John and Paul are working on a project for which they will receive the same grade. 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. The utility to each of them would be their grade minus their own effort. So for a given choice of x and y the utility of Paul's is given by the 2 max{x, y} - x while the utility of John is 2 max{x, y} - y.
The possible choices for effort level are 1 and 2.
How can write down the payoff matrix for this game?
1. Explain which outcomes are Pareto efficient?
2. Identify the best response functions.
3. State all the Nash Equilibrium of the game.