Stag Hunts

let's talk about hunting specifically hunting stags and rabbits now you might think that's a very strange example but it's an example given by jean-jacques rousseau in his discourse on the origin of inequality in the second discourse he talks about this problem as paradigmatic of the problem of social evolution and societal cooperation the basic idea is this two hunters decide to go out hunting they can either hunt for a stag which requires the cooperation of both or they can go after a rabbit something they could catch on their own well the payoff for getting a stag is much greater than the payoff for getting a rabbit a rabbit might feed one or two people but a stag well that could feed maybe the whole village so the stag is a significantly bigger game to hunt and it's harder it requires cooperation but on the other hand it feeds a group for a long period of time so there's a real advantage to doing that well let's think about these two hunters again let's imagine that there's me and there's you as our two players here in the game and we've each got two options our options are to hunt stag or to hunt the hair once again i'm going to represent the outcome matrix here with ordinals rather than cardinals simply because how much the stag is worth compared to the hair and so on let's not get into the cardinal values that might indicate that let's just think about what's my first choice what's your first choice and so on so if i think about this i think well all right my first choice is to get that stag and let's say we can get it or at least have a really good chance of getting it if we work together so my first choice is that we work together and get the stag now what happens if i hunt the hair and you hunt the stag or you hunt this the hair and i'm hunting the stag that's really dangerous for me right because then i'm going to bring home nothing if i'm hunting the stag one you're hunting the hair i am doomed to failure i'm going to get nothing you at least get the rabbit and so that's my last choice i'm basically guaranteed to get nothing out of that well suppose i decide to hunt hair then in a certain sense it doesn't even matter to me whether you're off hunting a hair or whether you're hunting the stag you might think i'm a little bit rough maybe if i'm hunting the the hair while you're hunting the stag after all then i've got the hair hunting to my own here we've got two of us chasing after the available supply of rabbits and maybe that disadvantages us so in this case we'll say yeah my second choice is that i just go after the hair while you have the stag that means my third choice is well we're each just hunting rabbits of course we switch around and look at this from your point of view and it's pretty much the same you say my first choice is to get that snag so i'd like to do that my second choice is that you go off hunting or that i go off hunting the stag while you hunt the hare that's your second choice but then you say well my third choice is that we each hugged hair but then your worst option is really if you go hunting the stag and i'm hunting rabbits because then you're guaranteed to fail so we get those ordinal preferences well let's think as we did last time about each person and where they're better off i look at this and i say well all right i can't control what you do but if you hunt stag i get either my first choice or my second choice depending on my selection of hunting a stag or hunting the hair well i'd prefer my first choice so i prefer that option to this option now over here on the other hand i get my worst option if i'm hunting the stag while you're hunting the hair but i get my third if i'm hunting the hair and you are too so i definitely prefer my third choice to my fourth choice i'd rather have a pretty good chance of getting a rabbit that have no chance at all i'd rather have a pretty good chance of getting a rabbit than no chance at all of getting either a rabbit or the stack now let's look at it from your point of view you are thinking well i can't control what that crazy bottom hack does but you're thinking i can hunt stag or i cannot tear so i can choose one of the other of these so let's say i go hunting stag then you think well i've got a choice between my first and second options i prefer my first but then suppose i go off hunting rabbits well then you've got a choice between your fourth and third you definitely prefer the third now let's combine those think about what that means about what's likely to happen i don't have a dominant strategy notice that this arrow points up this one points down that tells me well what's best for me depends on what you do if you're going to hunt stag i should have stagged if you're going to hunt the hair i should hunt the hair and you look at it and you think the same thing these arrows go in opposite direction if i'm hunting stag you should too but if i'm hunting rabbits you should too and so we trace again the arrows to see where they end and they end here and here so both of those are nash equilibria we've got one nash equilibrium here and a second one here this yields the larger payoff on the other hand it's a bit risky because if i commit to this and then you don't go along oh i get my worst option so this is riskier but it is more rewarding this is much less risky but on the other hand not nearly as rewarding why do i say less risky well partly because notice what happens if you're doing the other thing uh in this case i actually end up a little better off you look at this and you think yeah if you choose to hug the stag and actually my odds of getting a bunny rabbit approved so if i go for rabbits that's not really risky at all i don't really in fact i'm a little better off if you do the other thing that i'm expecting you to do and notice that in either case i can't unilaterally improve my situation i can't improve my situation by taking the other option here nor here and the same is true for you so these are nash equilibria but notice one of them is much better than the other in this case admittedly riskier for both of us but nevertheless that gives both of us our first choice that's a great option here we each get our third choice we're both worse off on this option than we are on this option but it's a nash equilibrium and neither of us has a dominant strategy so it's a toss-up which way this is going to go now notice what happens here this one is best it has the highest payoff it's payoff maximal but on the other hand it's risky this one is way less good but it's also less risky and a lot of decisions among people end up being like this there's an option that is the one that's most promising offers us the highest reward but is also riskier it depends on what other people are doing we've got to trust them to make a similar choice and we might be able to actually reach some kind of agreement with them but then again will they keep the agreement now in this case if we're keeping the agreement they have an incentive to keep the agreement but again they have to be willing to trust us so what tends to make the difference between these two is well a matter of trust is there enough trust between the parties to make this work if there's not enough trust they tend to opt for this less good but on the other hand a lot less risky so think about all of the ways in which you might find this happening in society or within an organization or in the behavior of the organization itself let's take a simple example and think about countries it might be that we all are much better off if we can agree to a certain policy on the other hand it will also work though much less well for all of us if we pursue this alternative policy this is best for all of us on the other hand it's risky because if we commit to it and the others don't we're in trouble good example might be arms control agreements they've often been analyzed as prisoners dilemmas and indeed in a practical circumstance they can be but they can also be stag hunts because it might turn out that the best