Complex Nash Equilibrium Exercise

n farmers simultaneously decide how much quantity of wheat to produce. The
quantity produced by the kth farmer is denoted qk, and the total quantity produced by all
farmers is denoted by Q = q1 + q2 + . . . qn. The production cost is equal to 0. The price of one
unit of wheat is equal to p = exp(−Q).
1. Describe this interaction as a strategic form game.
2. Show that each farmer has a dominant strategy and find the corresponding equilibrium
payoff.
3. Find the profile of strategies that maximizes the total profit of all farmers. Explain why
this profile is not a Nash equilibrium.
4. Assume now that the price of one unit of wheat is equal to p = (1 + Q)
^−2N . Find the
unique Nash equilibrium and corresponding equilibrium payoffs.
Does someone know how to solve this?