The best strategy is to do the deal and stick with it. True, if any of the others defect, you will all lose. But the game will be played again and again, and the result will approach an equilibrium in which those who defect are excluded, and those who remain will trust each other.

Thomas Hobbes (1588-1697) extended this strategy to a political philosophy in which he argued that the natural state of man was in a society, and once you joined it you could not defect. (Leviathan) David Hume (1711-1776) thought cooperation was ultimately good for the individual: I learn to do a service for another man without bearing him any real kindness, he wrote, because I believe that he will do the same for me. And he will help me because I will do a favor for him again. And both of us will help others. (A Treatise of Human Nature, III). John Rawls' Theory of Justice (1971) suggests that when a man doesn't know how the outcome will effect everyone, he chooses a strategy that will satisfy his minimum requirements no matter how things turn out - he would chase the rabbit.

If no one cooperates for the shared reward you end up with the "tragedy of the commons" where that which is shared by the most people is cared for the least.  It is always somebody else’s job to pick up litter in the park or keep the river clean.  This is usually prevented by some sort of social contract that forces each member to do (or pay to be done) what he would not otherwise see to be in his best interest. Or to be in the interest of so many that the portion of responsibility falling upon him is very small.

In game theory, a new branch of applied mathematics, the "best" strategy is the one which most efficiently delivers rewards to all players. Pareto, Hicks and Nash have each defined "best" differently: the best outcome for each player, the best outcome for all players together, or multiple strategies working together in equilibrium to give each player the best outcome. The great insight of game theory, though, is to see that rarely is the game played only once. The best outcome is a steady state of mutual reward. John von Neumann achieved this in proposing "Mutual Assured Destruction" as the model for international military competition, in which nations equipped with massive weapons systems have an incentive not to attack each other because an attack by any of them would mean destruction for all.