To be specific, in the Dawes, Tomes, Mousely, Grubbs Fidelity Fiduciary Bank. http://elliotlipnowski.com/
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I think there’s still an opportunity for price discrimination since the thing you’re screening on is how much time people are happy to spend on consuming the same content. And extra steps take time—so it’s similar to coupon clipping as price discrimination.
My reasoning: the marginal cost is negligible relative to revenue, so it's a demand question. I think charging more to listen double-speed is effective price discrimination, since I would guess the people that want the fast version are less price-elastic.
This could be an argument for fairness of the "=rp" answer.
Your way of phrasing is way better: if I listen to a book at double speed, should Spotify want to charge me more (>rp), less (
I think I disagree, but I’m curious about your reasoning.
Thank you!
Fun micro #econsky problem set question: If p is the price Spotify charges for unit-speed listening (replacing a budget with a price for simplicity) and r>1, should they price r-speed listening =rp, >rp, or
Spotify account gives a budget of audiobook hours before needing to pay for more hours, but if you listen to a 10-hour book at double-speed (so 5 listening hours), it counts as 10 hours of your budget. So they price r-speed listening at exactly r times that of unit-speed listening.
Wednesday Addams is fashionable af
Boat question.
Schumer, Jeffries propose strongly-worded letter to counter RFK Jr.'s purge at the CDC.
I was under the impression these were called "siblings"
I didn’t know this!
I should check!
A kind of mechanical approach modifies Hart and Schmeidler's program to check, for every product set B of action profiles, whether some strict CE has marginal supports B_i. Then A^S is the largest B that passes the test (or empty if nothing does). But there must be something more interpretable!
1) The set CE^S is convex. 2) There's a product set A^S of action profiles such that (i) CE^S is contained in Δ(A^S), and (ii) if CE^S is nonempty, then something in CE^S has support A^S. 3) The closure of CE^S is just the intersection of CE and Δ(A^S). So it all comes down to what A^S is.
Has anybody developed the theory of STRICT correlated equilibria of a finite game? #econsky #mathsky #ECsky #TCSsky I was playing around with it a bit, and here are some things that are easy to show about the set CE^S of strict correlated equilibrium distributions.
Thank you! This is all super helpful.
The set of textbooks not being a lattice, it could be that so such textbook exists.
Probably the ideal book would have Stone duality as an advanced chapter? But I don’t really know enough to know what I want. I suspect I want the least advanced book among those that (1) defines a distributive lattice, and (2) has the word “continuous” somewhere in it.
Seeking #mathsky book recs. I want a good textbook on basics of partial orders, lattices, and interactions of the same with basic topological notions like compactness. Does anybody have any book they like?
Perfect!
Fun, imprecise #mathsky question: Give a "nice" characterization of which subsets X of [0,1] are complete lattices. [Note, this is harder than the question of which X are complete *sub*lattices, and is much harder than the question of which X are lattices.]
Does anybody else here ever look for the ebook version because the hard copy is in another room?
It's nothing obscure—it's in Kallenberg. But I just saw for the first time today. - By orthogonal projection, an L2 RV x admits a conditional expectation T(x). - By Jensen or direct argument, T is (weakly) L1-contractive. - But L2 is dense in L1, so T extends to (bounded linear map on) L2.
A tiny #mathsky note on conditional expectations. I'd previously seen two standard existence results of different strengths: a) For square-integrable RVs (L2) via a super easy Hilbert space argument. b) For integral RVs (L1, a bigger class) via Radon-Nikodym—harder! But (a) can actually prove (b)!
Some recommended Independence Day #econsky reading
Everywhere I go, children gleefully throw things at me
Seeing how my kids fare in racing other kids at the playground is a VERY clear paternity test
This sounds cool! I don't know anything about "services". Will try to figure it out.
During grad school, saw Bob Balaban three times in NYC, in three different neighborhoods. Once in a cafe, once on a bus, once on a subway.
