We should really be calling it Rabbit Hunt rather than Stag Hunt.
The schelling choice is rabbit. Calling it stag hunt makes the stag sound schelling.
The problem with stag hunt is that the schelling choice is rabbit. Saying of a situation “it’s a stag hunt” generally means that the situation sucks because everyone is hunting rabbit. When everyone is hunting stag, you don’t really bring it up. So, it would make way more sense if the phrase was “it’s a rabbit hunt”!
Well, maybe you’d say “it’s a rabbit hunt” when referring to the bad equilibrium you’re seeing in practice, and “it’s a stag hunt” when saying that a better equilibrium is a utopian dream.
So, yeah, calling the game “rabbit hunt” is a stag hunt.
I used to think a lot in terms of Prisoner’s Dilemma, and “Cooperate”/”Defect.” I’d see problems that could easily be solved if everyone just put a bit of effort in, which would benefit everyone. And people didn’t put the effort in, and this felt like a frustrating, obvious coordination failure. Why do people defect so much?
Eventually Duncan shifted towards using Stag Hunt rather than Prisoner’s Dilemma as the model here. If you haven’t read it before, it’s worth reading the description in full. If you’re familiar you can skip to my current thoughts below.
In the book The Stag Hunt, Skyrms similarly says that lots of people use Prisoner’s Dilemma to talk about social coordination, and he thinks people should often use Stag Hunt instead.
I think this is right. Most problems which initially seem like Prisoner’s Dilemma are actually Stag Hunt, because there are potential enforcement mechanisms available. The problems discussed in Meditations on Moloch are mostly Stag Hunt problems, not Prisoner’s Dilemma problems -- Scott even talks about enforcement, when he describes the dystopia where everyone has to kill anyone who doesn’t enforce the terrible social norms (including the norm of enforcing).
This might initially sound like good news. Defection in Prisoner’s Dilemma is an inevitable conclusion under common decision-theoretic assumptions. Trying to escape multipolar traps with exotic decision theories might seem hopeless. On the other hand, rabbit in Stag Hunt is not an inevitable conclusion, by any means.
Unfortunately, in reality, hunting stag is actually quite difficult. (“The schelling choice is Rabbit, not Stag… and that really sucks!”)
Rabbit in this case was “everyone just sort of pursues whatever conversational types seem best to them in an uncoordinated fashion”, and Stag is “we deliberately choose and enforce particular conversational norms.”
This sounds a lot like Pavlov-style coordination vs Tit for Tat style coordination. Both strategies can defeat Moloch in theory, but they have different pros and cons. TfT-style requires agreement on norms, whereas Pavlov-style doesn’t. Pavlov-style can waste a lot of time flailing around before eventually coordinating. Pavlov is somewhat worse at punishing exploitative behavior, but less likely to lose a lot of utility due to feuds between parties who each think they’ve been wronged and must distribute justice.
When discussing whether to embark on a stag hunt, it’s useful to have shorthand to communicate why you might ever want to put a lot of effort into a concerted, coordinated effort. And then you can discuss the tradeoffs seriously.
[...]
Much of the time, I feel like getting angry and frustrated… is something like “wasted motion” or “the wrong step in the dance.”
Not really strongly contradicting you, but I remember Critch once outlined something like the following steps for getting out of bad equilibria. (This is almost definitely not the exact list of steps he gave; I think there were 3 instead of 4 -- but step #1 was definitely in there.)
1. Be the sort of person who can get frustrated at inefficiencies.
2. Observe the world a bunch. Get really curious about the ins and outs of the frustrating inefficiencies you notice; understand how the system works, and why the inefficiencies exist.
3. Make a detailed plan for a better equilibrium. Justify why it is better, and why it is worth the effort/resources to do this. Spend time talking to the interested parties to get feedback on this plan.
4. Finally, formally propose the plan for approval. This could mean submitting a grant proposal to a relevant funding organization, or putting something up for a vote, or other things. This is the step where you are really trying to step into the better equilibrium, which means getting credible backing for taking the step (perhaps a letter signed by a bunch of people, or a formal vote), and creating common knowledge between relevant parties (making sure everyone can trust that the new equilibrium is established). It can also mean some kind of official deliberation has to happen, depending on context (such as a vote, or some kind of due-diligence investigation, or an external audit, etc).
