Prisoner's Dilemma

Prisoner’s Dilemma.
Imagine two prisoners are separately offered the same deal: if one of them testifies and the other doesn’t talk, the talker will go free and the holdout will go to jail for 10 years. If both refuse to talk, the prosecutor will only be able to put them in jail for six months. If each prisoner rats out the other, they will both get five-year sentences. Not knowing what the other prisoner will do, how should each one act?

This dilemma could be applied to many tournament situations.
It is very typical for blackjack tournament weighting based on our perception (profiling) of opponents. The opponent could be perceived as “no other info available -average”, or “socially average conscience –median”, or as to a specific degree enemy or friend, or as sophisticated, mathematically inclined person, etc., etc.
What’s your thoughts?

The quoted “Prisoner’s Dilemma” comes from the NYT:
http://www.nytimes.com/2007/07/31/s...feef4645acdfcced&ex=1186027200&pagewanted=all

S. Yama

 

don't know if Prisoner's Deliumma applies to tourney situations

as it deals with cooperation - while tourney play doesn't benefit from cooperation as such - unless it is a 'collusion' situation from the beginning -

I think you play other players based on your perception of their knowledge and poise/personality - and assume they will make the best play they can for themselves - that may let you make a bet/play - based on the assumption they will bet/play a certain way for their own advantage -

 

if 2 advance

they are just betting smart for themselves - if one advance - they will be betting to win regardless - unless they do an on-the-spot- deal to chop - that would be bad form -

 

tell

Ok if you don't tell you have a more or less even chance of either 10 years or 6 months

if you tell then 5 years or 0 years

So the answer is easy squeal as fast as you can is a win win situation

this of course does not take into account the squealers get murdered in the shower scenerio which means you in fact definately don't do much time either way with option B

Final table here i come......

 

I'm not sure that the Prisoner's Dilemma is applying in these situations. A key element for the prisoner's dilemma is that even though it is in both of your best efforts to cooperate, it is always even better for YOU to violate that trust, at least on that particular hand.

For example, in Ken's scenario, where BR1 and BR2 are way ahead of BR3, it is their combined interest to keep betting low. However, it's not clear to me that BR1 or BR2 have anything to gain by breaking the trust, while convincing the other person to keep the agreement.

 

I agree with toonces. There does not have to be explicit collusion between the two parties in the Prisoner's Dilemma; the very nature of the problem ensures a conflict of interest -

• Whatever the other prisoner does it is always in your best interest to betray him, saving yourself 6 months in jail if he doesn't talk, and 5 years if he does.
• If you believe the other prisoner is equally aware of the situation, then you might suppose that you could both come to the conclusion that following your own best interests paradoxically condems you to five years in jail, when you only need serve 6 months and hence you should both stay quiet.
• But dare you trust them?

The essence of the Prisoner's Dilemma is the conflict between mutual self interest and individual self interest, plus the exact symmetry of the situation - the two prisoners are faced with precisely the same decision making process.

 

Prisoners

Is it Paris and Nicole ?

 

Collusion?

Monkey,

Where exactly did S.Yama specify in his original scenario that no collusion could take place between the two prisoners?

Maybe it’s me. But I just can’t see it.

Andy

 

Actually in "Prisoner's Dilemma" they have only two options: Rat or Don't Rat,
plus they don't know about each other’s decision. To compare it to the TBJ we have to assume that there is a secret bet option on the last hand and, as mentioned in above example, players have only two betting options, say min or max. Otherwise with two min bets behind, BR2 may consider also anything more than 1/2 max bet, but less than max bet to take low if BR1 bets max, and still have a chance to take high over BR1 by DD.

 

deciding others fate

The original Prisoner’s Dilemma (PD) deals with non-zero-sum game and brings forth aspects of cooperation -but that was not the reason why I posted it here.
I thought it was interesting for those of us previously being not familiar with it; and that it does do have a lot of elements that tournaments players need to embrace.