Well now you have the twitter interaction as a distinct entry.
How do you use LaTeXit for email? You just copy-paste math images into email?
LaTeX for gmail is no longer supported!!! 😭 Does anybody have any easy solutions to help me quickly write math in emails? #mathsky
This sounds really cool!
Thank you! Will check this out.
Wanted: a program that will read me a mathematical paper in audio. Obviously best if it’s smart about (e.g.) when the symbol “X” should be pronounced “ex” and when it should be pronounced “big ex”. Has anyone in our brave new LLM world made this?
I often make myself a lemma DAG as a refereeing aid when I’m refereeing a paper with intricate proofs. This thought came up when I made one for coauthors, we decided to put it in the paper, and I thought “It’d be cool if this were standard/easy to put in every theory paper.”
😱
@jasonhartline.bsky.social, you promised me yesterday that if I posted stuff here, you'd like it
When you ask a computer scientist to tell you their model
It’s obscene
Does anybody else sometimes try to reprove math results they've "known" for years just to feel something?
Why? - That language is known to be o-minimal, meaning the only definable subsets of the reals in that language are unions of finitely many intervals. - The set {t: exp(it)=1} is an infinite discrete set.
Fun, easy-but-a-bit-surprising #mathsky fact: there's no way to describe the complex-to-complex exponentiation function in terms of {0,1,+,x,<, and, or, not, exists} and the real-to-real exponential function.
Whether it’s Barack Obama wearing a tan suit to a press conference or Donald Trump running a multi-billion dollar crypto scam from the White House, both men tested the limits of presidential propriety.
Papal duties have really gotten too expansive for one person
The average American has three friends
Weird phenomenon when working in applied mathematical fields: just learning that an object has a NAME is already a nontrivial advance. The reason is that various objects happen to show up in our one-off papers, but then having a name can mean some math nerds have developed a general theory of it.
The dynamic moral hazard model is pretty cool
What I *hope* is inflatable Jesus
Kevin Sorbo for some reason
This reply is so versatile
Tangentially relatedly, I only recently realized how weird it was that we would sing the Canadian and Israeli national anthems every morning. (It's not weird that we sang Jewish prayers—it's a Jewish summer camp!—but a national anthem is not a prayer.)
I guess the community this specific summer camp serves is right-of-center (compared to the median Israeli) on all things Palestine, but expressing a political view "off the job" shouldn't be disqualifying! I don't know why I feel a need to vent, especially since none of my followers know this camp.
I'm on an email list for the Winnipeg Jewish summer camp I went to as a kid. It seems they just fired the camp director (who I remember being a camper when I was a counselor there—fuck I feel old) for *liking* a "Free Palestine" post on social media somewhere. This seems bananas to me.
WE ARE BACK next week!!! On Thursday, 24 April 2025, Alexander Wolitzky (MIT) will present "Marginal Reputation" (joint work with Daniel Luo). Our guest panellists: Jeff Ely and Elliot Lipnowski. Share the news! @jeffely.bsky.social @elliotlip.bsky.social
Underrated benefit of a standing desk: when I (regularly) spill an entire cup of water on my desk, the desk/floor/computer/papers get soaked but I stay happily dry
Is it just me, or is the shinier tracking/comment function in Overleaf way less usable than the one we had a couple months ago?
congratulations to all basketball teams. i’ll never know how you get the ball to bounce like that but whatever you’re doing, keep doing it
3yo needs to work on his “yes and” technique
Yeah, you can download source code on arXiv.
Holy shit, thank you! Excited to try this out.
here you go lemmatree.streamlit.app tried it on a random paper i found on arxiv econ.th ; seems to work fine
Great question! This seems like it should be much easier to do with TeX. I'd already be happy if I could do with with access to the TeX (to use for my own papers), but I'd be extra happy to do it with access only to the PDF (as a reading/refereeing aid).
