3y19

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...

93y

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.

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)