Looking at the prisoners dilemma at uni… I think I have it but would love some thoughts from you.

I thought that game theory got more difficult when you increase numbers to three, and the possibility of cooperation however, having thought it through I have come up with..

If you have two co-operating, you essentially have one person.. so two cooperating and not confessing means the lowest possible penalty for both.. essentially that makes them one person.

So initially we have …. both are cooperating and don’t say a word knowing that the other one also didn’t confess…

both are now up for one year each – the best possible outcome for both who are cooperating..

The third person, who knows they have no collusion with the others would be better off to now confess.. so now we have 0 for the third person and the other two who have already not confessed – get ten.. assuming they know the other two don’t confess, but even if they don’t know… then we have still the better option to confess (6 is better than 10).

is that working for you lot?

The problem occurs only when the police have no idea who is in collusion… how do we work out that table?

Wait, are these guys allowed to communicate with each other?

Have a look at the Unscrupulous Diner’s Dilemma, Arts. It’s a generalisation of the Prisoner’s Dilemma to n participants.

dv, the Prisoner’s Dilemma is a standard introductory problem in Game Theory. The prisoners are assumed to not be able to communicate, and there will be no personal repercussions if they betray the other prisoner (so the other won’t try to exact revenge.)

btm said:

Have a look at the Unscrupulous Diner’s Dilemma, Arts. It’s a generalisation of the Prisoner’s Dilemma to n participants.

dv, the Prisoner’s Dilemma is a standard introductory problem in Game Theory. The prisoners are assumed to not be able to communicate, and there will be no personal repercussions if they betray the other prisoner (so the other won’t try to exact revenge.)

Yes I’m familiar but Arts’s use of the word colluding made me think this was some variation where they could work together

dv said:

btm said:

Have a look at the Unscrupulous Diner’s Dilemma, Arts. It’s a generalisation of the Prisoner’s Dilemma to n participants.

dv, the Prisoner’s Dilemma is a standard introductory problem in Game Theory. The prisoners are assumed to not be able to communicate, and there will be no personal repercussions if they betray the other prisoner (so the other won’t try to exact revenge.)

Yes I’m familiar but Arts’s use of the word colluding made me think this was some variation where they could work together

I am trying to extend it to what might happen in the real world. If you had three suspects (they know they are suspects) and two of them cooperate with each other before being brought in for questioning.. eg “Neither of us say nothing” then they have a known outcome.. and therefore, I think, that makes them one ‘person’. that is the outcome is only going to be neither confess.

this now makes the third person be the one who holds all the power, however what happens if this person doesn’t know the other two are in collusion?

I’m trying to make. bigger grid, but that gets harder.. I will look at BTM’s unscrupulous dinners dilemma. thanks :)

totc

Don’t like game theory.

It gave us the cold war, with nuclear missiles on the brink.

Game theory assumes that: there is a winner, and that everyone is driven by immoral selfishness. Neither of those is true.

mollwollfumble said:

Don’t like game theory.

It gave us the cold war, with nuclear missiles on the brink.

Game theory assumes that: there is a winner, and that everyone is driven by immoral selfishness. Neither of those is true.

Yeah, lets go back to proper hot wars like we used to have.

But I agree with line 3.

mollwollfumble said:

Don’t like game theory.

It gave us the cold war, with nuclear missiles on the brink.

Game theory assumes that: there is a winner, and that everyone is driven by immoral selfishness. Neither of those is true.

prisoners/criminals are often driven by immoral selfishness.

Arts said:

mollwollfumble said:

Don’t like game theory.

It gave us the cold war, with nuclear missiles on the brink.

Game theory assumes that: there is a winner, and that everyone is driven by immoral selfishness. Neither of those is true.

prisoners/criminals are often driven by immoral selfishness.

isn’t there two sides to game theory, zero sum and non zero sum?

ok.. so I have read about Dinner Dilemma..

the thing that struck me here was that the DD shows a

now antisocial types do not generally have unselfishness or social considerations… the UDD shows a thought experiment but it:

“account for possible unselfishness and social considerations.”

which generally antisocial types do not have..

I have a scenario that needs attending…

we have three suspects. The police think that two of them are in collusion (that is they will both tell each other prior to the interview what they are going to say/do – if anything). they need to interview them all to find the correct suspect..
I guess we are essentially turning the theory around.. how can the police use game theory (the prisoners dilemma) to flush out the guilty?