Strategies for Iterated Prisoner's Dilemmas

[Music] now in a prisoner's dilemma each person plays their dominant strategy nevertheless they all end up worse off they could have done better by cooperating so what happens when we're playing these games again and again if it's a one-off situation then typically people defect they are not going to cooperate but if they are involved in iterated plays of this if i have to be involved in games that are prisoner's dilemmas with the same people over and over again we start realizing that we're better off if each of us cooperates and so cooperation can emerge in those settings we face this question of strategy in a lot of settings in life we're thinking about how to deal with people we have to deal with frequently we're going to interact with these people a lot maybe at work maybe within our families maybe in our group of friends and so the question is well how do we do that how do we do that productively given that we might be sometimes facing prisoners delights but often we're facing stag hunts or prisoners dilemmas how do we rationally approach that let's take the worst case scenario imagine that we're facing prisoners dilemmas again and again and we decide what's going to be our play how do we deal with that court sort of situation well we formulate a strategy we decide here's my strategy for interacting with these other people given that we're going to be doing this again and again i'm going to be learning more and more about them as we play these sequences of simultaneous games so i want to know how to adapt how to respond to what they've done on prior plays that in general is going to be a question of strategy how do i cope in an environment where there is mutual power where the outcome of my action depends on what other people do we want to prosper individually we also want the group to prosper especially if we're thinking about the welfare not only of ourselves but of our family of our group of friends of our company and so forth well here are a number of strategies generally recognized in the literature this is far from all possible strategies there are many many indeed infinitely many possible strategies you could concoct but these are some of the most popular ones one of them routinely a winner in tournaments especially up to a certain point in the literature on this is called tit for tat the idea is this we start by cooperating but then we do what the other player did last time so i begin by cooperating if the other person cooperates with me i cooperate again but if they defect if they refuse to cooperate with me then next time i don't cooperate with them but of course we might be patient we might say well shall i retaliate yeah we've got a history of cooperation but this time that person betrayed me do i defect back do i decline to cooperate maybe but maybe i think i'll give them a second chance and so there is a variant of that tit for end hats you might say where i decide well i'm going to retaliate but i won't retaliate the first time i'll give you one or two mistakes i'll forgive those but up to a certain point and then i'm not going to forgive anymore i'm going to respond so we start by cooperating and we cop cooperate them unless the other player has defected a certain number of times in a row of course there are many other strategies here's one just always defect look at the situation and say look the best outcome for me is where i defect and you cooperate so i'm going to try to lure you into cooperating and i'm going to defect and i'm just going to do that all the time i'll stab you in the back every single time maybe you'll learn maybe you won't that's one strategy and indeed there are people who play the game of life that way they just defect all the time and behave entirely selfishly for themselves well that means there aren't many opportunities for cooperation with such a person to the extent that you cooperate with them you simply lose another strategy is simply to always cooperate cooperate no matter what decide look i i will forgive you may sin against me once or twice or three times or seven times or seven times seven times i will continue to forgive and so that's a situation where you cooperate no matter what no matter what the history is you cooperate there are many other strategies though one axelrod talks about is the friedman strategy you start by cooperating but then you always defect after the first defection so yes i'm a nice person but if you cross the line i'm done now notice here it says too many times so you might wait until the nth defection to always defect but in this case the idea is look even once i'll cooperate with you as long as you cooperate with me but the moment you defect it's over pal no more and there might be some issues that you consider hey unforgivable betrayals and then you're playing this strategy sorry that betrayal was unforgivable after this i just defect i refuse to cooperate with you here's another strategy that axelrod refers to as the joss strategy again you start by cooperating but then you do what the other player did last time as in tit-for-tat but occasionally maybe 10 of the time or whatever you sneak in a random defection so this is a case where you mostly cooperate but occasionally you try to get a little bit ahead you think yeah in general i'm trying to keep my contracts and my promises with you but occasionally i'm going to sneak one in okay occasionally i'm going to defect and hope you don't retaliate against me so the idea