# Teaching evolution and game theory, simultaneously

Posted 09 Sep 2010 / 3I just started a new semester of **The Evolution of Cooperation**, a class that I taught for the first time in the Fall of 2008 and was shelved for a couple of years while I worked on developing other new courses. Now I am excited to get back to the initial framework I laid out for the course and begin refining (all of my courses undergo significant “cultural evolution” from semester to semester).

I envision this course as an “upper division” course, but so far that has not been realized. Ideally my non-major students who really enjoyed my **Evolution** course would decide to take this course as an extension of the concepts presented in the entry-level course. A couple of realities are preventing this from happen. First, I have only taught three sections of **Evolution** in the past two years, so there are only so many students who are candidates for taking the course. Second, the reality for non-majors is that it is hard for them to prioritize courses that do not pertain to their focal studies. This means that I really cannot make Evolution a prerequisite, and this means that I end up with a group of students who may know very little about evolution.

This ignorance is not a huge disaster: I have built all my evolution courses so that they reinforce the basics of evolutionary biology repeatedly throughout the semester. But a larger problem is making sure that students do not carry misconceptions into the course that will interfere with their understanding of the more nuanced evolutionary issues tackled in this course. What I learned the first time I taught this course was that it was valuable to go over the basics of evolution on day one.

The problem with this kind of review is that it can be really boring. Expediency requires that we cover a lot of concepts pretty rapidly, but to do so through a quick-and-dirty lecture does not really get at what students do and do not know. So it is always a good idea to place the burden on students, to let them tell me what they know (and don’t know). A little quiz of some sort seems in order, but how to make it interesting? Oh, and I also don’t want to spend the entire first class session (mine are three hours long, once a week) just reviewing the basics of evolution: I also want to get students to think about the focal topic of the course, cooperation. How to deal with this dilemma?

The answer of course is to put my students into the Prisoner’s Dilemma whilst reviewing major evolutionary concepts. I have had a lot of success getting students to play the iterated Prisoner’s Dilemma in its most simple form, so why not spruce things up by adding in the extra dynamic of a quiz? The trick is to incentivize both cheating and cooperation in somewhat equal measures: to create a scenario wherein it is most profitable to cheat, but only if the other person is not cheating.

What I devised is an activity I am tentatively calling “Evolutionary Trivia Prisoner’s Dilemma”. Unless students have done some reading on the subject, this sounds to them like a bunch of random words concatenated together, so there’s no risk in giving away the secret of the activity. Pairs of students (or triplets, see below) are each given a worksheet to complete. The front page of the worksheet contains an overview of how the activity works, instructions, and a set of “principles of evolutionary biology”. Each player has five unique principles of evolutionary biology, different from her partner. On the back side of the worksheet is a ten-question multiple choice quiz designed to determine if students understand the basics of evolutionary biology. Even if the student has no idea what the answer to each question is, she can use her list of “principles of evolutionary biology” to choose the right answer. The problem is that each player only has five principles, which means to get all of the quiz questions correct she must either be really knowledgeable or somehow gain information from her partner.

Below are a pair of these worksheets, labeled so that Player A is paired with Player B:

Evolutionary Trivia Prisoner's Dilemma Worksheet AEvolutionary Trivia Prisoner's Dilemma Worksheet B

To start out the activity, I allow the students to read through the entire first page of their worksheet. I then point out the two major “rules” of the activity: that the paired players cannot share directly their “principles of evolution” list, and that they must record their answer to the quizzes separately and secretly. After reviewing the instructions, I allow the students to discuss each quiz question and record their answers.

The students are made aware of the way that points are awarded, which sets up the dilemma. If the wrong answer is provided, no points are awarded, so there is an incentive to try to get the right answer. If both players get the right answer, they each receive equal points. If only one player gets the right answer, that player receives the largest possible number of points. This means that the most profitable strategy would be to mislead your partner, tricking her into recording the wrong answer. But what students discover is that they have pretty substantial clues (in their list of “principles of evolutionary biology”) for half of the ten multiple choice questions, but have no aid whatsoever for the other half, so the opportunity to either cooperate (by each providing help on quiz questions relevant to information they possess on their “principles of evolutionary biology” list) or defect (by each refusing to provide information they possess, or worse yet to provide misinformation) is presented to both players.

