Pricing and the Prisoner's Dilemma

May 20, 2015

Competitive pricing is a complex topic that’s important to most businesses. Do you want to cooperate or compete? One of the best illustrations of this dynamic—the prisoner’s dilemma—originated in game theory and will help you understand the circumstances behind each option.

First, it is illegal to collude with your competition to keep prices high. You and your competitors should never discuss pricing in any format. However, by understanding the prisoner’s dilemma, you will better understand what economists call “implicit collusion.” This is when industry prices stay high because no competitor acts aggressively. In other words, competitors seem to cooperate without colluding.

Imagine you are arrested by the police for robbing a bank. You, of course, are innocent. They also arrest another person for the same crime. In the interrogation room, the police say, “We’ve caught your accomplice. You guys are in trouble. You should confess now to make your sentence easier.” Then they explain the possible sentences:

  • If both you and the other person confess, you each get three years in prison
  • If neither of you confesses, you each get one year in prison
  • If you confess and the other person doesn’t, you go free and he spends five years in prison
  • If the other person confesses and you don’t, he goes free and you spend five years in prison

Here’s what you have to consider. If the other person confesses, you will get three years if you confess and five years if you don’t. So, it makes sense to confess. But assume the other person doesn’t confess. Then you will get one year if you don’t confess and go free if you confess. Again, it makes sense to confess. It seems that no matter what the other person does, you’re better off confessing. The same logic is true for the other person. The rational outcome to this game is always for both parties to confess. 

Here’s the dilemma: If both parties confess, each spends three years in prison. However, if neither confesses, each gets one year in prison. Although they are better off cooperating with each other, individual incentives encourage them to confess. 

Let’s apply this dilemma to pricing. Assume you and a competitor have an equal share in the market and relatively high prices with nice profit margins. Should you lower your price? Let’s see what the payoffs look like:

  • If you both cooperate and keep prices high, you each make $10 million in profit
  • If you both compete and lower prices, you each make $5 million in profit
  • If you lower prices and your competitor doesn’t, you make $13 million in profit and your competitor only makes $2 million
  • If your competitor lowers prices and you don’t, your competitor makes $13 million and you make $2 million

The dilemma: In every scenario you are better off when you lower your price. The same is true for your competitor. But, if you both lower the price, you each make only $5 million in profit. Whereas if you could find a way to cooperate, without either of you lowering your price, you would each end up with $10 million. 

The prisoner’s dilemma represents a situation where two players both do better when they cooperate but have incentives not to cooperate. It’s the same with pricing. 

What’s the solution to the prisoner’s dilemma? Frankly, there is no solution to the game as described. But there is a solution if you tweak the game so that two players can play over and over, which is what we have with pricing. You set a price this month, next month, the month after and so on. And, as you make the next decision, you can see what your competitor did.

Empirical testing and experiments demonstrate that the best solution to this repeated prisoner’s dilemma is a strategy called tit for tat. The simple explanation is that you start out cooperating and then do whatever your competitor just did. 

Let’s assume you and your competitor start out with high prices. Then, if your competitor decides to lower their price to gain share during one period, you do the same the next period. If your competitor keeps their price low, you do too. If your competitor believes you will follow this strategy, he doesn’t have an incentive to lower prices. 

The same holds true for you. If you believe your competitor will follow you if you lower prices, then you have no incentive to do so. Economists call this implicit collusion (because that’s what it is). 

Now this starts to make more sense. Without talking to each other, firms cooperate with higher prices simply because of the threat of lowering prices. 

It’s like companies that claim “We will match our competitors’ prices.” Although this sounds like a win for buyers, it is really a clear statement to competitors: Don’t bother lowering prices; it won’t do you any good. Essentially, this is a company announcing that it will follow the tit-for-tat strategy with the idea of supporting higher market prices. 

But beware: Sometimes you may mistake moves your competitors make as aggressive pricing when in reality they aren’t. Jumping to that conclusion may start a price war. 

For example, imagine you and your competitor have been cooperating, when suddenly your competitor lowers their price. Now you feel compelled to lower your price too. But perhaps your competitor only wanted to get rid of some old inventory. Now you’re in a price war, or at least in an alternating high-price, low-price game. 

When there’s a good reason to temporarily lower the price, it’s important to notify your market in a way the industry will understand. For example, perhaps you can create a press release explaining that you have a glut of perishable inventory and are offering a short-term price decrease. (But check with your legal department first.) If competitors don’t realize the price decrease is temporary, they might follow suit and you’ll end up with a permanent price decrease. Remember, price wars are easy to get into and hard to get out of. 

On the other hand, perhaps you can use lessons from the prisoner’s dilemma in your favor to raise industry prices. A common tactic in the airline industry is for one airline to announce fare increases. One reason is to get other airlines to follow suit. If they don’t, the fare increase won’t stick. This is also why almost all airlines add the same types of fees at the same time. 

Your competitors may be trying this as well. Imagine you read in your local trade magazine, “XYZ Corporation is raising rates due to increased costs.” You could be thinking, “Excellent, now we’ll gain more share. Those guys are so stupid.” But what happens when you don’t follow by raising your prices? They’ll bring their prices back down. What happens if you match their price increase? Industry profits will go up. 

When I’ve conducted classroom exercises where two “companies” compete in the repeated prisoner’s dilemma by raising and lowering prices, the following inevitably holds true: The most profitable companies are those allowing their competitors to make a profit too. In other words, they cooperate often. If you compete aggressively, odds are good your competitors will as well, and neither of you will make as much profit. Now you have a difficult decision to make: Do you want to win, or do you want to make a profit? 

Price is important in every deal and every competitive situation; it’s equally important to be smart about how you use it. Be sure to watch your competitors’ pricing carefully, don’t jump to conclusions, and when you make price changes, try to be clear about why you’re making those changes. Finally, if your goal is to put your competitors out of business, be prepared for your own profits to suffer too. 

 

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