On the competitive harvesting of marine resources

Alberto Bressan, Vasile Staicu

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Abstract

The paper is concerned with the optimal harvesting of a marine resource, described by an elliptic equation with Neumann boundary conditions and a nonlinear source term. We first consider a single agent, whose harvesting effort at various locations is described by a positive Radon measure. Necessary conditions for optimality are derived, complementing the existence result proved in [A. Bressan, G. Coclite, and W. Shen, SIAM J. Control Optim., 5f (2013), pp. 1186-1202]. The second part of the paper deals with a competitive scenario, where several groups of fishermen, from different coastal towns and hence with different cost functions, harvest the same marine resource. We prove the existence of a Nash equilibrium, which is characterized in terms of a suitable variational inequality.

Original languageEnglish (US)
Pages (from-to)3961-3984
Number of pages24
JournalSIAM Journal on Control and Optimization
Volume57
Issue number6
DOIs
Publication statusPublished - Jan 1 2019

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All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics

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