This likely goes without saying, but I just tried asking free ChatGPT to do this with a paper and it failed dismally.
Somebody should make a tool that takes a mathematical paper and autogenerates a "lemma flowchart" that depicts which lemmas etc. are direct inputs to which other results.
Cancel-worthy take: we just bought a variety of Girl Scout cookies, and they’re really nothing special. Like, every flavor is clearly worse than an Oreo.
defining additive scoring rules
Hart (1985) characterizes NE payoffs in this exact setting, and there are papers that study sequential rationality with *discounted* payoffs in this or related settings. But I'm specifically interested in sequential rationality (which could bind off-path) without discounting.
Game theory question: Has anybody studied equilibria with some sort of SEQUENTIAL rationality constraint in two-player undiscounted infinitely repeated games with one-sided incomplete information and perfect monitoring?
I can afford the fattiest cheeses, and my grocery budget reflects that
A little disheartening to realize TV characters I used to code as “big fat guy” when I was younger are now similarly proportioned to me
Is "Ain't No Mountain High Enough" a modal claim or merely a topographical observation?
Will listen!
Haven't read this yet, but looks interesting from the abstract spaces-cdn.owlstown.com/blobs/xswqjf...
In the US, dynamic programming (specifically, the hazards of omitting a transversality condition) enters every election.
Economist Mark Carney is in the race for Prime Minister. He was accused of plagiarism because standard terms in the model setup look like in other papers. There’s a newspaper quote from Meg Meyer (who I didn’t know was his advisor) clarifying that it’s not sketchy.
(I know you’re being funny, but I’m anxious about fucking around on this point)
No she isn’t
My hero of an American-working-in-the-UK economic theorist being quoted as a character witness in the Canadian federal election was not on my bingo card
A very old Soviet joke, from an especially dark time: Foxes are fleeing the USSR in droves. Q: Why are you running away? Fox: The Soviets passed a new law that they’re going to arrest all camels. Q: But you’re foxes! Fox: Yeah, why don’t *you* try proving to the NKVD that you’re not a camel.
I don’t think so. My preferred pronunciation of u_i(x|y) is “the utility of x given y”.
So I think we should start using u_i(a_i | a_{-i}) for the first one. Then, in my example: - Payoff u_2(x,y) will mean 1 uses x and 2 uses y. - Payoff u_2(x|y) will mean 1 uses y and 2 uses x.
Notation idea for game theory. - It's convenient to use notation u_i(a_i, a_{-i}) for the profile with i using a_i and others using a_{-i}. - It's convenient to order players and let a=(a_1,...,a_n). - These conventions can conflict: e.g. in a symmetric game, which payoff is u_2(x,y) talking about?
Gonna rename my proof appendix "Choreography and Merriment"
Some do theory as a super efficient way of avoiding it
A word of #mathsky advice: if you used duality an even number of times, you probably didn't need to use duality.
I feel like a CS person is more equipped to answer that, no? Basically take your caricature of everything you don't like about the median talk by an economist and say "don't do that".
May especially be of interest to #ECsky folks
This seems like a cool #econsky paper
Nobody’s too hot for that book
I just tried to read 3yo a book. He proclaimed “I’m too hot for this book” and walked away, and honestly I can relate.
Key & Peele's baby Forest Whitaker sketch is one of the more honest portrayals out there of the parenting experience
Burt’s got a fever, and the only prescription is more Cobel
Okay, we get it, the US medical system isn't perfect
Even static games of pure common interest can have Pareto dominated equilibria. So the thing I'm struck by here is how, once the game is discontinuous at infinity, Perfect Information seems to lose some of its wow factor.
Yes! I thought of this example when I was playing around with variants of the simple one-player counterexamples of the OSD principle. But note that this example (though @yesthatsme.bsky.social gives a nice proof it also relies on discontinuity at infinity) doesn't hinge on failure of OSD principle.
