Naturally, F is monotonically increasing in R and decreasing in Ropp
You’re treating resources as one single kind, where really there are many kinds with possible trades between teams. Here you’re ignoring a factor that might actually be crucial to encouraging cooperation (I’m not saying I showed this formally :-)
Assume there are just two teams
But my point was exactly that there would be many teams who could form many different alliances. Assuming only two is unrealistic and just ignores what I was saying. I don’t even care much if given two teams the correct choice is to cooperate, because I set very low probability on there being exactly two teams and no other independent players being able to contribute anything (money, people, etc) to one of the teams.
This is my position
You still haven’t given good evidence for holding this position regarding the relation between the different Uxxx utilities. Except for the fact CEV is not really specified, so it could be built so that that would be true. But equally it could be built so that that would be false. There’s no point in arguing over which possibility “CEV” really refers to (although if everyone agreed on something that would clear up a lot of debates); the important questions are what do we want a FAI to do if we build one, and what we anticipate others to tell their FAIs to do.
You’re treating resources as one single kind, where really there are many kinds with possible trades between teams
I think this is reasonably realistic. Let R signify money. Then R can buy other necessary resources.
But my point was exactly that there would be many teams who could form many different alliances. Assuming only two is unrealistic and just ignores what I was saying.
We can model N teams by letting them play two-player games in succession. For example, any two teams with nearly matched resources would cooperate with each other, producing a single combined team, etc… This may be an interesting problem to solve, analytically or by computer modeling.
You still haven’t given good evidence for holding this position regarding the relation between the different Uxxx utilities.
You’re right. Initially, I thought that the actual values of Uxxx-s will not be important for the decision, as long as their relative preference order is as stated. But this turned out to be incorrect. There are regions of cooperation and defection.
Analytically, I don’t a priori expect a succession of two-player games to have the same result as one many-player game which also has duration in time and not just a single round.
You’re treating resources as one single kind, where really there are many kinds with possible trades between teams. Here you’re ignoring a factor that might actually be crucial to encouraging cooperation (I’m not saying I showed this formally :-)
But my point was exactly that there would be many teams who could form many different alliances. Assuming only two is unrealistic and just ignores what I was saying. I don’t even care much if given two teams the correct choice is to cooperate, because I set very low probability on there being exactly two teams and no other independent players being able to contribute anything (money, people, etc) to one of the teams.
You still haven’t given good evidence for holding this position regarding the relation between the different Uxxx utilities. Except for the fact CEV is not really specified, so it could be built so that that would be true. But equally it could be built so that that would be false. There’s no point in arguing over which possibility “CEV” really refers to (although if everyone agreed on something that would clear up a lot of debates); the important questions are what do we want a FAI to do if we build one, and what we anticipate others to tell their FAIs to do.
I think this is reasonably realistic. Let R signify money. Then R can buy other necessary resources.
We can model N teams by letting them play two-player games in succession. For example, any two teams with nearly matched resources would cooperate with each other, producing a single combined team, etc… This may be an interesting problem to solve, analytically or by computer modeling.
You’re right. Initially, I thought that the actual values of Uxxx-s will not be important for the decision, as long as their relative preference order is as stated. But this turned out to be incorrect. There are regions of cooperation and defection.
Analytically, I don’t a priori expect a succession of two-player games to have the same result as one many-player game which also has duration in time and not just a single round.