Non-convergent Nash equilibria on a circular market

We use the Hotelling-Downs spatial model of competition to investigate the behavior of competing firms when the location space is a circle. Unlike the standard Hotelling-Downs model we assume that customers with some probability buy from retailers other than the closest one. We characterise convergent Nash equilibria and non-convergent Nash equilibria depending on the vector of those probabilities.

Supervised by Professor Arkadii Slinko.