When we designed the new ECONS101 paper some years ago, I tried desperately to include two weeks of game theory. Ultimately, it proved unworkable, but my rationale for trying to include it was that it would allow more time to explore repeated games. One aspect of that is the end of game problem. In a repeated game, the outcome may differ from the Nash equilibrium, because the players may realise that some other outcome benefits them more over many plays of the game. For example, in the repeated prisoners' dilemma, the dominant strategy equilibrium is for both prisoners to confess, but the best outcome is obtained if both prisoners remain silent (for an example of this, see this post on the drug dealers' dilemma). In a repeated game, players may be more likely to cooperate (and both prisoners stay silent) in the hopes of future cooperation. The American political scientist Robert Axelrod noted that players cooperate because of "the shadow of the future".
However, there is a difference between what happens when a game is infinitely repeated (it is played many times without end), and when a game is finitely repeated (played many times, but the players know when it will end). In a finitely repeated game, both players have an incentive to cheat in the last play of the game. Knowing that the other player will cheat in the last round, then both players realise that there is little point in cooperating in the second-to-last round of the game, so both players will cheat in that round. And knowing that, there is an incentive to cheat in the third-to-last round, and then the same logic applies to the fourth-to-last round, the fifth-to-last round, and so on all the way back to the first round of the repeated game. In a finitely repeated game, any cooperation breaks down, and neither player should be able to trust the other player to cooperate. Notice that this wouldn't be the case for an infinitely repeated game, because since neither player knows when the game will end, they never know when they should start cheating.
That brings me to the example of contract cheating, which involves a student outsourcing their assessment work to someone else to complete, usually for payment. Contract cheating has become a big issue at universities (see for example this 2017 article in The Conversation), and has been exacerbated by the shift to online teaching and assessment during the pandemic. Estimates suggest that around 8 percent of students may engage in contract cheating during their university studies. That might not sound like a lot, but that equates to hundreds of students at even a relatively small university like Waikato.
However, the up-front monetary payment that students face, and the chance that their cheating is detected and they are sanctioned, are not the only costs that students may face when they use contract cheating services. As this recent article in The Conversation notes, students may later be blackmailed by the contract cheating service, which threatens to reveal their cheating to the university unless further payments are made. In this new study by Jonathan Yorke, Lesley Sefcik, and Terisha Veeran-Colton (all Curtin University), published in the journal Studies in Higher Education (sorry, I don't see an ungated version online), 14 out of 587 students surveyed:
...stated that they directly or indirectly knew students who had been blackmailed by contract cheating services.
That's a disturbingly high incidence of blackmail, and something that students who engage these services should be concerned about. And if students were better advised of the risk of blackmail, contract cheating would probably decline. To see why, we can use some game theory and the end of game problem.
Consider a simple sequential game for a single assessment, as laid out in the decision tree (which we refer to as extensive form) below. The student makes a decision first, whether to engage in contract cheating or not. If they choose not to engage in contract cheating, the game ends, and their payoff (measured in utility) is based on the chances that they pass the assessment. If the student chooses to engage in contract cheating, then the cheating service chooses whether to blackmail the student or not. The payoff to the cheating service is profits from the fees or blackmail payment that the student pays.
There are three important aspects to this game. First, the Nash equilibrium of this game is for the student not to engage in contract cheating. To see why, we can use backward induction - essentially we start at the end of the game and work our way backwards, eliminating strategy choices that would not be chosen by each player. If the student chooses to engage in contract cheating, then the cheating service will choose to blackmail the student (because the payoff of 100 is greater than the payoff of 60). A rational student would then know that if they engage in contract cheating, they will get blackmailed, and their payoff will be -50. They won't get the payoff of 50, because the cheating service is going to blackmail them. Knowing this, the student is choosing between not engaging in contract cheating (and receiving a payoff of 15), and engaging in contract cheating (and receiving a payoff of -50). They are better off not engaging in contract cheating. That outcome is the subgame perfect Nash equilibrium in this game.
Second, many students are naïve. They don't realise that the cheating service can blackmail them. They think they are playing a different game, where they get to choose between the payoff of 50 (from engaging in contract cheating) and the payoff of 15 (from not engaging in contract cheating). The grey strategy and outcome are hidden from them. These naïve students think they are better off cheating, and will do so.
Third, this is actually a repeated game, because it is played over and over for each assessment that a student completes. That changes the incentives for the cheating service. Once a cheating service blackmails a student, the student probably isn't going to go back to that service. That means that the cheating service will receive a one-off payoff of 100. However, if the cheating service can encourage the student to return for more assessments, the cheating service will receive a payoff of 60 from every play of the game. Using the (made up) numbers from the game above, the cheating service only needs the student to pay twice in order to make them better off than they would be by blackmailing automatically. Strategically, the cheating service would therefore be better off overall by not blackmailing the student in each play of the game.
The repeated nature of the game affects naïve and rational students differently. The naïve students didn't realise that blackmail was an option at all, so from their perspective nothing has changed. The rational students may be tempted to engage in some contract cheating, even though they realise that the cheating service could engage in blackmail.
Of course, you can probably see where all this is going. The repeated game where the cheating service avoids engaging in blackmail only exists in an infinitely repeated game. However, this game is not infinitely repeated, because eventually the student is going to graduate, after which they won't need the contract cheating service any more. The contract cheating service has a strong incentive to string the student along, extracting fees from each assessment, and collecting evidence of the student's cheating, before blackmailing them in the last play of the game (which might even be after the student has graduated!).
In this finitely repeated game, the naïve students are hurt tremendously. At least if the game was not repeated, they get blackmailed in the first play. However, this finitely repeated game maximises the profits of the cheating service, by keeping the naïve student in the game until the very end. For the rational students, hopefully they are rational enough not only to recognise the possibility of blackmail, but also the end of game problem.
How can universities help students and mitigate the problem of blackmail from contract cheating services? Most universities now require students to complete an academic integrity module at the start of their studies, which impresses upon them that cheating (of various forms) is not allowed. One component of those programmes should certainly be (as discussed by Yorke et al.) to discuss with students the possibility of blackmail by contract cheating services, and how widespread (and growing) the practice is. At the very least, that will convert naïve students into more rational students by making them realise the full game that they are playing with the contract cheating services.
No comments:
Post a Comment