Real Candidacy Games: A New Model for Strategic Candidacy

We introduce Real Candidacy Games (RCGs)---a novel strategic candidacy model, where candidates have a continuous range of positions that affect their attractiveness for voters. We also allow candidates to have their own non-trivial preferences over the candidate set. We study RCGs with restricted and unrestricted positioning strategies to establish conditions for Nash Equilibrium (NE) existence. That is, we investigate under what voting rules and tie-breaking schemes, a stable candidate positioning exists. While for several voting rule classes (e.g., Condorcet-Consistent) we obtain positive results, we also show that for some scoring rules there are examples without a NE for an arbitrarily large number of voters.