We consider a discrete-time version of the fish war model, where a regulator imposes a moratorium on fishing activities whenever the stock reaches a predetermined critical low value. The moratorium will be in place until the fish stock recovers, that is, attains a desirable value. We obtain conditions on the parameter values such that a moratorium could be avoided, and its optimal duration when its imposition is deemed necessary. We propose a coordinated harvesting strategy profile and determine when it matches the Nash equilibrium in linear-state strategies. Numerical examples show the significant influence of the fish reproduction rate on the length of a moratorium regime and the equilibrium properties of the coordinated strategy profile.
Published March 2022 , 23 pages
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