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

Signalling as a strategic game

Loosely speaking, a signal can be defined as a behavior or phenotype produced by one individual (the signaller) that serves to influence the behavior of a second individual (the signal receiver) by transmitting information. As discussed by Maynard Smith and Harper (1995) - who consider in detail the terms and definations associated with signalling - this definition highlights two important aspects of signalling:

  • Signals carry information from a signaller to a receiver.
  • Signals influence receiver behavior.
Thus every instance of communication can be viewed as fundamentally game-theoretic process: in communication, two individuals choose actions (signal and response, respectively), the payoffs of which depend on the choices of both individuals.

Schematic diagram of signalling

The figure above provides a schematic diagram of communication viewed as a signalling game. The signaller knows something about the state of the world, and must select a signal with which to share this information. The signaller weighs the benefits of accurately representing the world against the benefits of misrepresenting the world, and from this chooses a signal. The receiver must select a response, and in doing so must choose how to interpret the information provided by the signaller. The receiver thus weighs the benefits of heeding the signal should it be ``honest'' against the costs of heeding it should it be misleading.

Communication will be stable when the signaller and receiver pursue strategies (the choice of a signal given the state of the world, and the choice of a response given the signal, respectively) that together comprise a signalling equilibrium. A signalling equilibrium is simply a pair of signaller and receiver strategies such that neither party gains from unilateral change in strategy.

By the definition of a signal given above, we know that receiver behavior will be affected by the signaller's provision of information. At a signalling equilibrium, then, the receiver must on average gain from heeding the signal, i.e., the signal must be reliable on average. This, in turn, tells us that the signaller must be honestly representing the state of the world. We can thus infer that on average, the incentive to the signaller to misrepresent the state of the world must be outweighed by the incentive not to do so.

But why would that happen? There are a number of possibilities. When interests of signaller and signal receiver coincide, the signaller has no incentive to misrepresent the state of the world to the receiver, and indeed may have an active incentive not to do so. Under coincident interests, it is easy to see why signallers would be inclined to accurately represent the world in their signals. But when interests conflict, the signaller will have an incentive to misrepresent the world in the choice of signals. Clearly, for the signals to nonetheless be honest on average, this incentive must be balanced by a counterveiling incentive against misrepresentation. Much of honest signalling theory focuses on understanding the source and form of this counterveiling incentive.

Coming next:

The mathematics of costly signalling. Equilibrium selection in signalling games.

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