This Game Keeps Me Up At Night

This is one of my favorite mathematical thought exercises! I promise you'll like it too.

The prisoner's dilemma is one of (is?) the most famous examples in mathematical game theory. The game is sort of a paradox since it appears both players would be better of cooperating, yet the best decision (for both players) is to defect (not cooperate)!

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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information.

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[BriTheMathGuy]

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[guydror]

I think that the problem with the example at the end is that some people might value their reputation more than 1 or 2 points, therefore cooperating is actually the correct choice

[weirdfrog]

In your example, defecting incurs a hidden social cost as well. So the points don't necessarily correspond to utility!

[der.Schtefan]

There is a huge difference between Prisoner's Dilemma and the repeated prisoner's dilemma with memory.

[BriTheMathGuy]

You chose to defect too, didn't you? Be honest.

[CjqNslXUcM]

I think you missed the point your professor was trying to make. An iterated prisoners dilemma is an entirely different game and ties in to the evolution of cooperation.

The reason we have concepts such as reputation and revenge is that life in many ways resembles game theory, and overall, tit for tat cooperation is the dominant strategy by far for the individual. We see this play out in nature and human societies all the time.

[Mutual_Information]

The classroom experiment is very interesting. To me it suggests.. punnet squares make for bad models. They just aren’t complete representations of all the decision factors.

[marcusscience]

What if instead of just choosing once, you and your opponent could choose over and over again times and add to your score each time? In that case, provided both players are rational and know it, a good strategy will be to always cooperate each time, unless your opponent defects, in that case you retaliate by defecting afterwards, partly to make up for your loss (though only to a certain extent), but mainly to disincentivise your opponent from defecting. You defecting is always worse off for your opponent no matter what they choose, and even if they had defected before it would still be worse for them than if you both cooperated. That way, your opponent wouldn’t defect so as not to provoke you and be worse off, and also knowing that you wouldn’t either with the same reasoning. This way, you can both end up being better off with mutual cooperation.

[mikecaetano]

You were going to see the other students in the class again right? The dynamics of the prisoner's dilemma change in a context of iterated play. Cheat me once, shame on you; cheat me twice, shame on me!

[oleksandrpopovych]

Defecting is a better strategy simply because there are no other objectives for agents playing, but humans, we have also social objective (bring benefit to the group), and this objective doesn't captured by solution explained.

[harlanweid]

Interesting that if you know that you play with the exact copy of yourself, best strategy is to cooperate. Which leads to an interesting question: if both actors know the rules and play perfectly aren't they exact copies?

[angeldude]

Applying a little empathy and altruism to acknowledge that winning is _not_ the objective, then the winning strategy becomes not to maximise _your_ points, but to maximise _everyone's_ points. So now, 1 cooperate and 1 defect is 5 points, 2 defects is 2 points, and 2 cooperates is 6 points. Cooperating is always the better outcome as long as you're not just playing for yourself. Same as in the class since the payouts were 1, 0, and 2 for 1 of each, 2 defects, and 2 cooperates respectively.

[rogerkearns]

I'm thinking of it as a psychopath detector test.

[Szabolcs]

That's because the listed "payment" isn't the REAL payment, as the game is not played in isolation. The real payment includes one's reputation in the class which outweighs these bonus points.

The game's best strategy also changes in case there are repeated games for similar reasons.

[nealcarpenter]

This game gets even more interesting (like Prisoner's Dilemma) if you play repeatedly. (Ie. allowing for learning and/or 'revenge'.) There was an experiment done years ago where the winner (winning program) (with repeated games) would cooperate till 'betrayed' by the other player, then go for 'defecting'.

[richardbloemenkamp]

Collaboration (price agreement) is forbidden in a kapitalist market. Companies are required to compete with eachother and not divide the market among the players. That's why, for example, many shops that sell similar goods in a city (clothes shops, computer shops, gas stations, banks) end up in the same streets even if they would collectively earn more if they were distributed over the whole city.

[atlasxatlas]

defecting isn't always better because the other player isn't equally likely to defect and cooperate.
maybe if we consider the expected payout including those odds - then the "best strategy" will be different?

[JossoJJossoJ]

If it was not absolute grading, adding 1 pt to each student's final score doesn't change the deviation of the distribution.
Hence, all cooperating or all defecting are essentially the same.

[arulrana]

defecting just means the opponent can never come out on top

[HeavyMetalMouse]

"I'm going to pick Defect every time. You should pick Cooperate, and here's why: If I'm telling you the truth, I'll pay you 2.5 points for your trouble, which is still better than you could do defecting when I've clearly stated I will defect - there is nothing you can do that gets you better than that deal, since I guarantee you I'm going to defect. But if you think I'm lying, then you should still pick Cooperate, because if I'm lying and I'm actually going to Cooperate, then we'll both win 3, which is *even better*. But I'm going to pick Defect, which you can believe because there is zero benefit to me in lying about it."

Over multiple rounds of play, this produces very nearly the best possible outcome, and only 'breaks down' on the last round of a multi-round game, where I no longer have any reason to convince you I'm trustworthy to continue going along with me, and might screw you over on the bribe. How well this strategy works depends on the relationship between the 'Cooperate/Defect' payoff and the 'Defect/Defect' payoff. In the Professor's example, the 'bribe' is 1.5 points, meaning that both players gain 0.5 points of credit, which is better than they can do with both Defecting. As long as the total payout between both players in the Cooperate/Defect scenario is higher than the Defect/Defect scenario, and as long as the reward is transferable, this works.