3D Karaoke (3DK) is getting hot in Manhattan. For those who are new to the experience, 3D Karaoke comes with special 3D glasses that give you the image of an enthusiastic audience that screams and shouts as you sing along. You can choose your preferred audience. There is currently one 3DK bar in the Village, but two new companies have announced plans for creating their own bars: K-R-Us and the company you work for, BAStar. The company that owns the technology has given one-bar licenses to these two entrants with the assurance that they will be the only two licenses issued in Manhattan for years to come.

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

(a) Suppose BAStar and K-R-Us must decide simultaneously where to locate. Describe the game played between the two firms. Are there any dominant strategies in this game? What is the Nash equilibrium?

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