Common resources, optimality and taxes in dynamic games with increasing number of players

In the paper we examine the problem of exploitation of a common renewable resource. We use two kinds of models of this problem: games with finitely many players and games with a continuum of players. Equilibria in both cases are calculated and the payoffs are compared with payoffs in the situation in which each player behaves as a single owner of the resource. Various concepts of optimality are considered: optimality in the sense of property, Pareto optimality, maximization of a social welfare function of specific type and environmental sustainability. Another issue is the problem of enforcement of assumed profiles by so-called “linear” tax systems. Special attention is paid to the comparison of games with finitely many players and their continuum-of-players limit game.