Ambiguity in election games

We construct a model in which the ambiguity of candidates allows them to increase the number of voters to whom they appeal. We focus our analysis on two points that are central to obtain ambiguity in equilibrium: restrictions on the beliefs that candidates can induce in voters, and intensity of voters' preferences. The first is necessary for a pure strategy equilibrium to exist, while the second is necessary for ambiguity in equilibrium when there exists a Condorcet winner in the set of pure alternatives (e.g. the spatial model of electoral competition), and when candidates' only objective is to win the election. In this last case, an ambiguous candidate may offer voters with different preferences the hope that their most preferred alternative will be implemented. We also show that if there are sufficiently many candidates or parties, ambiguity will not be possible in equilibrium, but a larger set of possible policies increases the chance that at least one candidate will choose to be ambiguous in equilibrium.