Relying on calculus in monopolistic competition

210 Part III: Market Structures and the Decision-Making Environment

The worst possible payoff in this situation is $25 that occurs if Global raises fares.

3. International determines its worst possible payoff if it raises fares.

The worst outcome is $29 that occurs if Global reduces fares.

4. International applies the maxi-min rule and raises fares.

International Airline raises fares because it results in the best possible worst outcome — $29 is better than either $27 or $25.

The maxi min rule is a very conservative strategy. It has a major problem because it looks only at the worst possible outcome. You don’t even consider other possible outcomes. So, applying this rule means you would probably never invest in a business. Investing in a business means you might lose money. If you just hold onto your money, you won’t lose it.

Another problem with the maxi min strategy is you ignore what your rival may choose. A better way to make decisions in game theory is to anticipate what your rival may do. For example, in playing the board game Monopoly, if your opponent already owns the orange properties of Tennessee Avenue and New York Avenue, when you land on St. James Place, you should buy it to prevent your opponent from getting a monopoly. You take into account that your opponent will certainly buy St. James if she lands on it.

What happens if International Airline anticipates Global’s decision. In this case, if International reduces fares, Global charges the same fare, because that has the highest payoff — $32. If International charges the same fare, Global reduces fares to earn $38. If International raises fares, Global also raises fares to receive $41. These cells are marked with a “G” in Figure 12-2.

Alternatively, what happens if Global Airline anticipates International’s decision. In this case, if Global reduces fares, International charges the same fare, because that has the highest payoff — $36. If Global charges the same fare, International charges the same fare to earn $42. If Global raises fares, International reduces fares to receive $44. These cells are marked with a “I” in Figure 12-2.

The Nash equilibrium

The game illustrated in Figure 12-2 ultimately results in International Airline deciding to charge the same fare and Global Airline deciding to reduce fares. This outcome is called a Nash equilibrium. A Nash equilibrium exists when no player can improve his or her payoff by unilaterally changing his or her action given the actions chosen by other players. In order to reach a Nash equilibrium, each player chooses the action that maximizes the payoff conditional on others doing the same.

Chapter 12: Game Theory: Fun Only if You Win

So, in Figure 12-2, if International Airline changes its decision to either reduce or raise fares given that Global Airline has reduced fares, its profit is less than the $36 it receives from charging the same fare. Similarly, if Global Airline changes its decision to either charge the same fare or raise fares, its profit is less than the $38 it receives from reducing fares. International and Global airlines are in a Nash equilibrium because neither airline can improve its payoff given the decision made by the other player. The Nash equilibrium is indicated by the cell with I and G.

To find where a Nash equilibrium exists, simply note the firm’s highest payoff cell given each decision its rival can make. Do the same thing with the rival. A cell that has the highest payoff for both firms is a Nash equilibrium.

Losing because of the prisoner’s dilemma

A prisoner’s dilemma refers to a game where players choose something less than the optimal combined actions.

Figure 12-3 presents the payoff table of monthly profits for two competing restaurants — Bob’s Barbecue and Clara’s Cafeteria. Both Bob and Clara are deciding whether or not to expand their menus, and the resulting payoff depends upon not only the decision each of them makes but also on the decision their rival makes. In determining the ultimate payoff, you should first identify whether or not either restaurant has a dominant action. To identify any dominant actions and determine the ultimate payoff, you take the following steps:

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Figure 12-3:

A prisoner’s dilemma.