In Part II of the Tragedy of the Commons 4-part series, I rehash the professor’s analysis of the game played in class. You should read Tragedy of the Commons: Part I — The Setup for a description of the game before reading this section.
The professor, who I shall refer to as J, claims that the optimal strategy for a perfectly rational player is to always defect. The reasoning begins with the observation that defection always yields more money than cooperating: a cooperating player puts $100 into the pool and receives $75 of it back for the effort. A defecting player, however, receives the initial $100 given and a share of any money put into the pool by cooperators.
J argues that the perfectly rational player will realize this. The perfectly rational player will also observe that a rational player will defect on the last turn because there is no chance of retaliation. Because of this, the perfectly rational player should also realize that, because a rational player will defect on the last turn, anyway, so if playing rational players, it makes no sense to cooperate in the second last turn. Using backwards induction, the rational player reaches the conclusion that the only logical move is to defect for the entire game. If the perfectly rational player is not playing a rational player, defecting is still the most logical option because it is the dominant strategy (that is, defection on any given turn always results in a better outcome than cooperating).
Based on this reasoning, J argues that the rational player should defect every round because no opponent will ever score better than the always-defecting player, hence, this is the strategy the rational player will adopt to maximize his/her chances of winning the real money in the class. Can you find any faults in this argument?
Stay tuned for my analysis of the game in Part III on Wednesday and an application of the results to individual decision making processes as it applies to some contemporary social issues in Part IV.