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# Allocation of workforce

Firm A and 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.
a. 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, 0-2.) Is this a constant-sum game?
b. Does either firm have a dominant strategy (or dominated strategies)? What is the predicted
outcome?

#### Solution Preview

See the attached file. The matrix shows each firm's payoff in each market. For example, the first box on the left shows that firm A will make \$15 million in market I and \$12 million in market II if it allocates one sales person to market I and 2 to market II while B allocates 1 to market I ...

#### Solution Summary

Use of game theory to determine the allocation of salespersons between two markets.

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