Party competition for votes in free and fair elections involves complex interactions by multiple actors in political landscapes that are continuously evolving, yet classical theoretical approaches to the subject leave many important questions unanswered. Here Michael Laver and Ernest Sergenti offer the first comprehensive treatment of party competition using the computational techniques of agent-based modeling. This exciting new technology enables researchers to model competition between several different political parties for the support of voters with widely varying preferences on many different issues. Laver and Sergenti model party competition as a true dynamic process in which political parties rise and fall, a process where different politicians attack the same political problem in very different ways, and where today's political actors, lacking perfect information about the potential consequences of their choices, must constantly adapt their behavior to yesterday's political outcomes.