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