Question

Firm A and Firm B are battling for market share in two separate markets: I and II. Market I is worth $30 thousand (per week) in revenue and market II is worth $18 thousand (per week). Each firm has to decide how to allocate their sales people in the two markets. Firm A has three sales people and B has two. Each firm’s revenue share is proportional to the number of sales people the firm assigns in that market. For example, if firm A allocates two sales people in market I and firm B allocates one sales person there, then A’s revenue from market I will be [2/(2+1)]$30 =$20 thousand, while B’s revenue share is the remaining (1/3)$30
= $10 thousand . Note that if neither firm assigns a sales person in a market,
they split a market. Each firm’s strategy describes how they allocate sales people in the two markets. Thus firm A has four strategies:3-0, 2-1, 1-2 and 0-3, where the first number denotes the number of sales people deployed by Firm A in market I and the second number denotes the number of sales people deployed in market II. Similarly, B has three strategies: 2-0, 1-1 and 0-2.

(a) Complete the payoff matrix. (Note that payoffs indicate total weekly revenue for each firm from two markets.)

(b) Does either firm have a dominant strategy (or dominated strategies)? Explain. Determine the Nash equilibrium of this game.

Answer 1