# 11.5: A Duopoly Game

Here we have another example of a prisoner’s dilemma game. The table in Fig 11.3 above shows the payoff matrix of a duopoly game with two players A and B thinking of a strategy whether to advertise or not advertise. If company A decides to advertise, and company B also advertises, company B earns \$16 million profit. If company A doesn’t advertise and company B also doesn’t, then company B earns \$8 million profit. Therefore, the dominant strategy for company B, regardless of what A does, is to NOT advertise, because by not advertising company B earns higher profits, as shown by the payoffs.

Similarly, company A’s dominant strategy, regardless of what company B does, is to NOT advertise. The Nash equilibrium is shown on the bottom right box where both firms don’t advertise and earn \$8 million profit each.

The result of this prisoner’s dilemma is often that even though A and B could make the highest combined profits by cooperating in advertising, the two firms may well end up in a situation where they neither advertise and earn only \$8 million each in profits.