wo roommates John and Joe are playing a simultaneous game of cleaning the apartment. If neither of them clean, the apartment gets filthy and both get a utility of 2. If John cleans and Joe doesn't, John gets a utility of 1 and Joe gets a utility of 4. If Joe cleans and John doesn't, Joe gets a utility of 1 and John gets a utility of 4 and if both clean up the apartment, they each get a utility of 3.

If the apartment owner can somehow see the effort of the each of the room mates and punishes with a loss of 5 to any room mate who doesn't clean, is that likely to lead to a more efficient outcome?