Most interesting situations do not have a dominant equilibrium, and we most therefore look further. We can use our duopoly example to explore this case. In this example, which we call the rivalry game, each firm considers whether to have its normal price or to raise its price toward the monopoly price and try to earn monopoly profits.

The firm can stay at their normal price equilibrium, which we found in the price war game. Or they can raise their price in the hopes of earning monopoly profits. It is interesting that our two firms have the highest joint profits, where they earn a total of $300 when each follows a higher price strategy. This situation would surely come about if the firms could collude and set the monopoly price. At the other extreme is the competitive style strategy of the normal price, where each rivals has profits of $10.

In between are two interesting strategies where one firm chooses a normal price and one a high price strategy. The solution that we have discovered is actually very general one, which is called the Nash equilibrium after mathematics John Nash, who won the Noble Prize in economics for his contributions to game theory.

The firm can stay at their normal price equilibrium, which we found in the price war game. Or they can raise their price in the hopes of earning monopoly profits. It is interesting that our two firms have the highest joint profits, where they earn a total of $300 when each follows a higher price strategy. This situation would surely come about if the firms could collude and set the monopoly price. At the other extreme is the competitive style strategy of the normal price, where each rivals has profits of $10.

In between are two interesting strategies where one firm chooses a normal price and one a high price strategy. The solution that we have discovered is actually very general one, which is called the Nash equilibrium after mathematics John Nash, who won the Noble Prize in economics for his contributions to game theory.