Question

(Normal to Extensive Form Game) Consider the following pricing game between Bernie's Lemon Fizz and Adam's Orange Zip. Each can set a high, medium, or low price for the drink and their profits are given by the following table: Adam's Orange Zip High Price Medium Price Low Price Bernie's Lemon High Price 650, 300 200, 650 -400, 400 Fizz Medium Price 900, 150 600, 400 100, 100 Low Price 550, -200 400, 50 200, 100 a. What is the Nash Equilibrium of the above game when both firms choose price simultaneously? b. Draw a game tree (extensive form game) when Bernie commits to a price first. What is the outcome when Bernie chooses his price first? C. Draw a game tree (extensive form game) when Adam commits to a price first. What is the outcome when Adam chooses his price first? d. Compare the different outcomes. Is there an advantage to moving first in this game?

Answer 1

d)

Lemon Fizz, hange zip Respond HP MP - - (HP, MP) (200, 680) (MP, MP (600, 40 ME MP LP - LP (LP, LP) (200, 300) Oringe zip Lemon Fizz respond MP HP MP Le mp - Cup, MP) (90o, 150] & - (MP, MP ( 600, 400) - (2P, LPJ (200, 100) cm Hence, Common responses are Nash Equilibrium = (MP, MP), (LP, LP) in ( b or Response Response Goo, 650) no HP au minimumunun 7 u up H IBE MP 7 ml Euoo, 400) goo, 150) Response (600, 4000 C100, 100) C550, 200) (400, 50) (200,100) L Response HP LP 10 111 112 113 HV LR All respouses of A B would be maximizing its profit (MM) (600, 400 HP 65o, 30o) - Response HP IBM 900,150 C. A mp The HP ? (200, 600) Response - R 600, 400) 9 (400,50) fuoo 400) loo, 100) (550,-100) 114 115 He MP LP ~ (200,100) - Response A brotit is maximised at (MP, MP) (600, 400)

There is no change in profit . And it doesn't matter who moves first.