Implicit Agreements

How do you achieve a good outcome in a repeated prisoners’ dilemma game which has no last period? If possible, you should talk to your fellow player and convince him that both of you should play nice. Unfortunately, for two firms in a pricing dilemma it would be a violation of antitrust laws for them to explicitly agree to maintain high prices. Fear not, however, for in game theory land actions dominate words.

Imagine that you’re repeatedly playing the game in Figure 42 with another firm. Currently, both firms charge low prices. Figure 42 is a prisoners’ dilemma game in which individually you are both better off charging low prices, but collectively you would both benefit by jointly charging high prices. If you explicitly proposed to your competitor that both firms raise prices, you could go to jail. You should instead send a legal signal to your competitor, such as unilaterally raising prices this period.

Figure 42

For the game in Figure 42, charging high prices always makes you worse off this period. Thus, if your rival has always charged low prices, what possible motive could he assign to your setting high prices? He should interpret your price increase as an invitation for both of you to permanently raise prices. Of course, your rival might choose to temporarily take advantage of your high prices to make a high profit for himself. Your competitor might, however, accept your implicit invitation to move to a better outcome.

Let’s imagine that your rival joins you and increases his prices, too. Several periods go by while you both earn higher profits by jointly charging high prices. Why is your rival continuing to charge high prices? Is it because since you were nice to him he feels obligated to be nice to you? The only reason your rival would charge high prices in this game is because he fears that if he lowers his prices, you will too. Fear of retaliation, not obligation or kindness, keeps your rival in line.

Having a reputation for swift retaliation is vital to being able to sustain a good outcome in repeated prisoners’ dilemma games. Wimps can never achieve the “nice, nice” outcome, for their rivals will always exploit them. If others fear your wrath, however, the nice, nice outcome becomes obtainable since fellow players will grasp the consequences of betraying you.