Most problems which initially seem like Prisoner’s Dilemma are actually Stag Hunt, because there are potential enforcement mechanisms available.
I’m not sure I follow, can you elaborate?
Is the idea that everyone can attempt to enforce norms of “cooperate in the PD” (stag), or not enforce those norms (rabbit)? And if you have enough “stag” players to successfully “hunt a stag”, then defecting in the PD becomes costly and rare, so the original PD dynamics mostly drop out?
If so, I kind of feel like I’d still model the second level game as a PD rather than a stag hunt? I’m not sure though, and before I chase that thread, I’ll let you clarify whether that’s actually what you meant.
By “is a PD”, I mean, there is a cooperative solution which is better than any Nash equilibrium. In some sense, the self-interest of the players is what prevents them from getting to the better solution.
By “is a SH”, I mean, there is at least one good cooperative solution which is an equilibrium, but there are also other equilibria which are significantly worse. Some of the worse outcomes can be forced by unilateral action, but the better outcomes require coordinated action (and attempted-but-failed coordination is even worse than the bad solutions).
In iterated PD (with the right assumptions, eg appropriately high probabilities of the game continuing after each round), tit-for-tat is an equilibrium strategy which results in a pure-cooperation outcome. The remaining difficulty of the game is the difficulty of ending up in that equilibrium. There are many other equilibria which one could equally well end up in, including total mutual defection. In that sense, iteration can turn a PD into a SH.
Other modifications, such as commitment mechanisms or access to the other player’s source code, can have similar effects.
In the specific case of iteration, I’m not sure that works so well for multiplayer games? It would depend on details, but e.g. if a player’s only options are “cooperate” or “defect against everyone equally”, then… mm, I guess “cooperate iff everyone else cooperated last round” is still stable, just a lot more fragile than with two players.
But you did say it’s difficult, so I don’t think I’m disagreeing with you. The PD-ness of it still feels more salient to me than the SH-ness, but I’m not sure that particularly means anything.
I think actually, to me the intuitive core of a PD is “players can capture value by destroying value on net”. And I hadn’t really thought about the core of SH prior to this post, but I think I was coming around to something like threshold effects; “players can try to capture value for themselves [it’s not really important whether that’s net positive or net negative]; but at a certain fairly specific point, it’s strongly net negative”. Under these intuitions, there’s nothing stopping a game from being both PD and SH.
Not sure I’m going anywhere with this, and it feels kind of close to just arguing over definitions.
We should really be calling it Rabbit Hunt rather than Stag Hunt.
The schelling choice is rabbit. Calling it stag hunt makes the stag sound schelling.
The problem with stag hunt is that the schelling choice is rabbit. Saying of a situation “it’s a stag hunt” generally means that the situation sucks because everyone is hunting rabbit. When everyone is hunting stag, you don’t really bring it up. So, it would make way more sense if the phrase was “it’s a rabbit hunt”!
Well, maybe you’d say “it’s a rabbit hunt” when referring to the bad equilibrium you’re seeing in practice, and “it’s a stag hunt” when saying that a better equilibrium is a utopian dream.
So, yeah, calling the game “rabbit hunt” is a stag hunt.
In the book The Stag Hunt, Skyrms similarly says that lots of people use Prisoner’s Dilemma to talk about social coordination, and he thinks people should often use Stag Hunt instead.
I think this is right. Most problems which initially seem like Prisoner’s Dilemma are actually Stag Hunt, because there are potential enforcement mechanisms available. The problems discussed in Meditations on Moloch are mostly Stag Hunt problems, not Prisoner’s Dilemma problems -- Scott even talks about enforcement, when he describes the dystopia where everyone has to kill anyone who doesn’t enforce the terrible social norms (including the norm of enforcing).
This might initially sound like good news. Defection in Prisoner’s Dilemma is an inevitable conclusion under common decision-theoretic assumptions. Trying to escape multipolar traps with exotic decision theories might seem hopeless. On the other hand, rabbit in Stag Hunt is not an inevitable conclusion, by any means.
