Prisoner’s Dilemma

The scenario In the Prisoner’s Dilemma, you and Lucifer are picked up by the police and interrogated in separate cells without the chance to communicate with each other. In the Prisoner’s Dilemma, you and Lucifer are picked up by the police and interrogated in separate cells without the chance to communicate with each other.

You are both told:  If you both confess, you will both get four years in prison.  If neither of you confesses, the police will be able to pin part of the crime on you, and you’ll both get two years.  If one of you confesses but the other doesn’t, the confessor will make a deal with the police and will go free while the other one goes to jail for five years.

Can we make a payoff table? What are your decision alternatives? What are your decision alternatives?  Confess  Do not confess What are the states-of-nature? What are the states-of-nature?  Lucifer confesses  Lucifer does not confess

Payoff Table States of Nature Decision Alternatives Lucifer does not confess Lucifer confesses Do not confess Confess 2 years5 years 0 years4 years BUT Lucifer is not a state of nature. His payoff table looks like yours. So he will also confess.

So here’s the dilemma If you go with your best strategy and Lucifer goes with his best strategy – confess – then you will both be worse off than if you had both not confessed. If you go with your best strategy and Lucifer goes with his best strategy – confess – then you will both be worse off than if you had both not confessed. Requires cooperation of the other player. Requires cooperation of the other player.

Game theory An extension of decision theory An extension of decision theory Applications in: Applications in:  economics  competitive strategy (management)  political science  evolutionary biology. When US government auctioned transmission wavelengths for cell-phone and broadcast applications, both bidders and auctioneer (FCC) hired game theory expert to help them prepare. When US government auctioned transmission wavelengths for cell-phone and broadcast applications, both bidders and auctioneer (FCC) hired game theory expert to help them prepare.

Strategies for the Iterated PD The Golden Rule - "Do unto others as you would have them do unto you." The player always cooperates with opponent (doesn't confess). It's quite easy to take advantage of this innocent "turn the cheek" strategy. The Golden Rule - "Do unto others as you would have them do unto you." The player always cooperates with opponent (doesn't confess). It's quite easy to take advantage of this innocent "turn the cheek" strategy. The Brazen Rule - "Do unto others as they do unto you." The player begins with a cautious defection (he confesses), but after that he does whatever you did last. A similar strategy is usually called "tit-for-tat." The Brazen Rule - "Do unto others as they do unto you." The player begins with a cautious defection (he confesses), but after that he does whatever you did last. A similar strategy is usually called "tit-for-tat."

Strategies for the Iterated PD (cont) The Brazen Rule 3 - Almost the same as the Brazen Rule. The exception is that the player is a little more forgiving. If the opponent defects (confesses), the player will forgive the opponent about once every three times and cooperate the next time anyway. The Brazen Rule 3 - Almost the same as the Brazen Rule. The exception is that the player is a little more forgiving. If the opponent defects (confesses), the player will forgive the opponent about once every three times and cooperate the next time anyway.

Strategies for the Iterated PD (cont) The Iron Rule - "Do unto others as you wish, before they do it unto you." The player always defects (confesses). Both of you tend to accumulate a large prison sentence. The Iron Rule - "Do unto others as you wish, before they do it unto you." The player always defects (confesses). Both of you tend to accumulate a large prison sentence. Random – The player decides randomly which of the above four strategies to use, and you have to figure out for yourself which one he's chosen. The player does not randomly choose "confess" or "don't confess." Instead, he randomly chooses one of the above strategies and sticks with that one strategy until he randomly changes. Random – The player decides randomly which of the above four strategies to use, and you have to figure out for yourself which one he's chosen. The player does not randomly choose "confess" or "don't confess." Instead, he randomly chooses one of the above strategies and sticks with that one strategy until he randomly changes.

Play iterated prisoner’s dilemma White chip – confessBlue chip – do not confess White chip – confessBlue chip – do not confess Record your action (confess or not confess) and your compadre’s action. Record your action (confess or not confess) and your compadre’s action. Record the result – number of years spent in prison. Record the result – number of years spent in prison. First we will have 2 practice rounds to make sure everyone understands the play and recording. First we will have 2 practice rounds to make sure everyone understands the play and recording. I will start each round. I will start each round. We will play an unknown number of rounds – less than 15. We will play an unknown number of rounds – less than 15.