Problem
Assume a college is facing a financial crisis and they want to get rid of some tenured faculty members. Unfortunately for them there is a powerful union that represents the faculty. After months of negotiations the union gave the college administrators the right to dismiss one, and only one tenure faculty member.
The college administrators though wish to get rid of three faculty members-Al, Kurt, and Neal.
Someone in the college administration suggests the following plan: go to Al and offer him an early retirement package and tell him that if he does not accept the offer that he will be fired. If Al accepts, go to Kurt with the same offer. If Kurt accepts, then Neal is fired.
Assume that the cost of the early retirement package is $100,000 to the college and is worth $60,000 to each faculty member. If the college can get rid of the faculty member the college sees a gain of $250,000.
Set up the game tree and find the equilibrium. Explain your reasoning.