The rules of the mall location game, analyzed in Exercise S10 above, specify that when all three stores request space in Urban Mall, the two bigger (more prestigious) stores get the available spaces....

The rules of the mall location game, analyzed in Exercise S10 above, specify that when all three stores request space in Urban Mall, the two bigger (more prestigious) stores get the available spaces. The original version of the game also specifies that the firms move sequentially in requesting mall space. (a) Suppose that the three firms make their location requests simultaneously. Draw the payoff table for this version of the game and find all of the Nash equilibria. Which one of these equilibria do you think is most likely to be played in practice? Explain. Now suppose that when all three stores simultaneously request Urban Mall, the two spaces are allocated by lottery, giving each store an equal chance of getting into Urban Mall. With such a system, each would have a two-thirds probability (or a 66.67% chance) of getting into Urban Mall when all three had requested space there, and a one-third probability (33.33% chance) of being alone in the Rural Mall.

(b) Draw the game table for this new version of the simultaneous-play mall location game. Find all of the Nash equilibria of the game. Which one of these equilibria do you think is most likely to be played in practice? Explain.

(c) Compare and contrast the equilibria found in part (b) with the equilibria found in part (a). Do you get the same Nash equilibria? Why or why not?