Suppose two bars, “the Last Jar” and “Prince Alfred”, can choose to sell a pint of beer for either $8 or $10. For simplicity, assume that: these are the only two possible prices; there are no costs (e.g., there is no cost for obtaining and serving the beer), and each customer drinks exactly one pint of beer. There are two types of customers: professors and students. Professors are not price-sensitive and go to the bar closest to their department’s building. Thus, 25 professors from the Melbourne School of Engineering go to Prince Alfred, while 50 professors from the Melbourne Graduate School of Education go to the Last Jar. Meanwhile, the students, who are 200 in total, are price sensitive. They go to the bar with the lowest price –or, if both bars charge the same price, then they split evenly. Simultaneous game: Suppose that the two bars must choose what price to set simultaneously. a) Write the normal form of the game. b) What is the Nash Equilibrium (NE) of this game?
B3) Suppose two bars, “the Last Jar” and “Prince Alfred”, can choose to sell a pint of beer for either $8 or $10. For simplicity, assume that: these are the only two possible prices; there are no costs (e.g., there is no cost for obtaining and serving the beer), and each customer drinks exactly one pint of beer. There are two types of customers: professors and students. Professors are not price-sensitive and go to the bar closest to their department’s building. Thus, 25 professors from the Melbourne School of Engineering go to Prince Alfred, while 50 professors from the Melbourne Graduate School of Education go to the Last Jar. Meanwhile, the students, who are 200 in total, are price sensitive. They go to the bar with the lowest price –or, if both bars charge the same price, then they split evenly.
Simultaneous game: Suppose that the two bars must choose what price to set simultaneously.
a) Write the normal form of the game.
b) What is the Nash Equilibrium (NE) of this game?
Sequential game:
c) Suppose Prince Alfred chooses what price to set first. Then, after observing the price set by Price Alfred, the Last Jar chooses what price to set. Draw the extensive form game and find the subgame perfect Nash equilibrium (SPNE).
d) Does this sequential game have a first or a second mover advantage? Justify your answer.
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