We model a potentially mutualistic interaction between a species making antipredator alarm calls and a species which eavesdrops on those calls. Callers may or may not make deceptive alarm calls in order to kleptoparasitize food from eavesdroppers, which in turn may either heed or ignore all alarm calls. The two most likely outcomes in our model are either maximally deceptive callers and maximally trusting eavesdroppers, or persistently cycling strategy frequencies. The latter is favoured by low predator density, low density of any alternative honest alarm-calling species, ability of eavesdroppers to preferentially heed calls when costs of doing so are low and, in some cases, low food availability.