Complex dynamics analysis on fish stock harvested by two players with heterogeneous rationality

This paper formulates a duopoly game model with heterogeneous expectations assuming that two players with asymmetric information harvest fish from a common fish ground and sell it in an imperfectly competitive market. We study the existence and stability of this system's positive equilibrium characterizing the sustainable use of the renewable resource. Then show the complex dynamics of this system in different parameters though numerical simulation. We finally show the influence of the adjustment speed of the harvesting quantity on the set of initial conditions which give non-negative trajectories converging to an equilibrium (called as a feasible set). When the player accelerates the adjustment speed in order to achieve initial advantage, we discover that it leads to instability of system and makes the system sink into the chaotic state and thus makes the resources exhaust more easily.