The Nash Equilibrium And Why “Harkness Wallflowers” Are Bad Tacticians

The objective of a student is to learn. The objective of an academic is to teach. The guiding principles of these two entities seem to go hand in hand; each satisfies the other. A campus based on these axioms need never be studied under economic theory. There would be no game, no matrix in which agents could make decisions. But what if the motives of students and teachers were asymmetric? This more closely follows reality, which usually beckons the behavioral mapping of splintered interests.Oftentimes, students are more engaged in the pursuit of tangible achievements rather than wisdom. Accordingly, most teaching methods strive to incentivize learning via an assessment, or “score.” Edward Harkness was overly optimistic when he offered his method as a tribute to discourse. Humans, being selfish creatures, require more than just Socratic inspiration to participate in discussion. There must be incentives and choices between them. Our school has provided such, and thence, Harkness as a construct has become a non-cooperative game. Non-cooperative, in this sense, means that every player chooses his strategy without an obligation to match it with others.On this point, many of my peers have questioned the efficacy of real-world Harkness. Particularly, upper Ellena Joo has been quite prolific in publishing her concerns. She claims that the system is broken and unfair, especially disadvantaging “quiet introverts and perhaps even students who are raised in cultures that advocate qualities different from those espoused by Harkness.” I fundamentally disagree; the Harkness Method cannot be personified as some kind of prejudiced being. It is merely a system that has come to harness personal ambition in order to encourage communal learning. Harkness itself has no bias. To say that this apparatus is “imbalanced” is akin to accusing traffic laws of favoring safe drivers over terrible ones.Our school has made two assumptions in its current implementation of Harkness. First, that participation in conversation yields net knowledge for the classroom. Second, that withdrawal from conversation adds zero knowledge. In respect to these rules, Exeter proposes to its students a multitude of grade-based incentives, modeled in the payoff matrix below to the best of my ability. The following simulates a two-person discussion, in which both agents can choose between two strategies: participation or withdrawal. Participation, since it shares knowledge, is always rewarded a utility, or grade, of plus one. Withdrawal incurs zero utility, primarily because it produces no knowledge. When both agents withdraw from conversation, both are punished by the subtraction of one utility. This occurs because voided communication is viewed as total disinterest in even starting a discussion.There exists only one Nash equilibrium (see below), or most mutually-favorable state, in this game: cell (P, p). This is provable through a simple check. (P, p) is such that no unilateral movement can provide a more profitable income for both agents. From Bob’s perspective, regardless of whether Alice participates in or withdraws from discussion, he personally gains the most utility when he responds with participation. Hence, row P is his dominant strategy. The same is true for Alice in reference to Bob, except that her dominant strategy lies on column p. Conclusively, cell (P, p)—the only intersection of these dominances—is the singular Nash equilibrium.The ramifications of this are twofold. Foremost, although this model is simplified, it grasps the obvious trend behind today’s classroom discussions. “Harkness warriors” exist because constant speech is an incredibly logical way of securing higher grades. In fact, it is so egregiously sound that it brings me to my second point: why would anyone possibly choose to withdraw from conversation? As seen in the payoff matrix, withdrawal is never praised and on occasion is actually punished. It seems that one would have to be excessively self-deprecating, or perhaps masochistic, to choose to be silent.Joo claims the reason for withdrawal is shyness, awkwardness or fear. I simply attribute it to bad tactics. “Harkness wallflowers” are quiet because they do not know any better. In a way I can sympathize, because I used to be one as well, until I realized that the easiest way to improve my Harkness grade was to simply produce more remarks. This does not imply academic prostitution; by necessity my contributions must still maintain a standard of quality in order for my participation to merit its default reward.And with all due respect, I don't empathize with Joo’s claim that Harkness imposes cultural disadvantages upon international students. “When in Rome, do as the Romans too” is applicable here, especially because all Exonians are in attendance here of their own accord. I find it hard to understand why someone from a more insular culture should expect Exeter to adapt to his or her nature, instead of vice versa. God forbid these students should acclimatize and mature!Regardless of the environment in which they were raised, all Exonians must participate in Harkness or be relegated to inferior grades. In this regard, the administration, the student body and the game owe them nothing.Joo is justified in questioning the efficacy of Harkness. Teaching methods, teaching games, can only be refined if students wonder whether they have been incentivized properly and if the system is actually functional. The accusation of Harkness as fundamentally unfair toward introverts, however, is incorrect because the Method is a game designed to generate learning via competition. One cannot criticize a system for fulfilling its function. Moreover, the fulfillment of this function has in no way antagonized “Harkness wallflowers.” I prefer to see an endearing depth to the term “game.” Yes, games define losers and winners, but they do not institute them permanently. It is quite possible for a quiet student to adopt the dominant strategy of participation, given the right stimulus and knowledge of the possibility.