4D Karaoke (4DK) is getting hot in Manhattan. For those who are new to the experience, 4DKaraoke comes with special 4D glasses that give you the image of an enthusiastic audience thatscreams and shouts as you sing along. You can choose your preferred audience.There is currently one 4DK bar in the Village, but two new companies have announced plansfor creating their own bars: Z-R-Us and the company you work for, GAStar. The companythat owns the technology has given one-bar licenses to these two entrants with the assurancethat 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 eachnarrowed to the Village and Midtown. If both bars are located in the Village, then each willreceive a net profit of $10m. If both bars located in midtown then GAStar gets $19m and KR-Us $21m. If GAStar locates in the Village and Z-R-Us in Midtown, then GAStar gets $22mand Z-R-Us $9m. Finally, if BAStar locates in Midtown and Z-R-Us in the Village thenGAStar gets $9m and Z-R-Us $18m. (a) Suppose GAStar and Z-R-Us must decide simultaneously where to locate. Describe thegame played between the two firms. Are there any dominant strategies in this game? Whatis the Nash equilibrium? (b) Suppose now that your firm, BAStar, has the possibility of an early credible commitmentto a location. In other words, you can choose a location before Z-R-Us does so, and whenthe latter makes its location choice it will do so knowing what location GAStar has chosen.Represent and solve this game. What’s your firm’s benefit of being able to move first?
4D Karaoke (4DK) is getting hot in Manhattan. For those who are new to the experience, 4D
Karaoke comes with special 4D 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 4DK bar in the Village, but two new companies have announced plans
for creating their own bars: Z-R-Us and the company you work for, GAStar. 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 located in midtown then GAStar gets $19m and KR-
Us $21m. If GAStar locates in the Village and Z-R-Us in Midtown, then GAStar gets $22m
and Z-R-Us $9m. Finally, if BAStar locates in Midtown and Z-R-Us in the Village then
GAStar gets $9m and Z-R-Us $18m.
(a) Suppose GAStar and Z-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 Z-R-Us does so, and when
the latter makes its location choice it will do so knowing what location GAStar has chosen.
Represent and solve this game. What’s your firm’s benefit of being able to move first?
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