# @stem_antics on Instagram

- **Type:** Video
- **Original URL:** https://www.instagram.com/p/Dd_m8PmAUwH
- **Gondola URL:** https://gondola.cc/posts/71131434-stem-antics-instagram
- **Thumbnail:** https://img.gondola.cc/tr:w-,h-,fo-auto/postThumbnails/e62cf1dbd9.jpg
- **Posted:** 2026-10-02T13:40:03.000+00:00
- **Account Owner:** Stem Antics (@stem_antics) — https://gondola.cc/stem_antics

## Caption

Adding a road can make traffic worse. Not as a figure of speech, but as a mathematical result.

In 1968, German mathematician Dietrich Braess showed that adding capacity to a network can increase travel time for everyone when each driver picks the route that is fastest for them alone.

The classic setup:

- 4,000 drivers travel from Start to End
- Route 1: a congested road where time = T/100 minutes (T = number of cars), then a fixed 45 minute highway
- Route 2: the same two roads in the opposite order, 45 minutes fixed first, then T/100
- At equilibrium the drivers split 2,000 and 2,000, so every trip takes 20 + 45 = 65 minutes

Now add a free shortcut, a zero minute link joining the two congestion-dependent roads.

- Every driver sees that the variable road beats the 45 minute highway
- Everyone takes variable road, shortcut, variable road
- Each variable segment now carries all 4,000 cars, so the trip is 40 + 0 + 40 = 80 minutes
- No single driver can improve by switching back, so the system settles at a worse state

This is a Nash equilibrium that is not socially optimal. Individually rational choices produce a collectively worse outcome.

Why it matters:

- Network design is not just about adding capacity
- Selfish routing and system-optimal routing are different problems
- For linear congestion costs, Roughgarden and Tardos proved selfish routing is at most 4/3 worse than the optimum, a bound known as the price of anarchy
- The same math appears in power grids, data networks, and mechanical systems

The engineering lesson: when agents optimize independently, adding a link can quietly add new failure modes.

#stemantics #braessparadox #gametheory #networkscience #transportationengineering

## Stats

- **Views:** 8,361
- **Likes:** 72
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- **Comments:** 1

## Tags

transportationengineering, networkscience, gametheory, braessparadox, stemantics

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