We demonstrate that the Hotelling–Downs model with runoff voting always admits symmetric mixed strategy equilibria for any (even or odd) number of office-motivated candidates (provided they are at least four). In specific, (a) we show that the game does not admit any symmetric atomless...

This paper characterizes a unique mixed strategy Nash equilibrium in a one-dimensional Downsian model of two-candidate elections with a continuous policy space, where candidates are office motivated and one candidate enjoys a non-policy advantage over the other candidate. We show that if...

We know that a) two-player symmetric zero-sum games with non-empty equilibrium sets always admit symmetric equilibria and that b) two-player and multiplayer symmetric non-zero-sum games might have only asymmetric equilibria (Fey, 2012). But what about multiplayer symmetric zero-sum games? This...