Electoral equilibria with restricted strategies

We construct a spatial election model in which candidates inherit initial positions in the strategy space, presumably from previous political activity, and they are restricted to strategies close to their initial positions. We establish sufficient conditions for the existence of an equilibrium. The equilibrium need not entail an expectation of a zero plurality for each candidate. We then apply this model to a sequence of elections in which a series of opposition candidates challenge incumbents. Given certain regularity conditions, the result will be an apparent incumbency advantage, corresponding to that observed in recent congressional elections.