Paul and John are working on a project for which they will receive the same grade. The utility to each of them would be their grade minus their own effort. If Paul puts in x units of effort and John puts in y units of effort their grade will be equal to the higher of the two effort levels, x and y. So for a given choice of x and y Paul's utility is given by 2 max{x, y} - x while John gets a utility of 2 max{x, y} - y.
The possible choices for effort level are 1 and 2.
Write down the payoff matrix for this game.
a) Which outcomes are Pareto efficient?
b) Find the best response functions.
c) State all Nash Equilibria of the game.