Nash equilibria and the environment

While A Beautiful Mind had a good deal to recommend it as a film, the explanation of the Nash Equilibrium that was included leaves a good bit to be desired. The film explained that in a situation with multiple players, a most desirable objective, and many less desirable objectives, it is rational for each player to pursue the less desirable goals. This is because everyone going after the same thing will probably lead to nobody getting it. The strategy of pursuing the less desirable but more plentiful option therefore maximizes the chances of getting some level of payoff, even though it may not be the highest payoff possible in the game.

The essential characteristic of the Nash Equilibrium is similar to that of Pareto Optimality. Basically, both describe situations in which players do not want to change their behaviours unilaterally. Pareto optimality can be most easily be explained by considering a large group of people with items to trade voluntarily. Eventually, they will trade to the point where no more voluntary exchanges will occur. The arrangement may not generate the maximum possible level of utility that could be achieved with the goods in question; for instance, a person with a large stock of insulin would not transfer any to a diabetic who had nothing to trade for it.¹ In a Nash Equilibrium, no player would want to change the strategy they are employing, given that no other players are going to change their own strategies. For the equilibrium to exist, this must be true independently from any information they might receive about the strategies of the other players. For instance, learning that other players have certain thresholds beyond which they will behave quite differently might provide an incentive for any one player to alter their strategy.

While Pareto Optimality is mostly a thought experiment, the Nash Equilibrium is directly applicable to many situations in which there are problems of coordination. For example, it can be applied to climate change policy. Assuming that the policy of each state is set independently, there is no incentive for a single state to unilaterally cap emissions. The effect of one country doing so would be small, while the cost in that country would be high. Hence, inaction is a Nash Equilibrium. It is only through the development of a system that changes the strategies of many actors that a low-carbon outcome can be achieved.

The absence of a Nash Equilibrium can also be problematic, when addressing environmental problems. Imagine a conservation regime based around an international ban on the sale of tiger products. From the perspective of any one state, there is an incentive to violate the ban, provided everyone else will maintain their strategy of conservation. The lack of a Nash Equilibrium threatens to make the regime unstable.

While elements can be built directly into such games to encourage cooperation and discourage defection, they always seem likely to encounter these two kinds of problem. As such, it may be that the only way to establish stable environmental regimes that require sacrifice for the common good is to embed them in a larger super-game. Here, defection on one issue threatens the ability of the defecting state to achieve its aims in other areas. States that continue to emit large amounts of greenhouse gas or who undermine conservation regimes might find themselves unable to enter preferential trade arrangements and the like. In a general way, the perception of a state as being a responsible or irresponsible member of the international community imposes some such pressure. To do so more formally requires the prioritization of environmental issues by all governments involved, as well as a certain strength of will in following up such threats. Despite that, it seems more plausible that such a combined approach could yield desirable outcomes, as opposed to one that focuses on narrow issue areas.

[1] This assumes that the participants derive utility only from the objects being traded, and not from higher order phenomena such as the perception that the distribution that exists is desirable or fair. Agents that place some value upon the happiness of the other agents might generate outcomes quite different from the kind envisioned in neoclassical economics.

Author: Milan

In the spring of 2005, I graduated from the University of British Columbia with a degree in International Relations and a general focus in the area of environmental politics. In the fall of 2005, I began reading for an M.Phil in IR at Wadham College, Oxford. Outside school, I am very interested in photography, writing, and the outdoors. I am writing this blog to keep in touch with friends and family around the world, provide a more personal view of graduate student life in Oxford, and pass on some lessons I've learned here. View all posts by Milan