Question

In the oligopoly sector there are two companies, Enterprise A and Enterprise B, which compete for higher profits. To achieve this, they are considering whether or not to increase their advertising costs. If neither company raises its advertising costs, they split the market and earn € 7 billion each. Should both increase their advertising spending, they will again share the market but make less than € 5 billion each. Moreover, if only one company increased its advertising costs, it would achieve profits of € 8 billion while the other only € 2 billion.

Find the Nash equilibrium with the help of the odds table.

Answer 1

Solution:

First we create the payoff matrix as follows:

Two players are A and B; Strategy space for each = (increase the advertising cost, not increase the advertising cost)

Then, with (x, y) as payoff vector representing payoff of $x to Enterprise A and $y to Enterprise B, we have following payoff matrix:

		Enterprise B
		Increase	Not increase
Enterprise A	Increase	(< 5 billion, < 5 billion)	(8 billion, 2 billion)
	Not increase	(2 billion, 8 billion)	(7 billion, 7 billion)

Finding the Nash equilibrium (or mutually beneficial strategy set):

When enterprise A choose to increase the advertising cost, best response of enterprise B is to increase the cost as well, as then it receives a higher payoff (5 > 2). Similarly, if enterprise A chooses not to increase the advertising cost, enterprise B will still choose to increase the cost (ass 8 > 7). So, no matter what A chooses, B will increase the cost, so B's dominant strategy is to increase the advertising cost.

Going same way, we shall find that dominant strategy for A as well is to increase the advertising cost. Thus, our Nash equilibrium is (A, B) = (increase Ad cost, increase Ad cost), thereby earning (< 5 billion euros, < 5 billion euros)

Note: It has been assumed that when question says less that 5 billion euros, it must be slightly less than 5 billion euros (still greater than 4 billion euros)