People in Collegeville can do their shopping online or they can buy from local book stores, shoe stores, florists etc. Let x be the percentage of local shoppers and 100 - x the percentage of online shoppers (0 <= x <= 100). Online prices are lower than local prices. The price advantage is reduced, however, if more people shop locally. Local shopping also helps create a thriving local city center which makes local shopping more attractive and enhances the general quality of life for everyone in Collegeville. These effects are reflected in the following payoffs to local shoppers (Local (x) ) and online shoppers(Online (x))

Local (x) = 3

Online (x) = 60 + 2x

(a) Find all pure strategy Nash equilibria in this game among the shoppers in Collegeville.

(b) Now assume that the percentage share of local shoppers increases if Local(x) > Online(x): Describe the changes over time in the share of local shoppers if the initial percentage share of local shoppers is x = 95.

(c) Assume that online sales are dominated by a monopoly seller and that this online seller reduces its prices. With the new, low online prices, the payoff to online shoppers is given by Online(x) = 110 + 2x The payoffs to local shoppers are unaffected by the online price reduction. Describe the changes over time in the share of local shoppers with the low online prices, assuming as before that the initial percentage share of local shoppers is x = 95.

(d) After a while with low online prices the percentage share of local shoppers in Collegeville has dropped to 30. The online seller now raises prices to the previous level (that is, the payoff to online shopping is Online(x) = 60 + 2x). Describe the changes in the percentage of local shoppers starting from an initial position with x = 30. Explain your answer.