# @stem_antics on Instagram

- **Type:** Video
- **Original URL:** https://www.instagram.com/p/DXp0EVDj3cQ
- **Gondola URL:** https://gondola.cc/posts/64883919-stem-antics-instagram
- **Thumbnail:** https://img.gondola.cc/tr:w-,h-,fo-auto/postThumbnails/3db3dc2d7c.jpg
- **Posted:** 2026-04-27T23:21:22.000+00:00
- **Account Owner:** Stem Antics (@stem_antics) — https://gondola.cc/stem_antics

## Caption

Three players place points on a gold bar of length 1, one after another. Each gets the portion closest to their point (a 1D Voronoi split). Everyone plays optimally.

What can Player 1 guarantee?

Start from the end.

Player 3 (last mover) will always place themselves to steal the largest available gap. They react, not commit.

Player 2 knows this. So instead of chasing the biggest immediate slice, they position to limit how much Player 3 can steal.

Now Player 1 has to think two steps ahead: “Where do I place so that even after both optimal responses, I still get the most?”

Key insight:
If Player 1 does NOT start in the middle, they lose control.

* Suppose Player 1 shifts left.
* Player 2 moves toward the larger right side.
* Player 3 then jumps to the far right endpoint.
* Result: Player 1 gets squeezed into a smaller region.

This always punishes imbalance.

But if Player 1 starts exactly at 1/2:

* Player 2’s best move is symmetric (slightly left or right of center)
* Player 3 takes the opposite extreme
* The interval splits into three equal regions

Final outcome under optimal play:
Each player gets 1/3.

So the answer:
Player 1’s maximum guaranteed share is 1/3, achieved by placing at x = 1/2.

Even though Player 1 moves first, optimal play from others erases the advantage. The game equalizes.

Call to action:
Would this still hold with 4 players? Or on a circle instead of a line? Drop your intuition and remix this with your own variant.

#STEM #GameTheory #Math #Quant #InterviewPrep Optimization Algorithms Voronoi JaneStreet

## Stats

- **Views:** 1,331
- **Likes:** 40
- **Shares:** 0
- **Comments:** 4

## Tags

gametheory, stem, math, quant, interviewprep

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