To investigate the question mathematically, they describe the following game: Hypothetical participants start with an equal endowment of money. Faced with a tragedy of the commons, they are given two choices: cooperate (contribute a fraction of your endowment to fixing the problem) or defect (keep your entire endowment for yourself). If a minimum group investment is not met, everyone loses all their money. This adds a long-term consideration of risk to short-term choices. Over time, cooperators will increase as long as cooperating is perceived to be more successful than defecting. Cooperation will be more successful for small contributions and high risks. The size of the minimum group investment will also modulate behavior; if it’s high, it will be more difficult to initiate cooperation. But there’s a sort of “critical mass"—once you’ve reached that, a high minimum investment will lead to a high degree of cooperation. This is all reasonably intuitive. If you don’t have to pitch in much to fix a huge problem, you’ll take that deal. If the solution to the problem seems out of reach, you may consider contributing to be a waste until it looks tractable; then you’ll want to pitch in. Clearly, there’s a large social component to all this as well, and the researchers found the dynamics of small groups to be quite different from large ones. This is where it gets interesting. They found that, as you decrease the number of participants in the game, social influence makes the group more likely to cooperate. We can relate to that as well. Think back to our ranchers—if there are only three of them, it’s much less likely that one will try to freeload while letting the others deal with the problem. Why? Because the feeling of accountability grows. There’s social pressure to help shoulder the burden. (via Group dynamics key to avoiding tragedy of the commons) economics, game theory, rational actor?