Heather and David (players 1 and 2) are partners in a handmade postcard business. They each put costly effort into the business, which then determines their profits.
However, unless they each exert at least 1 unit of effort, there are no revenues at all. In particular, each player i chooses an effort level ei Ú 0. Player i's payoff is
where j denotes the other player.
(a) Prove that (0,0) is a Nash equilibrium.
(b) Graph the players' best responses as a function of each other's strategies.
(c) Find all of the other Nash equilibria.