Something about the Stag frame does make things click. In particular, it gets away from “cooperate/defect” and forces you to think about how much things are worth, which is a cleaner look at the actual game theory problem without confusing it with moralizing, and primes me to evaluate the sort of situations you’d run into here more appropriately.
All in all it sounds like, while I confess a little disappointment that you hadn’t thought through some of the things that appear most-obvious-in-retrospect, the experience sounds like a pretty reasonable first pass at the experiment.
When I tried to actually think of examples where a Stag frame might apply in a housemates sort of situation, the payoff matrix never seemed to match the hypothetical.
Specifically, in every example I could think of that is relevant to a housemates situation, one person choosing stag is a cost to them, but still a benefit to everyone else. So perhaps in a group of 10 choosing stag costs 20, but even if everyone else defects, still results in 5 (to be split among the group… And of course a much higher payout if everyone cooperates). This means everyone else wants you to choose stag, whether they cooperate or not. In fact, their highest payout situation might be to be the sole defector.
The example was given of maintaining a clean bathroom sink. One person trying to do this is still better for everyone else. Their effort does result in a slightly cleaner bathroom.
Can someone give examples relevant to this situation where the payoff of choosing stag (when others defect) is actually zero?
Can someone give examples relevant to this situation where the payoff of choosing stag (when others defect) is actually zero?
A simple example: suppose there’s some house event, and you think that everyone has agreed that attendance and punctuality are very important (because of common knowledge / teamliness considerations), and in order to make it easier to schedule the event you choose to make it higher priority than other important events. So you have to cancel that other important thing, you show up on time, and then some other people are late or not there, and you have this sense of “well, if I had known this is how seriously everyone else would take it, I really wish I was at X instead.”
The traditional game-theoretic stag hunt is a 2-player game, which makes the “everyone shows up” constraint much simpler to see that it’s meaningful. The constraint on the payoffs is that Stag Alone < Rabbit < Stag Together and Stag Alone + Stag Together < 2*Rabbit. (The dominance is non-strict if it’s <=, as in wikipedia’s given example for Stag Hunt payoffs.) Also, as you’re likely aware, 0 isn’t special for utility functions, and so we should just be looking for things where doing it alone is worse than doing a different thing is worse than doing it together, and doing a different thing is closer to doing it together than alone.
If you have an exercise buddy and the two of you agree to show up at the gym at a particular time, then “stag” is showing up at the arranged time (if both of you are there, you work out together and get supported by each other; if only one of you is there, the relationship and desire to exercise erodes) and “rabbit” is choosing to exercise at a more convenient floating time (or not at all).
In the context of a house of 11 people, typically how this manifests is something like either 1) the event is mandatory for everyone, and everyone shows up, and each time someone isn’t there it adds some cognitive cost of “yeah, we’ll do it just like three times ago—wait, were you there for that?” whereas each time everyone is there it adds common knowledge of whatever happened, or 2) the event is optional for everyone, and almost no one shows up, and the event is implicitly compared to mandatory events where everyone shows up. (I think one of the problems that we ran into was that events run by individual people that were optional had an average attendance of something like 2, which made it difficult for people to want to host events, which perhaps further reduced attendance?)
A realistic example which matches this payoff matrix very well is when everyone is using the same means of transport, and so has to wait for the last to arrive before they can leave. A more speculative one: trying to create an environment of group emotional openness and vulnerability, where one person being sarcastic and prickly can ruin it for everyone.
“Hadn’t thought through” is true for only a half to a third; thought through but missed the important insight is more frequently the case (e.g. thought about the costs of doing a thing on the fly, measured them, decided they were low, was wrong).
Something about the Stag frame does make things click. In particular, it gets away from “cooperate/defect” and forces you to think about how much things are worth, which is a cleaner look at the actual game theory problem without confusing it with moralizing, and primes me to evaluate the sort of situations you’d run into here more appropriately.
All in all it sounds like, while I confess a little disappointment that you hadn’t thought through some of the things that appear most-obvious-in-retrospect, the experience sounds like a pretty reasonable first pass at the experiment.
When I tried to actually think of examples where a Stag frame might apply in a housemates sort of situation, the payoff matrix never seemed to match the hypothetical.
Specifically, in every example I could think of that is relevant to a housemates situation, one person choosing stag is a cost to them, but still a benefit to everyone else. So perhaps in a group of 10 choosing stag costs 20, but even if everyone else defects, still results in 5 (to be split among the group… And of course a much higher payout if everyone cooperates). This means everyone else wants you to choose stag, whether they cooperate or not. In fact, their highest payout situation might be to be the sole defector.
The example was given of maintaining a clean bathroom sink. One person trying to do this is still better for everyone else. Their effort does result in a slightly cleaner bathroom.
Can someone give examples relevant to this situation where the payoff of choosing stag (when others defect) is actually zero?
A simple example: suppose there’s some house event, and you think that everyone has agreed that attendance and punctuality are very important (because of common knowledge / teamliness considerations), and in order to make it easier to schedule the event you choose to make it higher priority than other important events. So you have to cancel that other important thing, you show up on time, and then some other people are late or not there, and you have this sense of “well, if I had known this is how seriously everyone else would take it, I really wish I was at X instead.”
The traditional game-theoretic stag hunt is a 2-player game, which makes the “everyone shows up” constraint much simpler to see that it’s meaningful. The constraint on the payoffs is that Stag Alone < Rabbit < Stag Together and Stag Alone + Stag Together < 2*Rabbit. (The dominance is non-strict if it’s <=, as in wikipedia’s given example for Stag Hunt payoffs.) Also, as you’re likely aware, 0 isn’t special for utility functions, and so we should just be looking for things where doing it alone is worse than doing a different thing is worse than doing it together, and doing a different thing is closer to doing it together than alone.
If you have an exercise buddy and the two of you agree to show up at the gym at a particular time, then “stag” is showing up at the arranged time (if both of you are there, you work out together and get supported by each other; if only one of you is there, the relationship and desire to exercise erodes) and “rabbit” is choosing to exercise at a more convenient floating time (or not at all).
In the context of a house of 11 people, typically how this manifests is something like either 1) the event is mandatory for everyone, and everyone shows up, and each time someone isn’t there it adds some cognitive cost of “yeah, we’ll do it just like three times ago—wait, were you there for that?” whereas each time everyone is there it adds common knowledge of whatever happened, or 2) the event is optional for everyone, and almost no one shows up, and the event is implicitly compared to mandatory events where everyone shows up. (I think one of the problems that we ran into was that events run by individual people that were optional had an average attendance of something like 2, which made it difficult for people to want to host events, which perhaps further reduced attendance?)
A realistic example which matches this payoff matrix very well is when everyone is using the same means of transport, and so has to wait for the last to arrive before they can leave. A more speculative one: trying to create an environment of group emotional openness and vulnerability, where one person being sarcastic and prickly can ruin it for everyone.
“Hadn’t thought through” is true for only a half to a third; thought through but missed the important insight is more frequently the case (e.g. thought about the costs of doing a thing on the fly, measured them, decided they were low, was wrong).