Consider three major department stores—Big Giant, Titan, and Frieda’s— contemplating opening a…

Consider three major department stores—Big Giant, Titan,
and Frieda’s— contemplating opening a branch in one of two new Boston-area
shopping malls. Urban Mall is located close to the large and rich population
center of the area; it is relatively small and can accommodate at most two
department stores as “anchors” for the mall. Rural Mall is farther out in a rural
and relatively poorer area; it can accommodate as many as three anchor stores.
None of the three stores wants to have branches in both malls because there is
sufficient overlap of customers between the malls that locating in both would
just mean competing with itself. Each store prefers to be in a mall with one or
more other department stores than to be alone in the same mall, because a mall
with multiple department stores will attract sufficiently many more total
customers that each store’s profit will be higher. Further, each store prefers
Urban Mall to Rural Mall because of the richer customer base. Each store must
choose between trying to get a space in Urban Mall (knowing that if the attempt
fails, it will try for a space in Rural Mall) and trying to get a space in
Rural Mall right away (without even attempting to get into Urban Mall). In this
case, the stores rank the five possible outcomes as follows: 5 (best), in Urban
Mall with one other department store; 4, in Rural Mall with one or two other department
stores; 3, alone in Urban Mall; 2, alone in Rural Mall; and 1 (worst), alone in
Rural Mall after having attempted to get into Urban Mall and failed, by which
time other nondepartment stores have signed up the best anchor locations in
Rural Mall. The three stores are sufficiently different in their managerial
structures that they experience different lags in doing the paperwork required
to request an expansion space in a new mall. Frieda’s moves quickly, followed
by Big Giant, and finally by Titan, which is the least efficient in readying a
location plan. When all three have made their requests, the malls decide which
stores to let in. Because of the name recognition that both Big Giant and Titan
have with the potential customers, a mall would take either (or both) of those
stores before it took Frieda’s. Thus, Frieda’s does not get one of the two
spaces in Urban Mall if all three stores request those spaces; this is true
even though Frieda’s moves first.

Don't use plagiarized sources. Get Your Custom Essay on
Consider three major department stores—Big Giant, Titan, and Frieda’s— contemplating opening a…
For as low as $7/Page
Order Essay

(a) Draw the game tree for this mall location game.

(b) Illustrate the rollback pruning process on your game
tree and use the pruned tree to find the rollback equilibrium. Describe the
equilibrium by using the (complete) strategies employed by each department
store. What are the payoffs to each store at the rollback equilibrium outcome?

 

Leave a Reply

Your email address will not be published. Required fields are marked *

*

*

*