If being larger than competing conspecifics is important for fitness, then an unstable escalation of body size may result. In asexual populations, a cycling of sizes can occur but for sexual diploids, an irreversible size increase is more likely. Several factors can produce a stable distribution of sizes, but a single body size or even a narrow range of sizes cannot be stable. For example, enough environmental variance can produce stability without any genetic variability in the population. Or, with no environmental variance, a high cost of fighting between similar sizes or, for diploids, an increasing mortality with size may lead to a stable distribution of sizes. A game theory model is used to investigate the existence and form of a stable distribution of body sizes in a population.