This notion of dependency seems too binary to me. Concretely, let’s modify your example from the beginning so that P3 must grant an extra 10−10 utility to either P1 or P2, and gets to decide which. Now, everyone’s utility depends on everyone’s actions, and the game is still zero-sum, so again, so any strategy profile with p=q will be a stratified Pareto optimum. But it seems like P1 and P2 should ignore still ignore P3.
I agree with this. I think that the most interesting direction of future work is to figure out how to have better notions of dependency. I plan on writing some on this in the future, but basically we have not successfully figured out how to deal with this.
This notion of dependency seems too binary to me. Concretely, let’s modify your example from the beginning so that P3 must grant an extra 10−10 utility to either P1 or P2, and gets to decide which. Now, everyone’s utility depends on everyone’s actions, and the game is still zero-sum, so again, so any strategy profile with p=q will be a stratified Pareto optimum. But it seems like P1 and P2 should ignore still ignore P3.
I agree with this. I think that the most interesting direction of future work is to figure out how to have better notions of dependency. I plan on writing some on this in the future, but basically we have not successfully figured out how to deal with this.