The Theory of Honest Signalling

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Introduction: Part 1

Introduction: Part 2

The Basic Problem

The Basic Solution

Honest signalling in biology

Zahavi's handicap principle

Grafen's model

Attracting mates

Begging for food

Deterring predation

Contesting resources

Autumn color

Honest signalling in economics

Conspicuous consumption


The mathematics of honest signalling

Signalling as a game


Other resources

Carl T. Bergstrom

Using Mathematica

Contact Information

Department of Zoology
University of Washington
Box 351800
Seattle, WA 98195-1800

Honest signals in biology: Grafen's costly signalling theory

Zahavi's original formulation of the handicap principle was rather vague with respect to precisely why costly signals were inherently believable. Several answers - or rather, interpretations of Zahavi's argument - were quickly put forward. Grafen (1990) classifies these; here I have modified his terms slightly.

  • "Strategic Choice" Handicap - The strategic choice form of the handicap principle is the form typically considered in the current empirical and theoretical literature. In this formulation (often referred to as "costly signalling" rather than "the handicap principle"), each signaller chooses how large of a handicap to produce, taking his own quality and the receivers' expected responses to handicap size into account. Because the cost of the handicap and/or the benefit of the receivers' responses varies from one signaller to the next, different signallers choose handicaps of different sizes.

  • Survival Handicap - possession of the handicap signal increases the risk of death; only high quality signallers survive. Signal receivers can tell handicapped signallers are of high-quality, because they have "proven themselves" simply by surviving.

  • Amplifier or "Revealing" Handicap - signallers expend effort in order to make it easier for signal-receivers to judge their quality. For example, it is easier to judge the quality of athletes when they are running a marathon than when they are tossing back Buds and watching Cheers reruns.

  • "Condition-dependent" Handicap - the handicap is some feature that only certain signallers (e.g., the high-quality ones) are capable of producing at all. For example, irridescent featres may be a signal of this sort, because without a nutritious diet, limited physical wear-and-tear, and low parasite load, shiny feathers are simply impossible to maintain.

Due in part to this multiplicity of interpretations, Zahavi's proposal was followed by vigorous debate in the scientific literature. A number of authors put forth models in attempts to show that the handicap principle would, or would not, work. Many of the early treatments (and some of the current studies) took the form of population genetic models, either two-locus or quantitative genetic. But these population-genetic treatments did not easily handle the huge number of strategies that are possible in signalling games. An alternative approach was needed to resolve the issue conclusively.

This alternative approach was provided in a landmark paper by Grafen (1990); this paper placed the handicap principle solidly in the realm of game theory. Grafen's insight was to view the handicap principle scenario as a communication game, and to ask when costly signals could be equilibrium strategies in this game. Costly signalling theory - the primary subject of this tutorial and arguably the dominant area of signalling theory in biology today - was born.

In the next few sections, we will consider some of the various messages that animals send using costly signals.

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Last modified September 4, 2002
Copyright © 2002 Carl T. Bergstrom