Company 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. Company A must decide how to allocate its three salespersons between the markets; company B has only two salespersons to allocate. Each company's revenue share in each market is proportional to the number of salespeople the company assigns there. For example, if company A puts two salespersons and company 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 company's split a market equally if neither assigns a salesperson to it.) Each company is solely interested in maximizing the total revenue it obtains from the two markets.
a. Compute the complete payoff table. (Company A has four possible allocations: 3-0, 2-1, 1-2, and
0-3. Company B has three allocations: 2-0, 1-1, 0-2.) Is this a constant-sum game?
b. Does either company have a dominant strategy (or dominated strategies)? What is the predicted
outcome?