Question

1. Red Cross and American Blood Centers (ABC) are the major blood banks in the United States. Red Cross represents 47% of the market share and ABC represents 46% of the market share. This means the blood bank market is very close to a duopoly market structure. Both companies advertise aggressively. Construct a payoff matrix using the following information:

• If neither firm advertises, Red Cross and ABC both earn profits of $750 million a year.
• If both firms advertise, Red Cross and ABC both earn profits of $500 million a year.
• If Red Cross advertises and ABC doesn’t, Red Cross earns profits of $900 million and ABC earns profits of $400 million.
• If ABC advertises and Red Cross doesn’t, ABC earns profits of $900 million and Red Cross earns profits of $400 million.

Please use the information above to answer the following questions.

1. If Red Cross wants to maximize profit, will it advertise? Briefly explain.
2. Is there Nash equilibrium to this advertising game? If so, what is it?
3. What (if any) is the dominant strategy for each company?

Answer 1

a) If Red Cross wants to maximize the profit then it will not advertise because although it could raise the profit to $900 million. However, in that case, ABC will also choose to advertise. Both the companies will be in the situation of $500 million profit each.
If both the companies prefer not to advertise then their profit will be $750 million each.

b) Nash Equilibrium is the situation in game theory when each player has no incentive to deviate from the position in which they are in the setup. In the above example, there is a Nash Equilibrium in this game which can be identified by (1,3) or the situation where both choose not to advertise. This is the situation where both will highest payoff of $750 million each.

c) The dominant strategy is the option chosen by the player irrespective of other player's action which gives it a higher payoff.
There is no dominant strategy in this game.

Round 1:
   1: 2 is dominated by 1
   2: 4 is dominated by 3

Round 2:

Player 1 Strategies Eliminated = [2]

Player 2 Strategies Eliminated = [4]