This is a game theory question!

In a company, a team of n persons is working on a project. For the project to succeed, a specific task (an inspection task for example) must be undertaken by at least one person. This task is particularly unpleasant, and nobody was clearly mandated to deal with it. We model the interest of team members through the following pay-offs. If nobody takes care of the inspection, all members have a 0 pay-off. If someone checks, it has a pay-off of 2, and all others have a pay-off of 10. a) What are the Nash equilibria in pure strategies? b) What is the symmetric mixed-strategy Nash equilibrium. c) What is the success probability of the project for this equilibrium? How does this probability vary according to the size of the team? Comment. d) Assume now that, by its function, one of the team members (the "inspector") only decides whether or not to check after learning if others did. What are the perfect equilibria? What will happen if at the beginning of game, the inspector has the ability to credibly commit not to learn what others have done before deciding to check? if he can commit not to check? Why is it important that this commitment is credible