Question

Firm A and firm B are battling for market share in two separate markets. Market A is worth $30 million in revenue; market II is worth $18 million. Firm A must decide how to allocate its 3 salespersons between the markets; firm B has only 2 salespersons to allocate. Each firm’s revenue share in each market isproportional to the number of salespeople the firm assigns there. For example, if firm A puts 2 salespersons and firm B puts 1 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 4 possible allocations: 3-0, 2-1, 1-2, and 0-3. Firm B has 3 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?

Answer 1

A. Constant sum game: the game is said as constant sum game whose sum of pay off remain constant and 2 person constant sum game is always equivalent to zero sum game.

The constant sum game in the given case:

15,15	20,10	22.5,7.5
10,20	15,15	18,12

Therefore firm A has 3 strategies and firm B has 2 strategies.

If both the firms choose in market 1 then they use 2 sales person as best strategy.

B. If the strategy of one player is better than the other player than it is referred as dominant strategy. In this case dominant player will not be affected if the other player do not play. Therefore, in the given case firm A choose dominant strategy in both the situation.