We re-consider the problem of the great fish war developed by Levahri and Mirman when the information is incomplete and agents can form simple beliefs about the other's behavior. Beliefs must be consistent with observed actions. We derive the closed form expressions of the optimal policies, determine the steady state of the dynamics of fish population in our dynamic game, and compare it from an economic and environmental points of view to the non cooperative and cooperative cases. We study the conditions where our results lie in between both cases, and the implications of these findings.