Several species of simultaneously hermaphroditic seabasses living on coral reefs mate by alternating male and female roles with a partner. This is known as egg trading, one of the classic and most widely cited examples of social reciprocity among animals. Some of the egg-trading seabass species, including the chalk bass, Serranus tortugarum, switch mating roles repeatedly, having subdivided their clutch of eggs into parcels offered to the partner for fertilization. Here we attempt to understand these dynamics as a pair of evolutionary games, modifying some previous approaches to better reflect the biological system. We find that the trading of egg clutches is evolutionarily stable via byproduct mutualism and resistant to invasion by rare individuals that take the male role exclusively. We note why and how parceling may reflect sexual conflict between individuals in the mating pair. We estimate evolutionarily stable parcel numbers and show how they depend on parameter values. Typically, two or more sequential parcel numbers are evolutionarily stable, though the lowest of these yields the highest fitness. Assuming that parcel numbers are adjusted to local conditions, we predict that parcel numbers in nature are inversely related both to mating group density (except at low density) and predation risk.