Player 1 is a game theory instructor in a hypothetical university. There are n − 1students taking his course. The strategic interaction they face before and during angame can be modeled as an n-player extensive form game.Here are some information you should use:
The game must be online, with all open-ended questions.
The instructor is the first-mover: announcing the game rules before the game. Therules may include time restriction, live monitoring, or any other relevant item.After observing these rules, it will be the students’ turn to act. Well, since you arethe students here, you can easily figure out what your available strategies are. Forexample, a possible strategy is to complain about the rules, another possible strategyis to cheat in the game, or a much better strategy is to study for the game (can bemodeled as study “effort”, which is costly). The rest is up to you.It must be assumed that there are different types of students, possibly differing intheir preferences or their grades from the previous assignments. For example, somestudents would never cheat, some students would prefer cheating only if the rules arenot strict enough, and some students would cheat even under strict rules (perhaps, outof desperation). How you define students’ preferences is left to you.The main issue the instructor cares about is fair grading, which is measured by thenumber of non-cheating students. That is, to achieve fair grading, the instructor needsto minimize the cases of unethical behavior in the game (or, he should be able to detectan unethical behavior with a sufficient success level).
There is another thing the instructor may care about. If the students complain aboutthe rules, it gives a headache to the instructor. As the number of complaints increases,the headache gets worse. You can assume that the headache gives a negative utility tothe instructor, or instead, you can assume that he does not care about the headache.In order to complete your model, if you need an information that is not providedabove, you are allowed to assume anything you want, as long as they do not contradictwith the provided information.
In this question, you are asked to formulate a game-theoretic model that will essentially capture the strategic interaction described above. Then, you are asked to providea formal discussion on how to analyze the equilibrium of your model. Although youdo not need to report an equilibrium strategy profile, you are expected to write theequilibrium strategy for Player 1 (i.e., the starting point of the equilibrium path).
1So, the main question is: What is the optimal set of game rules for Player 1, as heanticipates how those different types of students would act before and during the game?
You are not expected to complete all details of the model or equilibrium analysis.
However, all essential elements should be included in your answer.