Fisheries management strategies in which large fish are selectively targeted and younger, smaller fish are protected can lead to disruption of stocks, truncation of the population size spectrum, and impaired recruitment. Balanced harvesting is an alternative approach, which distributes fishing mortality across a wide range of species and sizes in proportion to their natural productivity. Here, we investigate outcomes from an agent-based model of fishing, coupled with an ecological model for the dynamics of a single fish species in a small-scale fishery. In the model, individual fishing agents make decisions about whether to enter or exit the fishery, and what size fish to target, based on economic calculations about short-term profitability of alternative actions. Fishing mortality, aggregated across agents, affects the biomass and size structure of the stock, which in turn affects individual agents' yields, creating a feedback loop. We show that the autonomous fishing agents self-organise to produce a Nash equilibrium, in which yields are equalised across agents. The aggregate fishing mortality that emerges in this equilibrium state is closely aligned with the distribution of productivity across body size. We conclude that balanced harvesting is an emergent outcome of the model. This occurs despite the absence of any externally imposed regulations on total fishing effort, catch or target sizes. However, controls on overall harvesting pressure are required to avoid overfishing.