The rules of the mall location game, analyzed in Exercise 7, pecify that, when all three stores req uest space in Urban Mall, the two bigo r (more prestigious) stores get the available spaces. The original version of the game also specifies tha t the firms move sequentially in requesti ng mall space.
(a) Suppose that the three firms make their location requests simultane ously. Draw the payoff table for this version of the game and find all of the Nash equilibria . Which equilibrium is subgame perfect and why? Now suppose that when all three stores simultaneously request Urban
Mall, the t\lvo 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.
(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. Identify the subgame-perfect equilibrium.
(c) Compare and contrast your answers to part b with the equilibria found in part a. Do you get the same Nash equilibria? Why? What equilibrium do you think is focal in this lottery version of the game?