Here’s the payoff matrix for students in the A-B pairing:

The critical feature of this payoff matrix is that it provides the highest average payoff to players who continually cooperate, but the highest potential score can be earned by a player who gets all of her questions right while her partner gets all of his questions wrong. The big question is: will students withhold information or even deceive their fellow students to increase their point total?

In order to give students a better understanding of the “ecological conditions” inherent in every game and how these conditions affect the optimum strategy, I also provide a payoff matrix for a second set of players. Here are the worksheets for Players C & D:

Evolutionary Trivia Prisoner's Dilemma Worksheet C Evolutionary Trivia Prisoner's Dilemma Worksheet D

The only difference between these worksheets and those provided to Players A & B is the payoff matrix, which looks like this:

Unlike the conditions faced by Players A & B, the payoff matrix for Players C & D introduces an additional dilemma: cooperation to maximize points does not simply mean sharing information to assure that both players get the right answer. Instead, the optimal strategy is to “take turns” getting the right answer, as on average each player will do better if she alone gets the correct answer half of the time than if both players get the right answer for all ten quiz questions. In a way this also provides a new dimension in which to deceive: players could trick each other into believing that they are cooperating on this “I’ll get half right and you’ll get the other half right” strategy and then reap the benefits of maximum points on their half and at least some points on the remainder. It also sets up a situation in which complete isolation by each player (not sharing any information, which is a possible outcome of the game) could produce the same result as complete and honest cooperation.

What’s important to note is that both the A-B and C-D versions of this game have the same average outcome, which is four points per player per question. If players were to randomly decide to pick either the right or wrong answer (which is debatably a 50-50 chance, given the complex situation of a four-answer multiple choice question, hints that provide pretty solid help for half of the questions, and the choice to defect or cooperate), the average payoff in each version of the game would be the same.

In its maiden voyage in my small class of eight students, this activity came off really well. Surprisingly, there was nothing that really “went wrong” with it: a rare outcome for a first run of any classroom activity. In fact, students discovered some of the dynamics I described above before I had anticipated them.

I assigned two pairs to the A-B roles and two pairs to the C-D roles. After completing the activity, players in the A-B roles all earned the same number of points (54) in the same way: they cooperated completely, each recording the same exact answers, but missed one question on the quiz. One pair of players even ignored my clear instructions and were overtly reading their evolutionary principles off to each other, a kind of “rebellious cooperation” that spoke to their wish to avoid defecting on each other even at the cost of breaking a stated rule (I actually don’t mind rule-breaking in this context as it provides insights into students’ ultimate motivations, although sometimes it is hard to tell the difference between intentional rule-breaking and the more likely possibility that students simply failed to pay attention to the rule).

What is interesting about this outcome for the A-B players is that students gravitated so strongly towards the cooperative outcome. There seemed to be no interest in deceiving the other player in order to get more points, even if that was the strategy with the most potential for earning points. What students clearly expressed was that the total number of points per question that could be earned for cooperating (twelve) was preferable to the total number of points that could be earned by the pair through defection (ten).

The results for my two pairs of C-D players were less consistent but yielded additional valuable insights. One of my C-D pairs was frustrated by the difficulty of the questions, and earned fewer points not because of lack of cooperation but because of an inability (individually and collectively) to figure out what the right answer was. This actually provided an important lesson, which is that cooperation, even when it is true, is only as good as the skills that it pairs up. Two students who cannot figure out the answer are as successful working alone as they are in pairs. I of course had to point this out in class fairly gently, but I am pretty sure that most students grasped this reality.

My other pair of C-D players really showed some guile in figuring out the dynamics of the game quickly. Just like the two pairs of A-B players, these students cooperated consistently and ended up getting nine out of ten quiz questions correct. But these players also picked up on the fact that their communal payoff would be greater if they “took turns” getting the right answer. Insightfully they figured out that they should alternate who recorded the right answer; ironically (given that they missed one question), this meant that one player ended up getting five right and scoring sixty (60) points, with the player who had the bad luck of only getting four right left in sixth place overall with only forty-eight (48) points.

