What can game theory tell us about appropriate responses to climate change? I’m sure game theorists would posit that their discipline is immensely helpful but my natural skepticism of applying theoretical models to predicting complex human behaviour makes me doubt just how much game theory can help.
Having spent much of the last month developing agent based game theoretic models of various political phenomena however, I think it is clear that game theory can show what strategies wont work.
A Prisoner’s Dilemma
One locus of philosophical debate in game theory is which games best model social and political behaviour. The Prisoner’s Dilemma is probably the most famous of these although there is good reason to believe other games better describe the payoffs in human interactions 1. In normal form with traditional payoffs, a Prisoner’s Dilemma looks like this:
| 3,3 | 0,5 | | 5,0 | 1,1 |
If both players cooperate, they both receive a payoff of 3. If both defect, they both receive 1. If however one cooperates and the other defects, then the defector receives a payoff of 5 while the cooperator gets nothing.
The interesting thing about the Prisoner’s Dilemma is that rational agents who attempt to maximise their own welfare will always defect, even though the socially optimal strategy is to cooperate. This is because mutual defection is the only Nash Equilibrium in this game - regardless of what the other play does, it is always better to defect.
So is climate change a Prisoner’s Dilemma? Perhaps. It’s clear that mutual cooperation - everyone consuming and polluting no more than their fair share - is the socially optimal strategy. If we all use more CO2e than our fair share allows, then we destabilise the current environmental equilibrium and basically the fuck the planet. It’s also clear that not using more than one’s fair share while others consume unchecked has a low payoff for the cooperator, and high payoff for the defector, and negative outcome for the system. With these observations in mind, we can construct a payoff matrix something like this:
| 1,1 | -5,3 | | 3,-5 | -3,-3 |
The ratios between each quadrant is debatable. Exactly how much worse is it to cooperate with a defector than to defect with one? Regardless, the relative differentials between quadrants seems correct. Mutual cooperation benefits both individuals and is socially optimal. Mutual defection has negative effects on the system without discriminating between agents. Cooperating with a defector imposes the most cost on an agent because they lose relative to defector - who doesn’t incurring the same economic costs of reduced consumption - while the system damage is less than in mutual defection. And finally, defectors only benefit when others cooperate.
When played for a known fixed number of rounds, the rational response of each agent is to defect, thereby destroying the system. When played over an indeterminate number of rounds however, the dominant strategy is tit-for-tat - cooperate first and then respond in kind. Cooperators perform well with their own kind and generate the socially optimal outcome. If everyone would just do their bit, the problem would be solved.
Defectors however, suffer when interacting with their own kind and only benefit at the expense of cooperators. Because of this, the presence of just a few defectors in the company of cooperators leads to them quickly dominating. When defectors are present, just doing your own fair share is a recipe for defeat and destruction. Recycling, Earth Hour, using less - all these well intended actions are useless in combating climate change if they are our only actions when defectors (of which there are many) are present.
Tit-for-tat on the other hand, enables cooperation with it’s opening friendly move and punishes defectors and limits their relative performance. When played in game theory tournaments, tit-for-tat consistently outperforms all other strategies. So why don’t we just adopt a tit-for-tat strategy and solve this climate change problem once and for all?
The problem is that tit-for-tat only dominates when the costs of non-cooperation are limited to those not cooperating. When we model the problem of climate change as a Prisoner’s Dilemma however, our actions are non-discriminatory.
When I cooperate in the climate change game, I don’t play against everyone else one at a time, I play against everyone simultaneously with a single action. That means I can’t cooperate with cooperators and defect against defectors. Instead, I have to cooperate with everyone or defect against all. The nature of the my action in the climate change game - use no more than my fair share of resources or use more than my fair share of resources - means that I cannot discriminate my actions towards particular others. My actions are global. Tit-for-tat is not an available strategy.
But game theory is not completely useless. If we can find a way to discriminate our responses, then tit-for-tat once again becomes a viable strategy for dealing with climate change.
How might we do this? The cooperative requirement of tit-for-tat means that using no more than our fair share of resources is an essential action. To not cooperate in this regard means that we become defectors and destine the system to eventual destruction. But it also means that we also need to find some way of imposing costs on defectors while we cooperate.
How exactly we might do this is not something that can be answered by game theory. Perhaps we defectors could be punished impositionally through the use of fines or coercion. Perhaps defectors could be punished non-impositionally with something like trade sanctions or other refusals to cooperate. All that’s required however, is for the payoffs of defection to be changed.
Doing good by itself is not enough. Wrong doers must also be punished.
Brian Skrymm provides a good treatment on why the Stag Hunt is a better candidate in The Stage Hunt and the Evolution of Social Structure (2004) ↩