Great fish war with moratorium

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. When the players cannot avoid a moratorium under both cooperative and noncooperative modes of play, we propose a moratorium-free strategy profile that matches under some conditions the Nash equilibrium in linear-state strategies. We illustrate our results with some numerical examples.

Automated summary

We study a discrete-time fish war model with a moratorium on fishing activities when the fish stock reaches a critical low value. The moratorium is in place until the stock recovers to a desirable level. We determine conditions for avoiding the moratorium and find the optimal duration when it is necessary. When players cannot avoid the moratorium, we propose a moratorium-free strategy profile that matches the Nash equilibrium in linear-state strategies under certain conditions. Numerical examples are provided to illustrate our findings.