In analyzing the results of the game, students seemed to grasp the differing “ecological” component of each version, recognizing that the optimal cooperative strategy in each game was different. Students could see that the winning student gained the most points through a combination of ability (being able to identify right answers), strategy (deciding the best way to cooperate), and a bit of luck (happening to be the person who drew the five answers that were all correct).

In running this activity, it is somewhat important to make “winning” worth something. This is the problem faced by most game theoretical experiments conducted on humans: how does one make the payoffs significant enough to motivate players to try to maximize their payoff? I dangled extra credit points that would make it possible to skip one week’s homework assignment, a substantial but not ridiculously-generous reward. What is interesting about this reward is that consistently students do not see it as worth cheating each other for. In a discussion that followed our analysis of the game, students could see there was potential to “get ahead” by deceiving one’s partner. I am pretty sure that most students saw this potential from the beginning, but made a decision (conscious or unconscious) not to take advantage of their partner.

In discussing why no one was willing to defect on their partner, students seemed pretty clear on their rationale: given that one will have to work alongside one’s partner all semester long, a few extra-credit points simply are not worth the risk of having one’s reputation lowered in the estimation of the class. It is also possible that students were concerned that their choice to defect would be interpreted poorly by me as their instructor, and might worry that whatever points they gained in extra credit would be offset by later losses if I were to grade future work with bias. One would think that some students might have employed a “partial defection” strategy, defecting on only one question. This would have probably been enough to win the game (especially given the lock-step cooperation of the other groups), and could have easily been chalked up to an unintentional single error, but not a single player risked this. In fact, the C-D student who won by virtue of getting five questions right was somewhat embarrassed by winning, and went to some length to convince the class that she was simply the lucky person in her pair who got five rather than four correct. Although I do think that the “low stakes” reward for the winner is the primary reason why there was no overt defection (imagine a scenario where students are playing for their entire grade in the class, and perhaps you can anticipate a bit more deception), I also think that the students’ low tolerance for being perceived as deceptive is an interesting outcome of the activity. I am anxious to increase my sample size to determine whether these results hold up for larger samples of students. If you try out this activity, please post a comment below reporting on your results!

This activity is a lot easier to pull off with an even number of students, but if you have an odd number, I have provided a “triplet” set of sheets (for Players E, F, & G) below:

Evolutionary Trivia Prisoner's Dilemma Worksheet E Evolutionary Trivia Prisoner's Dilemma Worksheet F Evolutionary Trivia Prisoner's Dilemma Worksheet G

The payoff matrix for this setup is three-dimensional, so I will not try to represent it graphically, but it presents a different dilemma than the other two. If all players get the correct answer, the payoff is four (4) points each. If two players get the correct answer, the payoff is eight (8) points each. If only one player gets the right answer, her payoff is twelve (12) points. This looks superficially like the payoff matrix for Players C & D in that the payoff is identical if all players get the right answer or if only one player gets the right answer. It is identical to both the A-B and C-D versions in that the average payoff for all eight possible outcomes is four (4) points per player per question. But examined more closely, it actually provides the most points per quiz question (sixteen in total) if two players get the correct answer and the third does not. I have not had the chance to let students play this one, so it is hard to know whether any will pick up on this fact and either collude in a pair against the third (seems unlikely this could happen given students’ propensity not to cheat each other in pairs) or cooperate to intentionally have one player per question guess the wrong answer. Of course ten questions do not evenly divide amongst three players, so the “taking turns getting the right answer” strategy would be slightly more complicated to employ.

Cooperation, Evolution, Evolution Education, Game Theory, Lesson Ideas, MSCI-463, The Evolution of Cooperation
This is brilliant! I wonder though if the high probability of being exposed as deceptive influenced the outcomes. If it were more difficult for others to detect the cheater do you think the outcome would have been any different?