URL: http://economix.blogs.nytimes.com/2013/02/14/gaming-the-system/
We are all very familiar with being graded on a curve, and every year there are groups of students who joke about getting the entire class to skip the exam so everyone gets a 0% and they’re all curved to 100%. There are even well-documented examples of this very phenomenon occurring with success. On the surface, this phenomenon is the logical conclusion for any scenario with a curve. After all, your payoff is the same or better if everyone skips the exam as opposed to everyone taking the exam. So why don’t students do this more often? The article linked above explains that this phenomenon is so rare due to trembling hand equilibrium, a refinement of the Nash equilibrium theory we have studied in class. The article explains that there are two equilibria that could occur in this siutation. The first, where every student is certain that the other students will boycott the exam, and the second where at least one person suspects another student will not follow the boycott and then decides to break the boycott. The first case is considered trembling hand imperfect as the article states. Because if a student makes a mistake or wavers in their commitment to the boycott, the rest of the class is left with lower grades. By contrast, the second case is trembling hand perfect according to the article because the outcome is largely unaffected by the independent decisions of the other students. The article then concludes that this trembling hand equilibrium theory explains why more students don’t just boycott their exams.
This article connects the content that we learned in class about Nash equilibrium to real world examples where the number of players is much larger and more complex decision making is required. It also refines our understanding of existing Nash equilibrium examples and general game theory. For instance, this principle is similar to the prisoner’s dilemma in the sense that cooperation would increase the payoff for both prisoners much in the same way that cooperation between students increases their exam grades, but it also explains why this cooperation is so difficult to accomplish. The inherent uncertainty regarding the decisions of others makes it much more difficult to cooperate effectively when one player has so much at risk in the game.
Other references:
Gaming the System: A Game Theory Approach to Grading on a Curve
https://en.wikipedia.org/wiki/Trembling_hand_perfect_equilibrium