Imagine yourself sitting in your car in a campus parking lot that is currently full, waiting for someone to pull out so that you can park your car. Somebody pulls out, but at the same moment a driver who has just arrived overtakes you in an obvious attempt to park in the vacated spot before you can. Suppose this driver would be willing to pay up to $10 to park in that spot and up to $30 to avoid getting into an argument with you. (That is, the benefit of parking is $10 and the cost of an argument is $30.) At the same time he guesses, accurately, that you too would be willing to pay up to $30 to avoid a confrontation and up to $10 to park in the vacant spot.
a. Model this situation as a two-stage decision tree in which his bid to take the space is the opening move and your strategies are (1) to protest and (2) not to protest. If you protest (initiate an argument), the rules of the game specify that he has to let you take the space. Show the payoffs at the end of each branch of the tree.
b. What is the equilibrium outcome?
c. What would be the advantage of being able to communicate credibly to the other driver that your failure to protest would be a significant psychological cost to you?