The Prisoner's Dilemma Because of the complexity of oligopoly, which is the result of mutual interdependence among firms, there is no single, generally-accepted theory of how oligopolies behave, in the same way that we have theories for all the other market structures. Instead, economists use game theory, a branch of mathematics that analyzes situations in which players must make decisions and then receive payoffs based on what other players decide to do. Game theory has found widespread applications in the social sciences, as well as in business, law, and military strategy. The prisoner's dilemma is a scenario in which the gains from cooperation are larger than the rewards from pursuing self-interest. It applies well to oligopoly. The story behind the prisoner's dilemma goes like this: Two co-conspiratorial criminals are arrested. When they are taken to the police station, they refuse to say anything and are put in separate interrogation rooms. Eventually, a police officer enters the room where Prisoner A is being held and says: "You know what? Your partner in the other room is confessing. Your partner is going to get a light prison sentence of just one year, and because you're remaining silent, the judge is going to stick you with eight years in prison. Why don't you get smart? If you confess, too, we'll cut your jail time down to five years, and your partner will get five years, also." Over in the next room, another police officer is giving exactly the same speech to Prisoner B. What the police officers do not say is that if both prisoners remain silent, the evidence against them is not especially strong, and the prisoners will end up with only two years in jail each. The game theory situation facing the two prisoners is in Table 10.2. To understand the dilemma, first consider the choices from Prisoner A's point of view. If A believes that B will confess, then A should confess, too, so as to not get stuck with the eight years in prison. However, if A believes that B will not confess, then A will be tempted to act selfishly and confess, so as to serve only one year. The key point is that A has an incentive to confess regardless of what choice B makes! B faces the same set of choices, and thus will have an incentive to confess regardless of what choice A makes. To confess is called the dominant strategy. It is the strategy an individual (or firm) will pursue regardless of the other individual's (or firm's) decision. The result is that if prisoners pursue their own self-interest, both are likely to confess, and end up doing a total of 10 years of jail time between them.Prisoner B Remain Sent (cooperate Confess (do not cooperate with other prisoner) with other prisoner Prisoner Remain Silent (cooperate A gets 2 years. B gets 2 A gets B years, A gets 1 with other prisoner years Year Conless (do not cooperate A gets 1 year, B gets B A gets 5 years B gets 5 with other prisoner years Yours Table 10.2 The Prisoner's Dilemma Problem The game is called a dilemma because if the two prisoners had cooperand by both remaining silent, they would only have had to serve a total of four years of jail time before them. If the two prisoners cak work out some way of cooprenting so that neither one will confess, they will both be been off than if they each follow their own individual arlf-Interest, which in this case loads straight into longer jail mmm. The Oligopoly Version of the Prisoner's Dilemma The members of an oligopoly can face a prisoner's dilemma, she If each of the oligopolists cooperates in holding down output, then high monopoly profits are powible. Each oligopolis, however, mist worry that while it is holding down output, other firms are taking advantage of the high price by making ourpot and earning higher profits. Table 10-3 shows the prisoner's chilemima for a two-firm oligopoly-known as a duopoly, If Firms A and # both agree to hold down cutput they are acting together as a issopoly and will each earn $1,600 in profits, However, both firm' dominant strategy is to iscreme output, in which case eich will earn $400 in profits. Firm B Hold Down Output Increase Output (do not (cooperate with other firm) cooperate with other firm) Firm Hold Down Output (cooperate A gets $1,000. B gets A gets $200. B gets $1,500 A with other firm $1 000 Increase Output (do not A gets $1 500, B gets A gets $400, B gets $400 cooperate with other firm) $200 Table 103 A Prisoner's Dilemma for Oligopolists Can the two firma tru each other? Consider the simution of Firm A If A chillaks cut B will cheat on their agreement and increase ourput, then A will increase output, too, because for A the profit of 5:800 when both fins increase output (the boonma right-hand choice in Table 10.3) before un a profit of only $300 if A keeps ousput low and B raises ourput (the upper right hand choice in the table .If A chicka fut B will cooperate by holding down cusput, the A may seize the opportunity to earn higher profits by raising output. After all, if B is going to hold down output, then A. can cam $1,500 in profits by expanding output (the bocom left hand choice in the cable) compared with only $1,000 by holding down our put an weil (the upper left-band choice In the utte). Thing, firm A will reason that it makes sense to expand output if B hold, down cutpot and that it also makes sense to capand output if B raises outpot Again, B faces a parallel set of decisions that will lead B also to expand output The result of this prisoner's dilemma is ofen thus even though A and B could make the highest combined profits by cooperating In producing a lower level of output and acting like a monopolist, the two firms may well end up in a stilation where they pack increine output and rum only $030 rich In probes. The following Char It Up feating dicuters one cartel scandal in particularQUESTION 9 In the prisoner's dilemma, presented on pgs. 245-246 of the textbook, how many years of jail time do the prisoners get when each of them plays their dominant strategy? O 2 for A, 2 for B O 8 for A, 1 for B O 1 for A, 8 for B O 5 for A, 5 for B