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All of Ghislain Fourny's Comments + Replies

Ghislain Fourny1y3

Thank you for your comment, Vladimir_Nesov.

It is indeed correct that "the result be BE" is a false proposition in the real world. In fact, this is the reason why they are called counterfactuals and why the subjunctive tense ("would have") is used.

Nashian game theory is based on the indicative tense, for example common knowledge is all based on the indicative tense (A knows that B knows that A knows etc). Semantically, knowledge can be modelled with set inclusion in Kripke semantics: A knows P if the set of accessible worlds (i.e., compatible with A's actua... (read more)

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2Vladimir_Nesov1y
What does "closest world to ω in which P is true" mean? Is this still data extracted from a Kripke frame, a set of worlds plus accessibility, or does this need more data ("some sort of distance")? What sort of distance is this, what if there are multiple worlds in P at the same distance from ω, possibly with different truth of Q? Keeping to the example at hand, what are the possible worlds/counterfactuals here, just the (row, column) pairs? Their combination with possibly-false-in-that-world beliefs? Something else intractably informal that can't be divided by equivalence for irrelevant distinctions to give an explicit description? What is the accessibility in the Kripke frame? What are the distances? Is "the result is BE" just the one-world proposition true in the world BE? If some of the assumptions in my questions are wrong (as I expect them to be), what are the worlds where "the result is BE" holds? What does it mean to enact row A in the situation where the result is BE (or believed to be BE)? Or is "he would have instead picked A rather than B" referring to something that shouldn't be thought of as enactment? (I meant it's false in the world where it's believed, where row A would be taken instead as a result of that belief, so that in fact in that world row A is taken rather than B, so that the belief that row B is taken in that world is false. I didn't mean to imply that I'm talking about the real world.)
Conflict vs. mistake in non-zero-sum games
Ghislain Fourny3y19

Dear Nisan,

I just found your post via a search engine. I wanted to quickly follow up on your last paragraph, as I have designed and recently published an equilibrium concept that extends superrationality to non-symmetric games (also non-zero-sum). Counterfactuals are at the core of the reasoning (making it non-Nashian in essence), and outcomes are always unique and Pareto-optimal.

I thought that this might be of interest to you? If so, here are the links:

https://www.sciencedirect.com/science/article/abs/pii/S0022249620300183

(public version of the accepted m... (read more)

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9Nisan3y
Oh, this is quite interesting! Have you thought about how to make it work with mixed strategies? I also found your paper about the Kripke semantics of PTE. I'll want to give this one a careful read. You might be interested in: Robust Cooperation in the Prisoner's Dilemma (Barasz et al. 2014) [https://arxiv.org/abs/1401.5577], which kind of extends Tennenholtz's program equilibrium.