Prisoners’ Dilemma Scenario: You and an accomplice are arrested on suspicion of committing some nasty crime The District Attorney and the police have been unable to produce enough evidence to convict you of that offense

Prisoners’ Dilemma We do have enough evidence to convict you of some lesser charge The only way the DA can nail you for the more serious offense is if one of you rats out the other Conversely, you and your partner can largely elude prosecution if you both stay silent You and your partner are placed in separate holding cells and are unable to communicate with each other DA enters and offers you the following:

Rat Hang Tough Prisoners’ Dilemma

Don’t Cooperate with each other (rat) Don’t Cooperate with each other (rat) Cooperate with each other (hang tough) Cooperate with each other (hang tough) Prisoners’ Dilemma From your perspective, you and your accomplice are faced with the following:

Rat Hang Tough Prisoners’ Dilemma 0, 10

10, 0 Rat Hang Tough Prisoners’ Dilemma 0, 10

Rat Hang Tough Prisoners’ Dilemma 10, 0 0, 10 Row Player Column Player

Rat Hang Tough Prisoners’ Dilemma 10, 0 5, 50, 10

Rat Hang Tough Prisoners’ Dilemma 10, 0 5, 50, 10 1, 1

Rat Hang Tough Prisoners’ Dilemma 10, 0 5, 50, 10 1, 1 What to do? Which strategy should you select?

Rat Hang Tough Prisoners’ Dilemma 10, 0 5, 50, 10 1, 1 Dominant Strategy Dominant Strategy

Rat Hang Tough Prisoners’ Dilemma 10, 0 5, 50, 10 1, 1 Dominant Strategy Dominant Strategy

Rat Hang Tough Prisoners’ Dilemma 10, 0 5, 50, 10 1, 1 Nash Equilibrium Neither player can improve his/her position,

Rat Hang Tough Prisoners’ Dilemma 10, 0 5, 50, 10 1, 1 Nash Equilibrium Neither player can unilaterally improve his/her position

Prisoners’ Dilemma Generalized Form: Rank Outcomes, from most preferred to least preferred –1 = first choice –2 = second choice –3 = third choice –4 = fourth choice Choice is “cooperate” or “not cooperate”

Don’t Cooperate Don’t Cooperate Cooperate Prisoners’ Dilemma 4, 1 3, 31, 4 2, 2

Prisoners’ Dilemma Symbolic Form: We’re in a Prisoner’s Dilemma situation whenever: T > R > P > S Temptation to defect > Rewards of Cooperation Rewards > Punishment for Not Cooperating Punishment > Sucker’s Payoff

Prisoners’ Dilemma Note that even if we start at the cooperative outcome, that outcome is not stable Each player can improve his/her position by adopting a different strategy

Don’t Cooperate Don’t Cooperate Cooperate Prisoners’ Dilemma 4, 1 3, 31, 4 2, 2

Prisoners’ Dilemma But since both players have changed strategy we end up at the non-cooperative outcome, where both players are worse off than if they had chosen to cooperate

Don’t Cooperate Don’t Cooperate Cooperate Prisoners’ Dilemma 4, 1 3, 31, 4 2, 2

Prisoners’ Dilemma And, as we noted, this non-cooperative outcome is also a Nash equilibrium outcome; Neither player has any incentive to change strategy since whoever changes will do immediately worse by making the move

Don’t Cooperate Don’t Cooperate Cooperate Prisoners’ Dilemma 4, 1 3, 31, 4 2, 2

PD & Interest Group If a “collective good” is involved, individuals have little incentive to work towards achieving that good. Makes sense for others to do the work and sit back and reap the benefits of their labor But if that’s the case, then no one will do the work and the collective benefit won’t be delivered