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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?
Firm B
2,0
1,1
0,2
Firm A
3,0
18,12
22.5,7.5
30,0
Market 1
2,1
15,15
20,10
1,2
10,20
0,3
0,30
0,0
0,18
Market 2
18,0
9,9
6,12
12,6
13.5,
10.8,7.2
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