TurnTrout’s informal definition of ‘defection’ above looks right to me, where “a player defects when they increase their personal payoff at the expense of the group.” My point is that when people didn’t pick the same choice as me, I was previously modeling it using prisoners’ dilemma, but this was inaccurate because the person wasn’t getting any personal benefit at my expense. They weren’t taking from me, they weren’t free riding. They just weren’t coordinating around my stag. (And for my own clarity I should’ve been using the stag hunt metaphor
I can try to respond to your (correct) points about the True Prisoners’ Dilemma, but I don’t think they’re cruxy for me. I understand that defecting and cooperating in the PD don’t straightforwardly reflect the associations of their words, but they sometimes do. Sometimes, defecting is literally tricking someone into thinking you’re cooperating and then stealing their stuff. The point I’m making about stag hunts is that this element is entirely lacking — there’s no ability for them to gain from my loss, and bringing it into the analysis is in many places muddying the waters of what’s going on. And this reflects lots of situations I’ve been in, where because of the game theoretic language I was using I was causing myself to believe there was some level of betrayal I needed to model, where there largely wasn’t.
They weren’t taking from me, they weren’t free riding. They just weren’t coordinating around my stag.
I’d like to note that with respect to my formal definition, defection always exists in stag hunts (if the social contract cares about everyone’s utility equally); see Theorem 6:
A 2×2 symmetric game is a Stag Hunt when R>T≥P>S. In Stag Hunts, due to uncertainty about whether the other player will hunt stag, players defect and fail to coordinate on the unique Pareto optimum (Stag1, Stag2). In (b), player 2 will defect (play Hare2) when P(Stag1)<12. In Stag Hunts, formal defection can always occur against mixed strategy profiles, which lines up with defection in this game being due to uncertainty.
What’s happening when P(Stag1)<12 is: Player 2 thinks it’s less than 50% probable that P1 hunts stag; if P2 hunted stag, expected total payoff would go up, but expected P2-payoff would go down (since some of the time, P1 is hunting hares while P2 waits alone near the stags); therefore, P2 is tempted to hunt hare, which would be classed as a defection.
If that’s a stag hunt then I don’t know what a stag hunt is. I would expect a stag hunt to have (2,0) in the bottom left corner and (0,2) in the top right, precisely showing that player two gets no advantage from hunting hare if player one hunts stag (and vice versa).
T >= P covers both the case where you’re indifferent as to whether or not they hunt hare when you do (the =) and the case where you’re better off as the only hare hunter (the >); so long as R > T, both cases have the important feature that you want to hunt stag if they will hunt stag, and you want to hunt hare if they won’t hunt stag.
The two cases (T>P and T=P) end up being the same because if you succeed at tricking them into hunting stag while you hurt hare (because T>P, say), then you would have done even better by actually collaborating with them on hunting stag (because R>T).
TurnTrout’s informal definition of ‘defection’ above looks right to me, where “a player defects when they increase their personal payoff at the expense of the group.” My point is that when people didn’t pick the same choice as me, I was previously modeling it using prisoners’ dilemma, but this was inaccurate because the person wasn’t getting any personal benefit at my expense. They weren’t taking from me, they weren’t free riding. They just weren’t coordinating around my stag. (And for my own clarity I should’ve been using the stag hunt metaphor
I can try to respond to your (correct) points about the True Prisoners’ Dilemma, but I don’t think they’re cruxy for me. I understand that defecting and cooperating in the PD don’t straightforwardly reflect the associations of their words, but they sometimes do. Sometimes, defecting is literally tricking someone into thinking you’re cooperating and then stealing their stuff. The point I’m making about stag hunts is that this element is entirely lacking — there’s no ability for them to gain from my loss, and bringing it into the analysis is in many places muddying the waters of what’s going on. And this reflects lots of situations I’ve been in, where because of the game theoretic language I was using I was causing myself to believe there was some level of betrayal I needed to model, where there largely wasn’t.
I’d like to note that with respect to my formal definition, defection always exists in stag hunts (if the social contract cares about everyone’s utility equally); see Theorem 6:
What’s happening when P(Stag1)<12 is: Player 2 thinks it’s less than 50% probable that P1 hunts stag; if P2 hunted stag, expected total payoff would go up, but expected P2-payoff would go down (since some of the time, P1 is hunting hares while P2 waits alone near the stags); therefore, P2 is tempted to hunt hare, which would be classed as a defection.
If that’s a stag hunt then I don’t know what a stag hunt is. I would expect a stag hunt to have (2,0) in the bottom left corner and (0,2) in the top right, precisely showing that player two gets no advantage from hunting hare if player one hunts stag (and vice versa).
Also note that you can indeed make that entry (2,0) by subtracting 1 from every payoff in the game. The same arguments still hold.
T >= P covers both the case where you’re indifferent as to whether or not they hunt hare when you do (the =) and the case where you’re better off as the only hare hunter (the >); so long as R > T, both cases have the important feature that you want to hunt stag if they will hunt stag, and you want to hunt hare if they won’t hunt stag.
The two cases (T>P and T=P) end up being the same because if you succeed at tricking them into hunting stag while you hurt hare (because T>P, say), then you would have done even better by actually collaborating with them on hunting stag (because R>T).
I see, thx.