option is really that we don't commit to spending a large amount on developing weapons for example and neither does our competitor so we have peace we have prosperity because we don't have to spend all that money on defense and in general that's the best for everyone a situation where we're involved in an arms race involves a significant commitment of resources from both of us and so we're less well-off under those circumstances if that increases the chances of war of course then even worse off of that but let's even forget about that just think about the expenditures required well why don't we obviously then go for this one well look what happens if i commit to this but then you for example violate the agreement now i get my worst choice because i'm really defenseless against your greater power so i'm in a position of great danger now why is this only your second choice you gain a real international advantage over me but on the other hand you're having to spend a lot of money to do it and so it might be you think yeah we have an advantage but still is it worth spending that much to out maneuver them in terms of this arms race and so an arms race where building up those weapons and building up the military is very expensive and gains a limited international advantage for you can be very much more like a stag hunt than it is like a prisoner's dilemma now if we both just develop weapons we end up down here and that's less risky because neither of us has an advantage really by getting out of this situation unilaterally moreover we don't suffer really if the other person doesn't commit let's say we're in this less good situation um we're both committing a lot of money and you decide you know what i'm not going to do it anymore well you now lose a position internationally and so we gain strength relative to you but we don't have to spend any extra money to do it so there's a sense in which there's not much risk here we just gain if you decide not to continue with this arms race however here if we decide not to commit to further arms and you on the other hand pursue these weapons then we are in real danger how can this happen within an organization well here's a way suppose we're thinking about a group project in fact a lot of people have said this explains a lot about group projects you and i are supposed to work on this project together what's best for both of us is that we both fully commit to this here hunting the stag is doing our best on this project putting in hard work on it we'll do a good job and that's our best option but now suppose i actually decide to goof off in the project put in a half half-hearted effort well that's still pretty good for me the report is less good on the other hand you're working hard here and still in the end the report isn't all that good so you're wasting a lot of effort that's tough for you and you end up saying yeah gosh um i wish i hadn't put in that extra effort now if neither one of us works very hard on it and we do a kind of shoddy job well the result is shoddy but at least we didn't spend any effort on it here we get the shoddy report and you worked hard on it here we have the shoddy report but at least we didn't work very hard on it here of course i'm committing i'm working really hard but you're not so the report ends up shoddy and i had to work hard to do it so what's the result well it looks very much like this and there are going to be two nash equilibria one where we both work hard and do a good job in the project here one where neither of us works very hard and we end up with a shoddy product but still neither of us put in much effort so those end up being the situations now this one is clearly less good we end up with a much worse product here on the other hand it's less risky in that we're not at risk of wasting our effort if the other person doesn't go along here we get the best result best for the company best for our careers and so on but on the other hand it's risky if we put in that effort and the other person doesn't then we're in trouble because we end up with a shoddy product and we did a lot of the work it's not only that the work isn't that good and hey we had to work really hard for it now the other person could say well really i didn't have time to do it so if it's shoddy it's all that guy's fault and that causes problems for us so it is risky which means there's a real temptation to end up here now we're going to look at other kind of group project situations they're not all stag hunts or prisoners dilemmas but they easily can be and notice what happens in this situation if we can trust each other then we'll both commit to doing our part we'll do the best job but if we can't really trust that the other person is going to be fully committed to this then we're inclined not to fully commit either what's the moral of the story in part the moral is when we don't have a dominant strategy to play we have to think about well where the nash equilibria are and before i said a nice rule is seek a nash equilibrium but in this case there are two of them and so since there are multiple nash equilibria we have something of a coordination problem the stag hunt really is a coordination problem more than it is something like a prisoner's dilemma but it's a different kind of coordination problem in our simple driving game it didn't matter whether we all chose to drive on the right or drive on the left here it matters whether we hunt the stag or hunt the hare whether we fully commit to the relationship or the project or hold back on that commitment one outcome is much better than the other but the better one is riskier and there are a lot of things in life that are like that not just relationships or group projects a lot of investments are like that a lot of times just seeking success in whatever you're doing is like that you have to fully commit but that's risky it might all work out you might have wasted all that effort and in general that's the great danger posed by a stag hunt if it doesn't work out if the other person doesn't agree or if nature just doesn't end up conforming to your wishes you will have wasted a lot of effort now that's better than going to prison for a long time which is the downside of a prisoner's dilemma there if you commit that the other person doesn't or reality doesn't conform well then you're in real trouble you are much worse off here it's not exactly that you're worse off but you've risked a lot of effort for no gain and perhaps even for a loss so the stag hunt is one where you're in danger of well taking a risk committing a lot of effort potentially for no payoff maybe even being slightly worse off and that means that you've got to have trust that the other person is going to fully commit in order to make that justifiable if you're thinking of this in terms of nature like you're working hard on this invention or trying to prove this theorem or whatever it is that you're working on well you hope that that strategy you're pursuing will work but what if the world doesn't cooperate with you then the world is something like your opponent in this and you realize i could be wasting a huge amount of effort and sometimes that happens people take on a project they are committed to inventing this project and making it commercially viable for example or they're committed to proving this theorem for their dissertation or whatever it is and if it doesn't work out they will have wasted a huge amount of effort time and money on a project that in the end doesn't yield any results rather like hunting the stag and finding that in the end you're working on it all by yourself and can't possibly achieve your objective so much of life ends up looking like a stag hub problem where the best outcome is also the riskiest outcome and we have to decide whether to go for it or whether to settle

Channel: Daniel Bonevac

Views: 8,444

Rating: 5 out of 5

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Id: JmaXkJ-8_u8

Length: 16min 55sec (1015 seconds)

Published: Fri Oct 16 2020