012. (CentER Discussion Paper).