here is i'm going to cooperate as long as you do but occasionally i'm going to sneak in a jab there are many other strategies one might be just be random okay flip a coin do something random don't have any pattern to your actions at all now at first glance you might think that's a very strange thing to do but there might be situations where it's entirely a reasonable thing to do let's suppose for example i am playing a game against someone else and let's say it's a tennis game and they're wondering where i'm going to hit the ball it's good for me to randomize that to some extent i don't want to be predictable and the same thing might be true in various other competitive settings i'm going to be at a disadvantage if you know what i'm going to do suppose we're boxing i don't want you to know whether i'm going to try to jab with my left or my right i don't want you to know whether i'm going to take a punch at all or whether i'm going to step back or do this and the same thing can be true in lots of ordinary settings as well i don't want you to know what play i'm about to call i don't want you to know what kind of bid i'm going to put in on this contract i don't know want you to know exactly how i'm going to approach my application for that grant because i'm worried that if you know you're going to be able to steal that information so i'm going to be a bit random in my approach to things if i'm too predictable i can get into trouble here's another interesting strategy i call it the bully strategy the idea here is that you start by cooperating but then you do the opposite of what the other player did the last time so you cooperate with the stronger roughly you dominate the weak hence the picture of nietzsche that i have here this is something like master morality and nietzsche the idea is you'll find the weak you dominate them like the lion but on the other hand you get a bear lion cooperate with a bigger lion so this is well adapted sometimes to hierarchies cooperate with the people above you but defect against the people below you now that's not a very nice kind of boss i've worked with people like this and i've seen them rise in organizations sometimes personally it works out well for them but on the other hand eventually they get to a point where they anger enough people that they can't stay in that organization anymore and sometimes that happens slowly over a period of years sometimes it happens pretty fast and in general the higher they go the faster it happens but it is a sort of strategy and there are countries that pursue this in foreign policy there are people who pursue this in personal relations they are constantly judging you there was a well-known person in our department who left and went to another university ended up becoming very prominent but i was told the first time i met him listen never take a step back when you're talking to him stand your ground and if anything take a step forward because he's going to move forward toward you and want you to step back and the moment you do he's established his dominance and he will dominate you you're in trouble so you've got to stand your ground or ideally show that you're stronger and then he'll cooperate with you he was in effect playing this bully strategy most of the strategies we've looked at don't do as well as tit for tat in various tournaments where we take a variety of strategies and have them compete with one another but this one actually sometimes wins over tit for tat it's a highly competitive strategy we could call it pavlov and the idea behind this one is a little more complex we start by cooperating and we do what we did last time if the other player cooperated if not do the opposite this one is a little bit harder to grasp intuitively because it says do what you did last time if the other player cooperated that means if the other player cooperated well and you cooperated then cooperate again after all that was highly productive but if the other player cooperated and you defected and therefore you gained a significant advantage do it again hope he cooperates again so in short if the other player cooperated then you're better off so hey do whatever you did last time it worked that's the idea see whether what your last play was worked and so your cooperation worked because the other person cooperated yay do it again if on the other hand your defection worked because the other person cooperated do it again okay so see if it worked but now if the other player didn't cooperate if the other player defected then don't do whatever you did last time do the opposite so let's say last time they defected and you cooperated then you got clobbered don't do that again okay don't cooperate again defect on the other hand suppose you both defected well then that was highly destructive for both of you there were better outcomes out there and so in that case yeah try cooperation in other words if the other player defects basically you lose you could do better by cooperating so if the other player defects then do the opposite of what you did last time the play last time didn't work and so try to do the reverse so here's another way of putting the same point you begin by cooperating and then you cooperate if both players did the same thing last time if both cooperated or both defected but otherwise defect if the two players did different things last time

Channel: Daniel Bonevac

Views: 709

Rating: 5 out of 5

Keywords:

Id: 42emQKQcJcE

Length: 11min 33sec (693 seconds)

Published: Thu Oct 22 2020