To trade, or not to trade; that is the question

The black hamlet is a simultaneous hermaphrodite fish that does not fertilize its own eggs and whose reproductive success is strongly related to the number of eggs of other fish that it fertilizes. Its own eggs are an inducement to other fish to let the fish fertilize their eggs. Consequently, the hamlet engages in egg trading, a mating process in which one fish lets another fertilize its eggs in exchange for allowing it to fertilize the eggs of the other fish. It would be in a fish’s interest if the partner would spawn first allowing the fish to fertilize the eggs of the other fish while keeping its own eggs as a bargaining chip to make the same arrangement with another fish. Such behavior might not be viable in the long run, as the “gullible” fish would suffer low reproduction rates as compared with the “sophisticated, selfish” fish. Eventually, the latter would have only its own sort to deal with, which might even hamper the mating process. In addition, if male fish could participate in such a process, then male specialization might be more profitable than being an hermaphrodite. Instead of the preceding scenario, the hamlets egg trade under circumstances in which it is important to use time well. The egg trading process involves two fish spawing alternately, perhaps five or six times each. As a result the fish that spawns first has little at risk. The process is carried out slowly enough that neither fish has an incentive to “kiss and run.” The purpose of this paper is to model the hamlets’ mating as a game in which their chosen behavior is an equilibrium. We investigate two issues in particular: (1) Is it in the interest of an hermaphrodite fish to behave in a way that sustains the behavior that they follow? (2) If it were possible for hamlets that were specialized as males to deceive hermaphrodites into egg trading, would a population be sustainable in which such males were a significant fraction of the total?