By non-zero-sum game I mean the game where all cited chances for all possibilities will not add up to one, or one hundred percent. PD also offers (as Tirle_bj has noted) two decisions and not a string of decisions from a range of bets or playing decisions. To make a closer parallel to tournament blackjack we would have to consider only two decisions and interject additional player(s), who would add up game chances to one hundred percent, but then keep focus on the original two players only. I wonder myself if a closer theoretical but specific situation could be build.

What PD has in common with bj tournaments is the fact that often times weighting chances of other players' action by including psychology and then multiplying them by benefits (risk and rewards) is the fundamental function of blackjack (and other games) tournament strategy.
It also touches on fact that the fate of other players can be in our hands, sometimes with minimal, or even none-whatsoever, overall effects on our individual chances.
Then, it deals with agreed on, or presumed (realistic, imagined, or hopeful) cooperation for immediate or subsequent tournament actions - or lack of thereof – all of which will effect our tournament well being.

Fortunately collusion in blackjack tournaments is really very rare and not effective enough to cause concern.
However, even though I wished there were none, some forms of “collusion” fall into a gray area and it would be either unrealistic, too simplistic, or naive to categorically say that any particular person would or should have no part of it. But it is much more complicated matter than many people want or dare to admit, and it is subject for a separate discussion at another time.

Perhaps RKuczek was right that PD applies somewhat less to blackjack than to other games where a player can choose (knowingly or not) 100% correlating actions/options.
Blackjack is just one of many forms of tournaments where its core is based on game theory that encompasses countless other aspects that go beyond strictly and narrowly understood mathematics.
Actually, blackjack tournaments with different rules (that may call for utilizing dramatically different and sometimes even opposing playing strategies) are just a cluster of games on the same line where other tournaments, usually offered by casinos (like craps, baccarat, and others), reside.

Some members here may be wondering what are the situations where we can determine fate of other players. Here is the easiest example.
Let’s say it is the last tournament roll in game of dice, after which two players advance to the next round. You are BR1 and betting last. BR2 and BR3 bet equal amounts on separate eighteen combinations out of possible 36 dice combinations, and they are all-in.
You can just minimally “cover” each and every bet made, for up to 18 combinations. You can pick one or the other player and lock him out, or you could take away half chances from each, or take half of the combinations and leave to them the other half in any other proportions.

Similarly, in blackjack tournament, let’s say this is the last hand, two players advancing to next round. BR1 (Player A) busted and is left with 10,000 in chips. Other players busted their big bets and have very little chips left. The only other player, let’s call him Player B, has bet 2,000 out 9,000 bankroll and stood on hand total sixteen, dealer is showing nine. You have bet 6,000 all-in and have two cards tatal fifteen.
Push does you no good. You must win. You know that the chance for winning by standing or hitting is exactly 23% (there were couple excess big cards left in the deck).
If you stay you advance 23% of the times, Player B advances always, and Player A advances 77% of the times.
If you hit one time you still advance the same 23% of the times, but whenever you win your hand by beating dealer’s made hand you achieve it at Player B’s expense, and at the same time increasing Player A's chances.
So you can “manipulate” and make favors for one or the other opponent at no change to your own chances.

S. Yama

 

non-zero-sum game

I'm a little confused. Maybe I misunderstood the definition of non-zero-sum game, but here what I think.
Suppose prisoner A rats with the probability of X, that means he don't rat with (1-X). Now suppose B rats with the probability of Y, that means he don't rat with (1-Y).
Actually we have only four possible combinations (R,R); (R,DR); (DR,R); (DR,DR) = XY + X(1-Y) + (1-X)Y + (1-X)(1-Y) = XY + X -XY + Y -XY +
+ 1 - Y - X + XY = 1
Of course the EV is not necessarily 0 (by the way we can find X & Y when for given outcomes the total EV will be 0).
But again the sum of probabilities for all possible outcomes in any kind of life situation should be equal to 1 (or 100%)

 

a zero-sum game

simply means that a player can not win more, nor less, then the other player loses - wins and losses must sum up to zero -

this is a non-zero sum game - because there is an option which allows both players to have a positive result -

 

Thanks

Thanks, Rkuczek, now it is crystal clear for me.