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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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