Consider another version of the lobbying game introduced in this chapter. Suppose the payoffs are the same as presented earlier, except in the case in which firm X lobbies and firm Y does not lobby. In this case, suppose the government's decision yields x to firm X and zero to firm Y. Assume that x > 25. The normal form of this game is pictured here.
(a) Designate the (pure-strategy) Nash equilibria of this game (if it has any).
(b) Compute the mixed-strategy Nash equilibrium of the game.
(c) Given the mixed-strategy equilibrium computed in part (b), what is the probability that the government makes a decision that favors firm X? (It is the probability that (L, N) occurs.)
(d) As x rises, does the probability that the government makes a decision favoring firm X rise or fall? Is this good from an economic standpoint?