Problems with Tit for Tat

hi we've seen the tit for tat is a highly successful strategy for dealing with iterated prisoner's dilemmas but it does have some problems and i want to talk about some of those problems look at a variant that tries to fix those problems and then also look at a strategy that perhaps surprisingly manages consistently to beat tit-for-tat we've seen a strategy already that comes very close to it and sometimes defeats it namely the pavlov strategy it's actually very similar to tit-for-tat in a lot of ways but there are strategies well really a combination of strategies that can beat tit-for-tat and there's a nice example of how that might be done though it is only going to work in a certain limited range of cases first problems with tit-for-tat what kinds of issues arise what makes it less in some settings effective than some other strategies the first problem is that power relations sometimes make retaliation impossible so let's say you're in a hierarchy and it's your boss that is actually consistently defecting i once worked for a boss like that i put up with it for about two years and i quit that job and the reason was that i constantly felt that my boss was stabbing me in the back there was nothing i could do about that with a peer if they defect you can retaliate you can respond by defecting but what do you what do you do if your boss defects and stabs you in the back there can be often very little you can do to retaliate against somebody higher in the hierarchy and so that creates a problem the same thing can arise in all sorts of other kind of power relationships with people in positions of authority they can do various things to you and you're not really in a position to retaliate in those settings it really starts looking like bully and victim rather than like two people mutually seeking cooperation and so even if it turns out for the person higher above it would be better for them if you cooperated it's going to be very difficult for you to do anything else given the difference in power what about other settings friendship or love where there's a consistent relationship that you don't want to mess up by retaliating and if you get this sense that it's always this for that you're really losing the kind of sense of cooperation of being in this together of communal sharing to use the term from relationship regulation theory that we think is really vital to those relationships i remember a neighbor who was divorced and was dating some guy and she complained about precisely this of course she didn't know game theory she didn't put it in those terms but what it amounted to is that if he called and said hey when i have dinner friday night i said no i'm busy i can't do it friday night then the next time she suggested something she said hey you want to go to that festival on saturday no i'm busy it was always that kind of retaliation you say no to me well then i'm going to say no to you next time and so on and in the end it destroyed that relationship because she thought wait a minute this is a weird kind of you know i have to do this to get my reward i have to do that it was incompatible with the kind of sharing that ought to take place within a romantic relationship but i don't think it's just romance it can happen within friendships it can happen with productive co-worker relationships and all sorts of other things here's another problem it's easy to get into cycles cycles of retaliation and that can sometimes happen due to miscommunication or misperception i may think that a person has defected when in fact they haven't i may misread their behavior and in a setting like that i then retaliate but they're taken aback they didn't defect first in their opinion they didn't see what they did as any kind of defection and so they're upset and they i think they betrayed me they think i've betrayed them and in short we get into this cycle of retaliation that can destroy the friendship destroy the working relationship without actually either one of us in thinking we're initiating this problem so there is a serious problem of misperception in ordinary human communication can we always recognize cooperation and defection sometimes we may be inaccurate in our perception we may misread cooperation as defection or conversely we may misread defection as cooperation the person is pretending to cooperate while not really cooperating we may have no idea and so these mistakes can echo back and forth in the relationship there's no way to end the cycle and that's a problem we've talked about the importance of forgiveness well tip for chad is in a way not that forgiving i retaliate but then the other player playing tit for tat retaliates against my retaliation that i retaliate against their retaliation against my retaliation and so on here is a way of trying to repair these this is put forward by dixit and nalibuf in their book thinking strategically start by cooperating just as with tit-for-tat and cooperate until the level of apparent defection becomes unacceptable then referred to tit for tat now this is a vague sort of repair it's very close to tit for n tats for example except that requires that the defections all occur in a row you might think there's a certain total number of defections you want to tolerate or a certain percentage of defection it might be hey cooperate unless the ratio of defections to cooperations ends up being some at least unprovoked defections ends up being over 10 or over 20 or something like that and then you have a cutoff you say no more so there are different ways of pursuing this general idea it might be the number of defections the number of defections in a row the ratio of cooperations to defections we might identify this in a variety of ways but in short we keep cooperating we keep forgiving any defections up to a certain point and then we say okay enough but unlike some strategies that say enough i'm done with you i defect from now on this simply says now i play tit for tat now i retaliate against every defection until now i've been forgiving but that's it no more forgiveness so here's an example of how that might play out we've seen tit for tat playing joss where there's a random defection and notice it does set up this cycle of defections but what happens if we instead have a misinterpretation it has exactly the same effect this person cooperates but then instead of a random defection here from tit for cat it thinks it misreads this it thinks there's been a defection and so we get exactly the same pattern but in this case there was no intentional defection there was a misinterpretation that made us think that an action that was actually cooperative was really a defection it sets up the same destructive cycle now how could we get out of this well suppose we say i'm going to cooperate until the level of defections becomes intolerable then instead of defecting here and setting up the cycle we cooperate we say i forgive you okay we've been cooperating now what looks to me like a defection maybe i'm misinterpreting this maybe this is a one-time lapse i forgive you and in short what happens then is that pattern of of cooperation continues until there is a defection or until there's another misinterpretation so it solves that problem at least up to a certain point that does point to a serious problem with tit-for-tat when you get into those cycles of destruction of mutual retaliation there is no way out here is a picture of the hatfields and mccoys involved in a classic case of that kind of mutual retaliation well i've said that it is possible to beat tit for tat and to beat pavlov how do you do it you use what is known as the southampton strategy but it requires the cooperation of another player who is your partner and so the two of you have to work together to do it how does that happen it's illustrated in the movie talladega nights okay it is the shake and make strategy of ricky bobby and so here's how it goes you recognize your partner and then one always cooperates and one always defects the result is that the player who cooperates loses badly but the player who defects against that partner wins now of course that only works when they're playing against one another when they're playing against other people they simply use tit-for-tat or pavlov or in short do a productive strategy but when you recognize your partner you realize oh in interactions with you my role is to cooperate i go belly up and the other person says aha i recognize now what i do is defect and here's the idea you might think well yeah great for the person who is ricky bobby not so great for his partner who is constantly cooperating he never gets to win and so you might think well yeah okay great one of them wins but the other loses big however it's not quite that simple the winner can turn around and share the victory with a partner and so often it's set up in such a way that the payoff for this person is high enough that even if they share it with this person enough to make it benefit to them they're still better off the group in other words the two of them the pair are better off not just that player well that's a fascinating strategy it does require one person to consistently come in second place in those interactions to consistently lose in those interactions the other player to recognize here i've got the willing victim i can consistently win in those interactions

Channel: Daniel Bonevac

Views: 352

Rating: 5 out of 5

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Id: 3BJslvpEayc

Length: 10min 4sec (604 seconds)

Published: Tue Oct 27 2020