The rules of the mall location game, analyzed in Exercise S10 above, specify that when all three…

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.

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(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?

 

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