QUESTION

# (2) Simultaneous and Sequential (Hint:

(2) Simultaneous and Sequential (Hint: You will want to have a payoff matrix in (a) and then model this as a sequential game in (b) to answer)

Poke-Pizza is about to become the new hot restaurant trend in Manhattan (that's right poke on a pizza!). Two firms are looking to set up restaurants. Pizza-Poke, Inc. (PPI) and the company you work for, P2- Star. No new entrants are expected to follow and enter the market.

The two entrants are currently trying to determine their best locations, which they have each narrowed to the Village and Midtown. If both restaurants are located in the Village, then each will receive a net profit of \$10m. If both restaurants locate in Midtown, then P2-Star gets \$19m and PPI \$21m. If P2-Star locates in the Village and PPI in Midtown, then P2-Star gets \$22m and PPI \$9m. Finally, if P2-Star locates in Midtown and PPI in the Village, then P2-Star gets \$9m and PPI \$18m.

(a) Suppose P2-Star and PPI must decide simultaneously where to locate. Show a matrix showing the payoff structure for the firms in the game. Are there any dominant strategies in this game? What is the Nash equilibrium?

(b) Suppose now that your firm, P2-Star, has the possibility of an early credible commitment to a location. In other words, you can choose a location before PPI does so, and when the latter makes its location choice it will do so knowing what location P2-Star has chosen. Represent and solve this game. What's your firm's benefit of being able to move first?

(c) Suppose PPI has the option of moving first. Would it want to do so?