OK, I think that is clearer now. I assume you think the strategy to coordinate on should be determined by maximizing the planning utility function. Not by maximizing the action utility function nor finding the stable point of the action utility function. I agree with all of this.
The difference is that you think the self-locating probabilities are valid. The action utility function that uses them is valid but can only be used in superficially similar problems such as multiple drivers being randomly assigned to intersections.
While I think self-locating probabilities are not valid, therefore the action utility functions are fallacious. Whereas in problems where multiple drivers are randomly assigned to intersections, the probability for someone assigned to an intersection is not self-locating probabilities.
Pretty close. I do think that self-locating probabilities can be valid, but determining the most relevant one to a given situation can be difficult. There are a lot more subtle opportunities for error than with more familiar externally supplied probabilities.
In particular, the way in which this choice of self-locating probability is used in this scenario does not suit the payoff schedule and incentives. Transforming it into related scenarios with non-self-locating probabilities is just one way to show that the problem exists.
OK, I think that is clearer now. I assume you think the strategy to coordinate on should be determined by maximizing the planning utility function. Not by maximizing the action utility function nor finding the stable point of the action utility function. I agree with all of this.
The difference is that you think the self-locating probabilities are valid. The action utility function that uses them is valid but can only be used in superficially similar problems such as multiple drivers being randomly assigned to intersections.
While I think self-locating probabilities are not valid, therefore the action utility functions are fallacious. Whereas in problems where multiple drivers are randomly assigned to intersections, the probability for someone assigned to an intersection is not self-locating probabilities.
Pretty close. I do think that self-locating probabilities can be valid, but determining the most relevant one to a given situation can be difficult. There are a lot more subtle opportunities for error than with more familiar externally supplied probabilities.
In particular, the way in which this choice of self-locating probability is used in this scenario does not suit the payoff schedule and incentives. Transforming it into related scenarios with non-self-locating probabilities is just one way to show that the problem exists.