Measure-valued solutions to a harvesting game with several players

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

We consider Nash equilibrium solutions to a harvesting game in one-space dimension. At the equilibrium configuration, the population density is described by a second-order O.D.E. accounting for diffusion, reproduction, and harvesting. The optimization problem corresponds to a cost functional having sublinear growth, and the solutions in general can be found only within a space of measures. In this chapter, we derive necessary conditions for optimality, and provide an example where the optimal harvesting rate is indeed measure valued. We then consider the case of many players, each with the same payoff. As the number of players approaches infinity, we show that the population density approaches a well-defined limit, characterized as the solution of a variational inequality. In the last section, we consider the problem of optimally designing a marine park, where no harvesting is allowed, so that the total catch is maximized.

Original languageEnglish (US)
Title of host publicationAnnals of the International Society of Dynamic Games
PublisherBirkhauser
Pages399-423
Number of pages25
DOIs
StatePublished - Jan 1 2011

Publication series

NameAnnals of the International Society of Dynamic Games
Volume11
ISSN (Print)2474-0179
ISSN (Electronic)2474-0187

Fingerprint

Measure-valued Solutions
Harvesting
Game
Optimal Harvesting
Second Order ODE
Equilibrium Solution
Nash Equilibrium
Variational Inequalities
Well-defined
Optimality
Infinity
Optimization Problem
Necessary Conditions
Configuration
Costs
Population density

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Bressan, A., & Shen, W. (2011). Measure-valued solutions to a harvesting game with several players. In Annals of the International Society of Dynamic Games (pp. 399-423). (Annals of the International Society of Dynamic Games; Vol. 11). Birkhauser. https://doi.org/10.1007/978-0-8176-8089-3_20
Bressan, Alberto ; Shen, Wen. / Measure-valued solutions to a harvesting game with several players. Annals of the International Society of Dynamic Games. Birkhauser, 2011. pp. 399-423 (Annals of the International Society of Dynamic Games).
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Bressan, A & Shen, W 2011, Measure-valued solutions to a harvesting game with several players. in Annals of the International Society of Dynamic Games. Annals of the International Society of Dynamic Games, vol. 11, Birkhauser, pp. 399-423. https://doi.org/10.1007/978-0-8176-8089-3_20

Measure-valued solutions to a harvesting game with several players. / Bressan, Alberto; Shen, Wen.

Annals of the International Society of Dynamic Games. Birkhauser, 2011. p. 399-423 (Annals of the International Society of Dynamic Games; Vol. 11).

Research output: Chapter in Book/Report/Conference proceedingChapter

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Bressan A, Shen W. Measure-valued solutions to a harvesting game with several players. In Annals of the International Society of Dynamic Games. Birkhauser. 2011. p. 399-423. (Annals of the International Society of Dynamic Games). https://doi.org/10.1007/978-0-8176-8089-3_20