Didn’t know calculating expectation would take this long… Consider $n$ i.i.d. random variables $X_i$ drawn from Power Law distribution with support lowerbound $x_\text{min} = 1$ and the shape parameter $\alpha > 2$—in other words, the pdf of $X_i$ being $$ f_{X_i}(x) = (\alpha - 1) x^{-\alpha }, $$ and $$ F_{X_i}(x) =1 - x^{-(\alpha - 1)} \quad \text{ for }x \ge 1. $$ Btw, for the heavy-tailed distribution family, it can be more comfortable (and general) to understand random variable $X$ as $$ \Pr[X > x] \sim x^{-\alpha}....

So are advertisement good or bad? There’s no fixed answer. One view says it’s great cause advertisers have to pay for ads—so only sellers who believe that their own products/services are of good quality will use ads (if ads price and the ads market adjust appropriately)—then ads become informative and useful signals, and they would help consumers distinguish valuable products out of the sea of alternatives. Another view is that ads are more like competitors for attention—and it becomes a bad equilibrium now when seller would have to buy ads to at least get any attention....

Four papers (topic) from the C&A (complexity & algorithms) workshop 2025 that I personally found interesting (or, perhaps, just understood), hosted by Sun Yat-Sen University, Guangzhou China. Two EconCS papers: Persuasive Calibration Yiding Feng and Wei Tang, 2025 (Arxiv link) The paper studies a persuasion problem consisting of an information sender and a receiver. It’s somewhat like information design—but calibration replaced commitment to an information policy. The model is restricted to a state in [0, 1] (unknown success probability of a Bernoulli experiment)....

I’ve blogged about Mendelssohn’s Scherzo from a A Midsummer Night’s Dream previously (two interesting Mendelssohn paraphrases—Rachmaninoff’s genius piano transciption of Mendelssohn’s incidental music). But today let’s talk about the piece itself, in its most authentic orchestral form. Mendelssohn is a big fan of Shakespeare and particular the Midsummer play. The composer’s sister Fanny explained it this way. “From our youth on we were entwined in A Midsummer Night’s Dream, and Felix [Mendelssohn] particularly made it his own....

My undergraduate advisor Pinyan Lu has published a special introductory column for theoretical computer science in the Communication of CCF (China Computer Federation). The Chinese version is available here. TCS field is not only home to many powerful tools (and brilliant minds), but it also boasts a beautiful, elegant philosophical methodology—a way of thinking that is deeply fundamental. Snippets from the article: [TCS has] its unique internal way of thinking. I believe that most work in theoretical computer science follows a three-step pattern:...

See previous post for the idea: My Ex, Apple PR, and the Economics of (Not) Buying an iPhone — for iteratively updated products like iPhone, do consumers strategically decide on Wait-to-Buy? It turns out that the market does anticipate upcoming product and update expectations w.r.t. new information. When Trump first announced the Tariff raise, Apple Pro Fans quickly reacts and adjusted their policy for iPhone Purchase: Should you buy an iPhone right now?...

Companies react strategically to tariff raise: Apple transported five planes full of iPhones and other products from India to the US in just three days during the final week of March. The urgent shipments were made to avoid a new 10% reciprocal tariff. Gadgets Now Although Apple’s headquater is in California, iPhones are manufactured overseas—China, India. Apple currently assembles the entire iPhone 15 and iPhone 16 lineups in India as well as China....

I always like attending job talks. You learn something, be awed by cutting edge research, and from time to time, reflect on skills of academic presentations… Today’s topic is Multi-Objective Optimization (MOO). When sometimes for an optimization problem there are two or more conflicting objectives (e.g. fairness vs. efficiency), it is not guaranteed that a single solution simultaneously optimizes each objective. Naturally, we consider Pareto Efficiency as a major concept for solution—a solution where none of the objective functions can be improved in value without degrading some of the other objective values....

When will we get a “XXX is all you need” paper published in an economic journal? (This comes from an ML paper ‘Attention is All You Need’, which introduced ‘Transformers’—the tech behind ChatGPT. Since then, there’s been a flood of papers claiming ‘X is all you need’ especially in computer science papers… ) source: Types of Machine Learning Papers Reddit

PhD in different fields is vastly different. A very successful computer science PhD students is often expected to graduate with at least 10 papers, while economic PhDs need only one. Math PhDs can even do without a paper. For anyone who is applying for or considering a PhD in economics, this book is a good start: Getting a PhD in Economics by Stuart J. HillmonConsidering a graduate degree in economics? Good choice: the twenty-first-century financial crisis and recession have underscored the relevance of experts who know how the economy works, should work, and could work....