Counteracting “the tragedy of the commons” in an imperfect world

Abstract

Our research question is whether it is possible and how to counteract “the tragedy of the commons” if facing various limitations of real-world economies. To answer it, we derive regulatory tax–subsidy systems and self-enforcing environmental agreements in a problem of extraction of common renewable resources. The first considered limitation is that the feasible class of tax–subsidy systems may have a compl icated form, for example, there are transition periods for smooth reduction of fishing. The alternative limitation is that there is no institution that can impose taxes or subsidize, so sustainability can be achieved only by self-enforcing international agreements. The next limitation is in those agreements: we assume that it takes time to detect a defection. We study these enforcement tools in a continuous-time version of a Fish War type game with $n$ countries, with fish indispensable for their economies. We calculate the social optimum, a Nash equilibrium, and partial cooperation equilibria. The Nash equilibrium leads to the depletion of fish, while the social optimum typically results in sustainability. For partial cooperation, only two-country coalitions are stable. We calculate tax–subsidy systems that enforce maximization of joint payoff, also if there are additional constraints, and we propose an algorithm that looks for such a system in an arbitrary class of regulatory tax–subsidy systems. For the international agreement with imperfect monitoring, we are interested in the maximal detection delay for which the agreement remains self-enforcing. Counterintuitively, the more the players, the more stable the agreement.