Economics Game Theory 4320 (Games and Decision Making)

Three students are in a college course at a university and they have a test on Friday but decided to wait until Thursday to study. The students have all determined that because they have attended each class session and taken good notes that it would be okay to wait until the last minute to study. Each student wants to score higher than the other, so they decided to see who would get the highest score based on their studying techniques.There are two methods that they can use to study, which are self-study and study group.

Each student will start with a base grade of 70. They will have to decide if they want to study in a group or self-study. If all 3 study in a group, they will earn 10 points on the exam because 3 minds working together. If only 2 choose study group, they will earn 5 points on the exam. The person who studied alone will earn 3 points because while they did study extra, they did not get the benefit of the knowledge of the other 2. If 2 students choose to study alone and 1 in a group, then the person in the group loses 5 points since they spent all their time going to meet up point and didn't get the benefit of the other's knowledge. The other 2 students get 3 extra points.

In this scenario Student 1 and Student 2 choose the study group method, and student 3 chooses to self-study.

Instructions: This is a sequential game

1. Find the game utilities, playoffs, strategies, and outcomes
2. Find all Nash equilibrium and Sub game perfect, mixed strategy Nash equilibrium, and pure strategy Nash equilibrium
3. Find the Expect Value