That’s a very beautiful and imaginative idea! I have a couple questions about the next post you’re going to write, hope they’re not too far off the mark.
For games with multiple Nash equilibria, do the different reflective assignments correspond to different methods of equilibrium selection? Does that mean that bargaining problems, like the ultimatum game, get “outsourced” to the oracle?
In the symmetric Prisoner’s Dilemma, will your framework lead to mutual defection?
The reflective assignments correspond very directly to Nash equilibria (albeit in an n-to-1 manner, because given any finite game, a reflective assignment contains information about that game but also information about many other things). So I wouldn’t quite say that they correspond to methods of equilibrium selection—e.g., if two methods of equilibrium selection give you the same Nash equilibrium, they’re not distinguishable on the level of reflective assignments. But yeah, the question of what equilibrium gets played gets outsourced to the oracle.
And yeah, since these agents play Nash equilibria, they will defect on the symmetric PD. (I’m not advocating this as a desirable feature. :-))
Now I’m wondering how this compares to Paul’s probabilistic reflection. Are there some nice “consistency” axioms that are satisfied by one approach but not the other, or vice versa?
That’s a very beautiful and imaginative idea! I have a couple questions about the next post you’re going to write, hope they’re not too far off the mark.
For games with multiple Nash equilibria, do the different reflective assignments correspond to different methods of equilibrium selection? Does that mean that bargaining problems, like the ultimatum game, get “outsourced” to the oracle?
In the symmetric Prisoner’s Dilemma, will your framework lead to mutual defection?
Thanks! :-)
The reflective assignments correspond very directly to Nash equilibria (albeit in an n-to-1 manner, because given any finite game, a reflective assignment contains information about that game but also information about many other things). So I wouldn’t quite say that they correspond to methods of equilibrium selection—e.g., if two methods of equilibrium selection give you the same Nash equilibrium, they’re not distinguishable on the level of reflective assignments. But yeah, the question of what equilibrium gets played gets outsourced to the oracle.
And yeah, since these agents play Nash equilibria, they will defect on the symmetric PD. (I’m not advocating this as a desirable feature. :-))
Now I’m wondering how this compares to Paul’s probabilistic reflection. Are there some nice “consistency” axioms that are satisfied by one approach but not the other, or vice versa?