G401 September 24, 1998 Professor Rasmusen NOTES ON THE PRISONER'S DILEMMA In ``The Prisoner's Dilemma'', two prisoners, Messrs Row and Column, are being interrogated separately. If both confess, each is sentenced to eight years in prison; if both deny their involvement, each is sentenced to one year. If just one confesses, he is released but the other prisoner is sentenced to ten years. Table 1.1 ``The Prisoner's Dilemma'' Column Deny Confess Deny -1,-1 -10, 0 Row: Confess 0,-10 -8,-8 Payoffs to: (Row,Column). Each player has a dominant strategy. Consider Row. Row does not know which action Column is choosing, but if Column chooses Deny , Row faces a Deny payoff of -1 and a Confess payoff of 0, whereas if Column chooses Confess , Row faces a Deny payoff of -10 and a Confess payoff of -8 . In either case Row does better with Confess . Since the game is symmetric, Column's incentives are the same. The dominant strategy equilibrium is (Confess, Confess ), and the equilibrium payoffs are (-8,-8) , which is worse for both players than (-1,-1) . Sixteen, in fact, is the greatest possible combined total of years in prison. The result is even stronger than it seems, because it is robust to substantial changes in the model. Because the equilibrium is a dominant strategy equilibrium, the information structure of the game does not matter. If Column is allowed to know Row's move before taking his own, the equilibrium is unchanged. Row still chooses Confess , knowing that Column will surely choose Confess afterwards. ``The Prisoner's Dilemma'' crops up in many different situations, including oligopoly pricing, auction bidding, salesman effort, political bargaining, and arms races. Whenever you observe individuals in a conflict that hurts them all, your first thought should be of ``The Prisoner's Dilemma''. (What is above is an excerpt adapted from Eric Rasmusen, Games and Information, 2nd edition, Chapter 1). SPECIAL TO G401. 1. Each player's action has an externality for the other. If Row chooses Confess, that hurts Column, a negative externality. If Row chooses Deny, that helps Column, a positive externality. 2. The Prisoner's Dilemma can be adapted to N players instead of 2, to illustrate the Free Rider problem. In the adapted form, each of N players must decide whether to Cooperate or Grab, where to Grab reduces everybody else's payoff. 3. With either 2 or N players, the Prisoner's Dilemma can illustrate the Teams problem. Row and Column choose Work or Slack on their joint project. Work is like Deny; Slack is like Confess. The project is evaluated jointly, so if Row Works and Column Slacks, Column gets half the credit, but Row gets all the cost. 4. The Prisoner's Dilemma also illustrates the Oligopoly problem. Firms Row and Column each choose High Output or Low Output. 5. The Prisoner's Dilemma also illustrates political lobbying. Shipping lines Row and Column each choose High Lobbying Effort or Low Lobbying Effort in trying to get legalization of cartels. 6. The Prisoner's Dilemma is not inescapable, but to escape it, the players have to change the rules of the game. The Mafia used to change the rules by committing to a policy of killing anyone who chose Confess. This amounts to subtracting 100 from the payoff of anybody who chooses Confess. The FBI's Witness Protection Program has wrecked this policy, however, in recent years. (Still somewhat effective is for Row to kill Column before the games even starts.) 7. Another escape may be to have a repeated relationship--repeat the game each year for 20 years. 8. Another escape is legal contracts--Row and Column sign a legal contract to both Deny. Contracts are, of course, illegal for criminals (obstruction of justice) and for cartels (conspiracy in restraint of trade). 9. Another escape is to have a reputation for doing what you say you'll do. If Row has a reputation as a moral person, he can tell Column,"I'll Deny" and be believed. This, too, is problematic for criminals. 10. Other examples of the Prisoner's Dilemma: A. Two cola companies each must decide whether or not to introduce caffeine- free cola. B. Two countries must each decide whether to raise import tariffs.