Firm A and Firm B are battling for market share in two separate markets. Market I is worth $30 million in revenue, market II is worth $18 million. Firm A must decide how to allocate its three salespersons between the markets; firm B has only two salespersons to allocate. Each firm's revenue share in each market is proportional to the number of salespeople the firm assigns there. For example, if Firm A puts two salespersons and Firm B puts one salesperson in market I, A's revenue from this market is [2/(2+1)]$30 = $20 million, and B's revenue is the remaining $10 million. (The firms split a market equally if neither assigns a salesperson to it). Each firm is solely interested in maximizing the total revenue it obtains from the two markets.
1. Compute the complete payoff table. (Firm A has four possible allocations: 3-0, 2-1, 1-2, and 0-3. Firm B has three allocations: 2-0, 1-1, and 0-2). Is this a constant-sum game? Explain.
2. Does either firm have a dominant strategy (or dominated strategies)? What is the predicted outcome?
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Firm B
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2,0
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1,1
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0,2
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Firm A
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3,0
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18,12
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22.5,7.5
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30,0
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Market 1
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2,1
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15,15
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20,10
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30,0
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1,2
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10,20
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15,15
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30,0
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0,3
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0,30
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0,30
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0,0
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Firm B
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2,0
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1,1
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0,2
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Firm A
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3,0
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0,0
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0,18
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0,18
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Market 2
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2,1
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18,0
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9,9
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6,12
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1,2
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18,0
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12,6
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9,9
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0,3
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18,0
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13.5,
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10.8,7.2
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