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A case study in the chapter describes a phone conversation between the presidents of American Airlines and Braniff Airways. Let's analyze the game between the two companies. Suppose that each company can charge either a high price for tickets or a low price. If one company charges \$300, it earns low profit if the other company also charges \$300 and high profit if the other company charges \$600. On the other hand, if the company charges \$600, it earns very low profit if the other company charges \$300 and medium profit if the other company also charges \$600.a. Draw the decision box for this game.b. What is the Nash equilibrium in this game? Explain.c. Is there an outcome that would be better than the Nash equilibrium for both airlines? How could it be achieved? Who would lose if it were achieved?
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04:54
Yi Chun Lin
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we were using game theory to analyze this payoff matrix. These decisions that are made by american and Brand Airlines. So for this payoff matrix, I've designated our decisions as low prices and high prices. So we have american who is going to be in blue and Brandon, who is in red on this payoff matrix. Let's start with the information given we see that if one of them charges $300, so it's going to be our low price, it will earn a low profit if the other charges 300. So if they're both charging a low price, they're each going to earn these low profits. Now if one of them charges that low price of 300 and the other charges 600, that one's going to earn a high profit. So let's say America charges that low price. But we see Braniff charge a high price. We're going to see American earning high profits down here. Right. America is charging the 300 brand if the charges 600. So American gets those higher profits. Now let's do the opposite. Let's move to this. Let's say Braniff is charging the low price and America is charging the high price. Well then Braniff is going to be the one with the high profits. Now we have some more some more triangles filling. So let's move to the second bullet point. We receive that if one of these airlines charges $600, it will earn very low profit if the other charges 300. So supposing that American charges that high price of 600 and Brandon is charging low prices. We knew here is that Braniff gets the high profits. But that means America american is going to get very low profits now. So this will be the same in this bottom corner box. If brand of charges that high price and american charges a low price, american gets the high profits, but Brandon gets very low profits. However, if they both charged that high price of $600, they're each going to earn medium profits. All right now that we have created this payoff matrix, we filled it into completion. We want to know where this nash equilibrium lies. Well, the nash equilibrium is the point at which neither airline has any incentive to deviate from it. So what we see is that the nash equilibrium exists at this low price, low price. So they're both choosing low price. Neither has an incentive to choose high price. So let's work through this. So they're both charging low prices. Now suppose that american deviated and instead charged a high price. So they were earning low profits at this low price and now they chose to instead charge a high price. Well then their profits dropped to very low. So they're not gonna do that, they're going to continue to charge the low price. Now the same thing for Braniff. If they're charging a low price and they choose to deviate from that and choose a high price. Their profits are only going to drop now to very low. So we see the nash equilibrium exists at low price low price. However, for part C, we want to know if there's any better outcome for these airlines than a nash equilibrium and we see that there is and that's if they both charge a high price. So they're both charging high price, high price. They could each be earning medium profits. However, this isn't a nash equilibrium because they have that incentive to deviate right brand of could choose to charge a low price and earn high profits and american could do the same thing. They could choose to charge a lower price and also earn high profits. So if they wanted this to work for each of them to earn these medium profits, they would somehow have to cooperate with one another to agree to set their prices high. Or, in other terms, they would have to collude with one another in order to be able to earn those higher profits.
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