An ESS model of Zahavi's handicap principle is constructed. This allows a formal exposition
of how the handicap principle works, and shows that its essential elements are strategic.
The handicap model is about signalling, and it is proved under fairly general conditions
that if the handicap principle's conditions are met, then an evolutionarily stable
signalling equilibrium exists in a biological signalling system, and that any signalling
equilibrium satisfies the conditions of the handicap principle. Zahavi's major claims
for the handicap principle are thus vindicated. The place of cheating is discussed
in view of the honesty that follows from the handicap principle. Parallel signalling
models in economics are discussed. Interpretations of the handicap principle are compared.
The models are not fully explicit about how females use information about male quality,
and, less seriously, have no genetics. A companion paper remedies both defects in
a model of the handicap principle at work in sexual selection.