<p>This game has been studied in</p>

<blockquote>
  <p>Hee-Kap Ahn, Siu-Wing Cheng, Otfried Cheong, Mordecai Golin, René van Oostrum:<br>
  "Competitive facility location: the Voronoi game"<br>
  Theoretical Computer Science 310, 2004, pp 457-467</p>
</blockquote>

<p>There also are lots of follow-up works, as for instance</p>

<blockquote>
  <p>Sayan Bandyapadhyay, Aritra Banik, Sandip Das, Hirak Sarkar:<br>
  "Voronoi game on graphs"<br>
  Theoretical Computer Science 562, 2015, pp 270-282</p>
</blockquote>

CC BY-SA 3.0
2015-03-22T01:19:06.903Z
Still wondering -- has it been studied for $> 2$ players?
usul
CC BY-SA 3.0
2015-03-21T18:52:14.010Z
2015-03-21T18:52:14.010Z
Gamow
<p>Suppose that several agents need to place points (one per
agent) on the interval $[0,1]$. An agent's goal is to maximize the
volume of the Voronoi cell that contains his point. When $n$ agents must
place their points sequentially, is an optimal strategy known?</p>

<p>From what I was able to glean from the literature so far, it appears I am asking for the Stackelberg solution to an $n$-player Hotelling's game on a segment.</p>

CC BY-SA 3.0
2015-03-20T11:17:32.463Z
I am not asking people to solve this question for me, just wondering what is known about it -- and the obvious extension to 2 dimensions.
Aryeh
CC BY-SA 3.0
2015-03-20T13:15:51.543Z
I think these are usually called *Voronoi games*. I don't know much about them, but I think by searching that keyword you can find out what is known.
usul
CC BY-SA 3.0
2015-03-20T13:32:25.507Z
Thanks! I was only able to find references for 2-player Voronoi games.
Aryeh
CC BY-SA 3.0
2015-03-20T13:36:26.463Z
There may only be research for the 2-player case (don't know)....
usul
<gt.game-theory>
Stackelberg solution to $n$-player Hotelling's game on a segment
Aryeh
# Stackelberg solution to $n$-player Hotelling's game on a segment

(Asked by: username_0 on 2015-03-20)

Suppose that several agents need to place points (one per
agent) on the interval $[0,1]$. An agent's goal is to maximize the
volume of the Voronoi cell that contains his point. When $n$ agents must
place their points sequentially, is an optimal strategy known?

From what I was able to glean from the literature so far, it appears I am asking for the Stackelberg solution to an $n$-player Hotelling's game on a segment.

**Tags:** gt.game-theory

> **Comments:**
> **username_0**: I am not asking people to solve this question for me, just wondering what is known about it -- and the obvious extension to 2 dimensions.  
> **username_1**: I think these are usually called *Voronoi games*. I don't know much about them, but I think by searching that keyword you can find out what is known.  
> **username_0**: Thanks! I was only able to find references for 2-player Voronoi games.  
> **username_1**: There may only be research for the 2-player case (don't know)....  

---

## 1 answers

### Answer by username_2 on 2015-03-21. Score: 4 | Accepted answer

This game has been studied in

> Hee-Kap Ahn, Siu-Wing Cheng, Otfried Cheong, Mordecai Golin, René van Oostrum:  
> "Competitive facility location: the Voronoi game"  
> Theoretical Computer Science 310, 2004, pp 457-467

There also are lots of follow-up works, as for instance

> Sayan Bandyapadhyay, Aritra Banik, Sandip Das, Hirak Sarkar:  
> "Voronoi game on graphs"  
> Theoretical Computer Science 562, 2015, pp 270-282

> **Comments:**
> **username_1**: Still wondering -- has it been studied for $> 2$ players?  

---

