Massachusetts Institute of Technology14. 12 Game Theory final exam questions 2004

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14.12 Game Theory — Final 12/16/2004 Prof. Muhamet Yildiz Instructions. This is an open book exam; you can use any written material. You have two hour and 50 minutes. Each question is 25 points.... Please write each question on a separate page. Good luck! 1. Find a perfect Bayesian Nash equilibrium of the following game. .4 .6 00 21 10 1 2 22 31 12 1 2 D A d a δ α δ α Figure 1: 2. A soda company, XC, introduces a new soda and wants to sell it to a representative consumer. The soda may be either Good or Bad. The prior probability that it is Good is 0.6. Knowing whether the soda is Good or Bad, the soda company chooses an advertisement level for the product, which can be either an Ad Blitz, which costs the company c, or No Advertisement, which does not cost anything. Observing how strongly the company advertises the soda, but without knowing whether the soda is Good or Bad, the representative consumer decides whether or not to buy the product. After subtracting the price, the payoff of representative consumer from buying the soda is 1 if it is Good and −1 if it is Bad. His payoff is 0 if he does not buy the soda. If the soda is Good and representative consumer buys it (and therefore learns that the soda is Good), then the company sells the soda to other future consumers, enjoying a high revenue of R. If the soda is Bad and the representative consumer buys it, the company will have only a small revenue r. If the representative consumer does not buy the soda, the revenue of the company is 0. Assume that 0 < r < c < [Show More]

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