4 ms·

Students get class-wide 'A's by boycotting test, solving Prisoner's Dilemma

2 points by donohoe 14y ago

lutusp 14y ago
Strictly speaking, it's not "prisoner's dilemma" if the students can talk to each other and agree on a plan. In a real prisoner's dilemma, the participants have to guess at the motivations and actions of other participants. http://en.wikipedia.org/wiki/Prisoners_dilemma http://en.wikipedia.org/wiki/Prisoners_dilemma
- dragonwriter 14y ago
  That's not actually the problem; communication doesn't change the game theoretic situation. In the classic scenario from which PD gets its names, the conspirators are presumed to have mutually planned not to cooperate in the event of arrest, but each has an incentive to defect from the plan to maximize their own expected payout (or, actually, to minimize expected cost, but the two are equivalent.) One problem is that they can see eachother at the door and change their mind, so its not just advance communication but immediate interaction. The bigger problem is, since they could get the maximum grade by all cooperating, the payoff matrix is wrong for PD. PD requires that my maximum payoff is in the "I defect, other(s) cooperate" corner. Putting the maximum guaranteed payout in the all-cooperate scenario makes it a very different game, which no longer has a dominant strategy of defection.
  - lutusp 14y ago
    > That's not actually the problem; communication doesn't change the game theoretic situation. Umm, yes, actually, it does. If the participants can communicate their intentions, it's a different game with a different set of outcomes. From: http://en.wikipedia.org/wiki/Prisoners_dilemma http://en.wikipedia.org/wiki/Prisoners_dilemma Quote: "Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other."
    - dragonwriter 14y ago
      No, really, it doesn't. Despite Wikipedia's description of the illustrative scenario, absence of any communication isn't really important to the essence of PD. Its just a condition that avoids distraction in discussing the aspects you usually want to focus on, which is the payoff matrix. What changes it is if the payoff matrix is wrong, as it was in this case. The game theoretic aspects of PD are entirely dependent on the ordering of the payoffs such that the payoffs for strategies are (listing, in each scenario, the strategy of the actor whose payoff is under consideration first, and that of the other actor second) as follows: (defect, cooperate) > (cooperate, cooperate) > (defect, defect) > (cooperate, defect), which makes (defect, defect) the only Nash Equilibrium in the game and makes defection a dominant strategy since it always produces a better outcome than cooperation independent of the opponent's strategy. (Note, so long as this payoff matrix is maintained, communication is mostly irrelevant, since even knowing what the opponent is planning on doing, defection is always your best choice.) Changing the matrix, as was done here, so that the order is (cooperate, cooperate) > (defect, cooperate) > (defect, defect) > (cooperate, defect) makes both (cooperate, cooperate) and (defect, defect) Nash Equilibria and makes it so there is no dominant strategy. It also makes having clear indication of the other players intent (as is the case when the class is gathered outside of the door and can respond to each others actions) significant (as it is not in a pure PD) because then if there is a clear indication of intended action (which differs from a communicated plan, which can be a deception, and which in a pure PD almost certainly would be, since each player not only has an incentive to defect independent of the other player's strategy, but also an incentive to mislead the other player into cooperating) it makes sense to match it, since the best payoffs are always in matching the other players action -- whether cooperation or defection.
      - lutusp 14y ago
        > No, really, it doesn't. All I am saying is if it is called "prisoner's dilemma", then no communication is allowed. The game's logic depends on it. If the participants can communicate, they can agree on a strategy. This possibility of an agreement is outside the game's definition. > ... since the best payoffs are always in matching the other players action -- whether cooperation or defection. Yep. And being able to talk to the other player means the two participants can agree on a strategy in advance. It's not "prisoner's dilemma" because there's no dilemma.

2 points by donohoe 14y ago

Strictly speaking, it's not "prisoner's dilemma" if the students can talk to each other and agree on a plan. In a real prisoner's dilemma, the participants have to guess at the motivations and actions of other participants. http://en.wikipedia.org/wiki/Prisoners_dilemma http://en.wikipedia.org/wiki/Prisoners_dilemma

dragonwriter 14y ago
That's not actually the problem; communication doesn't change the game theoretic situation. In the classic scenario from which PD gets its names, the conspirators are presumed to have mutually planned not to cooperate in the event of arrest, but each has an incentive to defect from the plan to maximize their own expected payout (or, actually, to minimize expected cost, but the two are equivalent.) One problem is that they can see eachother at the door and change their mind, so its not just advance communication but immediate interaction. The bigger problem is, since they could get the maximum grade by all cooperating, the payoff matrix is wrong for PD. PD requires that my maximum payoff is in the "I defect, other(s) cooperate" corner. Putting the maximum guaranteed payout in the all-cooperate scenario makes it a very different game, which no longer has a dominant strategy of defection.
- lutusp 14y ago
  > That's not actually the problem; communication doesn't change the game theoretic situation. Umm, yes, actually, it does. If the participants can communicate their intentions, it's a different game with a different set of outcomes. From: http://en.wikipedia.org/wiki/Prisoners_dilemma http://en.wikipedia.org/wiki/Prisoners_dilemma Quote: "Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of speaking to or exchanging messages with the other."
  - dragonwriter 14y ago
    No, really, it doesn't. Despite Wikipedia's description of the illustrative scenario, absence of any communication isn't really important to the essence of PD. Its just a condition that avoids distraction in discussing the aspects you usually want to focus on, which is the payoff matrix. What changes it is if the payoff matrix is wrong, as it was in this case. The game theoretic aspects of PD are entirely dependent on the ordering of the payoffs such that the payoffs for strategies are (listing, in each scenario, the strategy of the actor whose payoff is under consideration first, and that of the other actor second) as follows: (defect, cooperate) > (cooperate, cooperate) > (defect, defect) > (cooperate, defect), which makes (defect, defect) the only Nash Equilibrium in the game and makes defection a dominant strategy since it always produces a better outcome than cooperation independent of the opponent's strategy. (Note, so long as this payoff matrix is maintained, communication is mostly irrelevant, since even knowing what the opponent is planning on doing, defection is always your best choice.) Changing the matrix, as was done here, so that the order is (cooperate, cooperate) > (defect, cooperate) > (defect, defect) > (cooperate, defect) makes both (cooperate, cooperate) and (defect, defect) Nash Equilibria and makes it so there is no dominant strategy. It also makes having clear indication of the other players intent (as is the case when the class is gathered outside of the door and can respond to each others actions) significant (as it is not in a pure PD) because then if there is a clear indication of intended action (which differs from a communicated plan, which can be a deception, and which in a pure PD almost certainly would be, since each player not only has an incentive to defect independent of the other player's strategy, but also an incentive to mislead the other player into cooperating) it makes sense to match it, since the best payoffs are always in matching the other players action -- whether cooperation or defection.
    - lutusp 14y ago
      > No, really, it doesn't. All I am saying is if it is called "prisoner's dilemma", then no communication is allowed. The game's logic depends on it. If the participants can communicate, they can agree on a strategy. This possibility of an agreement is outside the game's definition. > ... since the best payoffs are always in matching the other players action -- whether cooperation or defection. Yep. And being able to talk to the other player means the two participants can agree on a strategy in advance. It's not "prisoner's dilemma" because there's no dilemma.