Assume that N (variable, we dont know how many interest groups) economic interest groups are attempting to get a unique trade privilege and will hire lobbyists to try to win the prize. Suppose that a lottery game can be used to characterize this contest (sometimes called a rent-seeking contest) and that the prize is worth 50,000,000 dollars (of additional profits) and that the cost of lobbyists is $500/hr. Find the Nash equilibrium of this contest