Consider three major department stores - Big Giant, Titan, and Frieda's - that are contemplating opening...

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Consider three major department stores - Big Giant, Titan, and Frieda's - that are 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 poor 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 would rather be in a mall with one or more other department stores than be alone in the same mall, because a mall with multiple department stores will attract enough additional 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). 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 non-department 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 lag times in doing the paperwork required to request a 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 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. (a) Draw the game tree for this mall location game. (b) Using the rollback procedure, find the expected outcome of the interaction. Consider three major department stores - Big Giant, Titan, and Frieda's - that are 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 poor 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 would rather be in a mall with one or more other department stores than be alone in the same mall, because a mall with multiple department stores will attract enough additional 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). 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 non-department 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 lag times in doing the paperwork required to request a 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 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. (a) Draw the game tree for this mall location game. (b) Using the rollback procedure, find the expected outcome of the interaction.