Game Theory Question Sub Station has the only sub restaurant

Game Theory Question

Sub Station has the only sub restaurant in Town A and the only sub restaurant in town B. The sub market in each town yields a profit of $100K per year. Rival Sub Machine is considering opening a restaurant in Town A in year 1. If it does, the two stores will split the profit from the sub market there. However, Sub Machine will have to pay setup costs for its new store. These costs are $25K in a store\'s first year. Sub Station fears that if Sub Machine is able to make a profit in Town A, it will open a store in Town B the following year. Sub Station is considering a price war: if Sub Machine opens a store in either town, it will lower prices in that town, forcing Sub Machine to do the same, to the point where profits from the sub market will drop to zero This game is represented in the game tree below: SM don\'t open store in A open store in A (0, 400K) price war in A no price war in A SM (-25K, 20oK) don\'t open store in B open store in B (75K, 300K) price war in B no price war in B (50K, 200K) (100K, 250K) Figure 1: Extensive Form Game for Competition between restaurant chains The entry (100K, 250K) in the game tree comes about as follows. If there are no price wars, Sub Machine makes net profits of $25K in Town A in year 1, $50K in Town A ín year 2 and $25K ?n Town B in year 2, for a total of $100K. Sub Station makes profits of $50K in Town A in year 1, $100K in Town B in year 1 and $50K in Town A in year 2, $50K in Town B in year 2 Use backward induction to analyze this game. What is the sequentially rational equilibrium?

Solution

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Game Theory Question Sub Station has the only sub restaurant in Town A and the only sub restaurant in town B. The sub market in each town yields a profit of $10

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