Very nice. I had been thinking about doing this too, but you beat me to it.
In a subsequent post, I’ll critique these bargaining solutions, and propose a more utility-maximising way of looking at the whole process.
I’m guessing you are referring to Nash’s program here, and the Rubinstein bargaining process. Great. But if you are going to suggest an alternative to NBS and KSBS that is more “utilitarian” in spirit—well that would be interesting too.
But if you are going to suggest an alternative to NBS and KSBS that is more “utilitarian” in spirit—well that would be interesting too.
That’s what I’m suggesting; essentially it deals with how to maximise utility when you’re unsure about what games you’ll be playing. I’m still checking it, and ageing it.
I don’t think so; for instance, I don’t think Harsanyi’s solution is pareto-optimal—though I might be wrong about this, I’m not yet fully following it.
Well, if you think you can bargain to a Pareto-optimal solution, in a game with imperfect information, then I want to see that idea. Because with neither player having enough information to even recognize Pareto-optimality, I don’t see how their bargaining can bring them there.
Though perhaps you have a definition of Pareto-optimality in mind in which the optimality is “in the eye of the beholder”. Something like that might make sense. After all, in the course of bargaining, each party gains information about the state of the world, which may result in changes in their expected utility even without a change in objectively expected outcome.
Pareto-optimal in expected utility; and yes, “in the eye of the beholder”. The μSMBS I described http://lesswrong.com/lw/2xb/if_you_dont_know_the_name_of_the_game_just_tell/ are Pareto optimal (in the eyes of both players), even if they have different probability distributions over the games to be played (I put that in initially, then took it out as it made the post less readable).
Very nice. I had been thinking about doing this too, but you beat me to it.
I’m guessing you are referring to Nash’s program here, and the Rubinstein bargaining process. Great. But if you are going to suggest an alternative to NBS and KSBS that is more “utilitarian” in spirit—well that would be interesting too.
That’s what I’m suggesting; essentially it deals with how to maximise utility when you’re unsure about what games you’ll be playing. I’m still checking it, and ageing it.
Sounds like you are talking about Harsanyi’s Generalized Nash Bargaining Solution (pdf link).
I don’t think so; for instance, I don’t think Harsanyi’s solution is pareto-optimal—though I might be wrong about this, I’m not yet fully following it.
Well, if you think you can bargain to a Pareto-optimal solution, in a game with imperfect information, then I want to see that idea. Because with neither player having enough information to even recognize Pareto-optimality, I don’t see how their bargaining can bring them there.
Though perhaps you have a definition of Pareto-optimality in mind in which the optimality is “in the eye of the beholder”. Something like that might make sense. After all, in the course of bargaining, each party gains information about the state of the world, which may result in changes in their expected utility even without a change in objectively expected outcome.
Pareto-optimal in expected utility; and yes, “in the eye of the beholder”. The μSMBS I described http://lesswrong.com/lw/2xb/if_you_dont_know_the_name_of_the_game_just_tell/ are Pareto optimal (in the eyes of both players), even if they have different probability distributions over the games to be played (I put that in initially, then took it out as it made the post less readable).