Tragedy of the Commons

Recently, I have been reading up on game theory and how it can be applied to data science situations where multiple parties are making decisions that affect the system as a whole and each other. During this, I came across the argument called Tragedy of the Commons (TOTC), that illustrates the flaw in allowing individuals make decisions based on self fulfilling motives. TOTC refers to the conflict over scarce resources that results from the tension between individual selfish interests and the common good. This concept was popularized by Hardin (1968). The original example of TOTC is as such:

Consider a pasture shared by local herders. Each herder wants to maximize his yield, increasing his herd size whenever possible. However, each additional animal degrades the quality of the pasture itself. In a selfish situation, all the herders will want to maximize their herd size regardless of the damage it does to not only other herders but also the pasture itself. This is the TOTC. For those who have studied economics, this situation will be very familiar. In fact, TOTC is essentially the “free-rider” problem.

Formal Analysis

Now the natural question is to ask if there is a possible solution to the situation, perhaps some form of an equilibrium, that maximizes the yield for the herders, yet minimizes the damage done to the pasture. Let us consider a…