Unfortunately, in reality, hunting stag is actually quite difficult. (“The schelling choice is Rabbit, not Stag… and that really sucks!”)
This sounds a lot like Pavlov-style coordination vs Tit for Tat style coordination. Both strategies can defeat Moloch in theory, but they have different pros and cons. TfT-style requires agreement on norms, whereas Pavlov-style doesn’t. Pavlov-style can waste a lot of time flailing around before eventually coordinating. Pavlov is somewhat worse at punishing exploitative behavior, but less likely to lose a lot of utility due to feuds between parties who each think they’ve been wronged and must distribute justice.
Not really strongly contradicting you, but I remember Critch once outlined something like the following steps for getting out of bad equilibria. (This is almost definitely not the exact list of steps he gave; I think there were 3 instead of 4 -- but step #1 was definitely in there.)
1. Be the sort of person who can get frustrated at inefficiencies.
2. Observe the world a bunch. Get really curious about the ins and outs of the frustrating inefficiencies you notice; understand how the system works, and why the inefficiencies exist.
3. Make a detailed plan for a better equilibrium. Justify why it is better, and why it is worth the effort/resources to do this. Spend time talking to the interested parties to get feedback on this plan.
4. Finally, formally propose the plan for approval. This could mean submitting a grant proposal to a relevant funding organization, or putting something up for a vote, or other things. This is the step where you are really trying to step into the better equilibrium, which means getting credible backing for taking the step (perhaps a letter signed by a bunch of people, or a formal vote), and creating common knowledge between relevant parties (making sure everyone can trust that the new equilibrium is established). It can also mean some kind of official deliberation has to happen, depending on context (such as a vote, or some kind of due-diligence investigation, or an external audit, etc).
I’m not sure I follow, can you elaborate?
Is the idea that everyone can attempt to enforce norms of “cooperate in the PD” (stag), or not enforce those norms (rabbit)? And if you have enough “stag” players to successfully “hunt a stag”, then defecting in the PD becomes costly and rare, so the original PD dynamics mostly drop out?
If so, I kind of feel like I’d still model the second level game as a PD rather than a stag hunt? I’m not sure though, and before I chase that thread, I’ll let you clarify whether that’s actually what you meant.
By “is a PD”, I mean, there is a cooperative solution which is better than any Nash equilibrium. In some sense, the self-interest of the players is what prevents them from getting to the better solution.
By “is a SH”, I mean, there is at least one good cooperative solution which is an equilibrium, but there are also other equilibria which are significantly worse. Some of the worse outcomes can be forced by unilateral action, but the better outcomes require coordinated action (and attempted-but-failed coordination is even worse than the bad solutions).
In iterated PD (with the right assumptions, eg appropriately high probabilities of the game continuing after each round), tit-for-tat is an equilibrium strategy which results in a pure-cooperation outcome. The remaining difficulty of the game is the difficulty of ending up in that equilibrium. There are many other equilibria which one could equally well end up in, including total mutual defection. In that sense, iteration can turn a PD into a SH.
Other modifications, such as commitment mechanisms or access to the other player’s source code, can have similar effects.
Thanks, that makes sense.
Rambling:
In the specific case of iteration, I’m not sure that works so well for multiplayer games? It would depend on details, but e.g. if a player’s only options are “cooperate” or “defect against everyone equally”, then… mm, I guess “cooperate iff everyone else cooperated last round” is still stable, just a lot more fragile than with two players.
But you did say it’s difficult, so I don’t think I’m disagreeing with you. The PD-ness of it still feels more salient to me than the SH-ness, but I’m not sure that particularly means anything.
I think actually, to me the intuitive core of a PD is “players can capture value by destroying value on net”. And I hadn’t really thought about the core of SH prior to this post, but I think I was coming around to something like threshold effects; “players can try to capture value for themselves [it’s not really important whether that’s net positive or net negative]; but at a certain fairly specific point, it’s strongly net negative”. Under these intuitions, there’s nothing stopping a game from being both PD and SH.
Not sure I’m going anywhere with this, and it feels kind of close to just arguing over definitions.