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?