Three firms simultaneously and independently decide whether to enter a new market (call this action E) or abstain (action A). The payoff of each firm i = 1,2,3 that enters is Ui = 3 - 2k, where k is the total number of firms that enter the market. The payoff of each firm that abstains is 0.
(a) Write down all pure-action Nash equilibria and verify any (just one) of them.
(b) Find the symmetric mixed-strategy Nash equilibrium in which each firm i = 1,2,3 enters the market with probability pi* = p*. That is, determine the equilibrium value of p*.
(c) Find and verify any (just one) mixed-strategy Nash equilibrium different from those identified in (a) and (b).