Question 1 [13 marks) There are 3 rms - A, B, and C - that are considering entering a new market. The payoff for each rm that enters is: )t' i 65 where n is the number of rms that enter the market and x = 180. If a rm does not enter the market its payo is D. For parts (a) and (b), assume that all rms decide simultaneoust whether to enter or not. (a) (2 marks) Consider the set of pure strategy Nash equilibria in this game. Which among the following statements hold for all Nash equilibria of this game Oi. Firm A always enter the market Oii. Exactly one firm enters the market Oiii. Exactly two firms enter the market Ev. All three tirms enter the market On. Firm C never enters the market (b) (2 marks) In the unique symmetric mixed strategy equilibrium of this game, rms A, B, and C enter the market with same probability p where p E (01 1). For each of them, the expected prot in the mixed-strategy equilibrium is :r. The value of z: is: Oi. -12 Oii. 03 Oiii. 0.5 Div. 13 Ow. a (c) (1 mark) Now consider an extensive-form game where entry decisions are made sequentially. First rm A decides whether to enter or not. rm B decides second. and rm C decides last. Let a',- denote the number of decision nodes where rm I decides whether to enter or not. The total number of decision nodes, i.e. d A + 13 + dc is Di. 7 Oii. 5 Oiii. 4 Div. 3 Ov. s (d) (1 mark) Consider again the extensive-form game described in part (c). Let S, denote the set of pure strategies for firm i where i E { A, B, C). Let n; denote the number of elements in S;. Then MA + nB + nc is Oi. 6 Oii. 10 Oili. 14 Oiv. 22 Ov. 8 (e) (2 marks) In the unique subgame-perfect equilibrium outcome of this sequential move game, Oi. All three firms enter the market Oii. Firms A and C enter the market Oili. Firms B and C enter the market Oiv. No firm enters the market Ov. Firms A and B enter the market (f) (2 marks) As in parts (c)-(e), assume that, firm A decides first whether to enter or not. However, after that, firms B and C decide simultaneously whether to enter or not. How many subgame perfect equilibria are there in this game? Oi. 3 Oii. 1 Oili. 0 Oiv. 9 Ov. 2