Big game is seen as both a resource and a pest. They are valued by hunters and responsible for collective economic damage. The article aims at characterizing the collective optimum using natural resource economics. We analyze the optimal game management using a bio-economic model using the optimal control theory. We take into account all the costs and benefits related both to hunting and the game presence. The optimum targeted population is then compared with the hunter optimum that does not include damage caused by big game and, to open access equilibrium reflecting the selfish behaviour of hunters and externalities. This analytical framework provides an economic interpretation of the change in the context both of hunting and big game populations in France. In addition, it offers a target for the game management policies that could be implemented and recommendations on economic tools for these policies.