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 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?)