@JohnBaez I mean \(\cup\) as in ordinary union of ordinary sets, which might or might not have some elements in common. See posts #122 and #124 by @OwenBiesel. (You could say that they are both subsets of a set theoretic universe, but that's serious…
Question I just thought of: Given preorders \(X\) and \(Y\), define a new one \(X \oplus Y\) to be the transitive closure of \(X \cup Y\), i.e. the 'smallest' preorder that contains both \(X\) and \(Y\). What properties does this satisfy? (Also, doe…
I apologise @Justin, I also mixed up 'total' with 'not pre-'. Nevertheless, in a standard proof system (such as for propositional logic) derivability is not even a total preorder. (Yes, this sounds like the right term.) Pick two different atomic pro…
Regarding the meaning of equilibrium in economics, I'm one of the terrible people who says "we do it because it's mathematically convenient". Of course I don't believe that markets settle to general equilibrium in real life, or even that people play…
@Joseph, 'completeness' means that everything true (in some semantics) is provable (in some proof system). (It's a property of a pair consisting of a semantics and a proof system.) The proof systems in which everything is derivable from everything a…
Belatedly, yet another preorder: In an \(n\)-player non-cooperative game, outcomes live in \(\mathbb R^n\). Player \(i\) has a preference relation \(\geq_i\) on \(\mathbb R^n\) given by \(x \geq_i y\) iff \(x_i \geq y_i\), i.e. they prefer to maximi…
PS. @Bob Be careful about the reasoning "smart iff predicted recession" about economists. There are lots of economists making lots of predictions, and you risk perception bias. Many economists also take the safe option and deny their models have any…
Hi all! Pleased to meet you... let me know if I can help in any way.
The 'preferred' introduction paper to open games is https://arxiv.org/abs/1603.04641 . If you don't have the necessary background for it now, you definitely will before the end of…