#### Background.

The Hotelling game, originated in Hotelling’s seminal work in 1929 [@hotelling1929stability], modeled the competition of two servers on a linear market (e.g., two ice-cream vendors on a beach strip) as follows. Two servers choose a location on the line segment $[0,1]$, and the payoff of each server is equal to the length of the segment of points closer to it than the the other server (a.k.a. its Voronoi cell). Hotelling showed that if both servers locate themselves at the center of the line, then a Nash equilibrium would be reached, i.e., a situation in which neither server would rather relocate unilaterally. He next showed that three servers competing on the line reach no equilibrium state - in every configuration of servers there will be one server who can increase its profit by moving.

![Ice cream vendors on a beach strip.[]{data-label="fig:ice-cream"}](figs/ice-cream-vendors.jpg){width="50.00000%"}

#### Background.

The Hotelling game, originated in Hotelling’s seminal work in 1929 [@hotelling1929stability], modeled the competition of two servers on a linear market (e.g., two ice-cream vendors on a beach strip) as follows. Two servers choose a location on the line segment $[0,1]$, and the payoff of each server is equal to the length of the segment of 