The classical spatial model, first formulated by Hotelling (1929), focused on competition between two agents (interpreted either as business firms or political parties). Although competition between more than two agents was considered soon thereafter (for example, Chamberlain 1933), only in the last decade or so has sustained attention been paid to the multiagent case. This essay surveys the results of this attention, especially as regards competition between political parties or candidates for political office.

Broadly speaking, the literature divides into two streams: those works analyzing multi-item agendas, and those works dealing with elections in which more than two candidates or parties are competing. I shall focus on the second topic: models of multicandidate (or multiparty) electoral competition.

An increasingly important distinction among such models is that some models attempt to endogenize the number of candidates, letting the model predict what the equilibrium number should be, while others take the number of competitors as exogeneously given. In other words, some models allow entry, while others do not. Because Chapter 2 by Shepsle and Cohen covers the question of entry, I shall focus here on no-entry models. Such models are of course necessary parts of the more elaborate entry models, but they are also of interest on their own: The no-entry assumption accurately describes the situation of candidates in a race after the filing deadline (for getting names onto the ballot) has passed. It is true that the possibility of write-in campaigns exists, but it is also true that such campaigns are usually of negligible importance. No-entry models should therefore be useful in investigating the incentives of candidates in the post-filing stage of the campaign.