Bimatrix game equilibrium via nonlinear programming
These lecture notes (PDF) from Asu Ozdaglar give a bilinear program whose solution is the mixed-strategy equilibrium for a two-player, non-zero-sum game with finite action spaces—also known as a bimatrix game. I wanted to reproduce this highly practical result in a more accessible format and offer some implementation notes.
Advanced café techniques
Most cafés have separate lines for placing your order and picking it up. After you order, you move to the next line, and since drinks come out in more or less the order they were requested, the barista usually announces your drink around the time you get to the front of the second line.
However, for simple drinks like drip coffee, all the barista has to do is fill the cup, so they can often hand it to you right at the order counter. This also applies to pastries. If you are a rule-follower and immediately move to the second queue after ordering one of these items, it can actually slow things down, because your drink will typically be ready before those of the people ahead of you in line, and you’ll need to elbow your way to the front.
Advanced combinations such as “coffee and a hot croissant” are marginal. This could be a one- or a two-queue order. Such situations require careful planning and deft execution.
Driver’s ed should teach error recovery
I live near a one-way street, and drivers keep turning into it the wrong way by mistake. Most react by getting flustered and backing dangerously into the arterial, perhaps following an instinct to “undo” the error. The safer solution (in my eyes) is to park the car, wait for traffic to clear, then use a driveway to point yourself in the right direction.
Unfortunately, driver’s ed doesn’t teach you how to recover from mistakes like this—at least, mine didn’t. Instead, driver’s ed teaches the rules of the road and how to follow them. Once you have violated the law, even if by accident, you are in undefined territory. Hence, drivers develop a strong impulse to immediately “reverse” errors rather than identify a safe course of action.
Sports idea
A footrace, but the objective is to run as far as possible in a fixed amount of time rather than speeding through a fixed distance. The catch is that the time limit is drawn randomly at the start of the race, so you cannot strategize around it being a sprint or distance event.
I think a good choice of distribution would be an log-normal distribution with a mean of around four or five minutes and a fairly high variance. Perhaps we could clamp the maximum time at eight hours, out of respect for the athletes’ work-life balance.
I ran (ha) this idea by a friend who is a competitive marathoner and he said, “That sounds like hell.” This makes me think I am really onto something, because many popular sports sound like hell to those who are not yet good at them.
New logo
I created a new logo for the site today:
The old one was just a square with my initials, MK, which seemed a little too self-indulgent (not to mention that I share these initials with half of my extended family, so I can hardly claim them as my own):
The new logo still kind of forms a stylized letter m, if you imagine the three theme-colored vertical segments as hanging from the horizontal segment on top. It also kind of recalls the shape of the word Ill, which spells the start of the blog title and doubles as a fun bit of retro slang.