Game Theory 101 (#59): Tit-for-Tat in the Repeated Prisoner's Dilemma

gametheory101.com/courses/game-theory-101/
Grim trigger is an extremely vindictive strategy, forever punishing someone for a single misstep. Can less aggressive strategies still inspire cooperation?
Tit-for-tat begins by cooperating and then duplicates the opponent's strategy from the previous period. Consequently, a single defection does not lead to continued defection forever. It is a Nash equilibrium for two players to adopt tit-for-tat for sufficiently high discount factors, but we will later learn that it is NOT a subgame perfect equilibrium.
Nevertheless, tit-for-tat has performed very well in computer tournaments of the repeated prisoner's dilemma. Check out The Evolution of Cooperation for more about this. It's an excellent book: amzn.to/1oZNRv6

[@treeman258]

DAAAAAAAMN SPANIEL!! BACK AT IT AGAIN WITH THE GAME THEORY STRATEGIES!!!!!

[@linalee369]

My lecturer is from Harvard, but you explain much clearer! Thank you Spaniel!

[@PunmasterSTP]

How'd your class go?

[@kevincrossland1898]

You would think with increased repetitions of the prisoner's dilemma, that the thieves would get better at not getting caught... I guess the cops just keep getting better at catching them too! Thanks for helping me study for my Econ Final!

[@PunmasterSTP]

How'd your final go?

[@kevincrossland1898]

@@PunmasterSTP don't remember, but I think it went pretty well, I know I passed the class

[@PunmasterSTP]

@@kevincrossland1898 Awesome; I’m glad to hear it! What did you get your degree in?

[@Sam-fu8rp]

Thank you so much! This was so helpful.

[@rens652]

I'm trying to figure out how to do the algebra at 7:40 but i can't seem to figure it out, can anyone explain that?

[@reniasari8905]

Hi, my lecturer today explained the one step deviation (to defect) payoff as: 4+ (0𝛿) + (3𝛿^2) +(3𝛿^3) + ... = 1+ (1/(1-𝛿)) - 𝛿. I think what he means in that calculation is if the strategy of player 1 & 2 is: (D,C), (D,D), (C,C), (C,C), ... So after Player 1 deviate to D in the first period, player 2 play D in the second period. But after that, they're all go back to C in the subsequent period. DId I understand wrong, or he indeed took different approach to tit-for-tat? Thank you so much for the awesome content!

[@Iridiumalchemist]

I think it might be clearer if you indicated that you were comparing Tit for Tat vs Tit for Tat and similar for the Grim Trigger lecture since you could actually play one verse the other.

[@NE0KRATOS]

One question: if both players are smart, and they both know the payoff if they cooperate and if they defect, they also know that the other player could want to defect if he/she had a delta higher than a certain amount. While doing calculations for their respective payoffs, shouldn't they introduce the probability that the other player will defect as well? For example, suppose that it's our first turn. When we calculate payoffs and we want to know our payoff if we cooperate and if we defect, shouldn't we have something like this? Payoff if we cooperate: 3*p + 1*(1-p) Payoff if we defect: 4*p + 2*(1-p) Where p is the probability that the other player cooperates?

[@Tunde....Ballack]

Hi Man, when getting rid of the inequality equation, did you multiply by (1 - delta square). If you did, then shouldnt the left side be 3 - 3d? Just wondering if I'm missing something

[@Tunde....Ballack]

or is it a 1 - d2 being (1 + d)(1 - d)??

[@Gametheory101]

I can't be sure about what you are asking without a specific time stamp, but I think the trick is 1 - d^2 = (1 + d)(1 - d).

[@Tunde....Ballack]

ok great thanks. That's what I was asking.

[@technogiridhar]

What is the other book?

[@steph3834]

what does the delta represent? i am so confused at the conclusion where δ has to be greater or equal to 1/2. why would that mean cooperating is better??

[@danielklein5560]

it can be interpreted as how patient the players are. When my delta is 1 i dont care when i get my payoff. But with delta=0 i only care about the first round, because later rounds dont give me any payoff.

[@manasisamant7008]

Also , i feel delta represents dicounting factor . ( in which you value today's income more than tomorrow) . This is my interpretation.

[@mohsenhooshmand3170]

What's the other book?

[@lucapianca2593]

I ask for a doubt. I read that tit for tat means that if i continue to cooperate my opponent will do the same for the rest of the game, like you well described "on the path". So C-C, C-C, C-C forever. On the other hand, "off the path", i read that if i will deviate my opponent will do the same to punish me, so he starts to deviate. So i expect that my serie is: at first C, C. Then i will deviate, so it will be C, D. Then my opponent, in order to punish me, starting to deviate as well. So D, D . Then, i note that the deviation equilibria isn't so profitable as the initial one, so i start to cooperate again, so D, C. Finally, my opponent, seeing that i want to cooperate again, starts to cooperate with me and restore the initial situation. So C, C. To riassume we have C-C ; C-D ; D-D; D-C; C-C and so on. It could be a good interpretation? because i thought a lot about your mechanism and it doesn't convince me. Persuade me, that i'm wrong and you are right please :)

[@wergraphy4220]

Exam on Monday and I found you today... Damn...

[@PunmasterSTP]

How'd your exam go?

[@jeyasheelamj2350]

in the inequality 3+3 δ+3 δ2 +…..>=4+ δ+4 δ2 + δ3 ,sir what is the fourth term and next terms

[@James-bt9dr]

I think tit for tat only works if t>r>p>s and t + p ÷ 2 < r

[@V1CCZ3XX]

Swear to god this game is so misunderstood. There isn't a single reliable source with FIXED OUTCOMES, each website, each source has different numbers and I have seen even the strategies (cooperate and defect) being poorly understood. The example I studied in class says that if they both keep quiet (therefore cooperate), they serve 1 year each, which is the nash equilibrium profile of the game. If they both defect they spend 5 years, and the sucker's payoff is 10 years in prison compared to the other prisoner let free (so a payoff of 0). I simply don't understand anymore.

[@RosesAndIvy]

The exact numbers don't matter for the game. You can make it abstract by saying that mutual cooperation leads to payoff R, while mutual defection leads to payoff P. If one of the players defects, he gets payoff T, while the other player gets the payoff S. And importantly, T > R > P > S.

[@vincentrockel1149]

Isn't the name somewhat logically incorrect in that what you really get is either tat for tat or tit of tit. Tit for tat implies something different than the same.

[@MOUNIRIANZ1]

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