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Dynamic Games and Applications

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01-06-2015

Evolutionary Dynamics of the Handicap Principle: An Example

Author: Pierre Bernhard

Published in: Dynamic Games and Applications | Issue 2/2015

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Abstract

For a model developed in a companion paper, we investigate how adaptive dynamics might have led to the Bayesian equilibrium found. In an appendix, we also explain from a dynamic viewpoint a lack of equilibrium in a closely related model also invesitgated in the companion paper.

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We could, without loss of generality, normalize \(q_1=1\), taking the life expectancy of a best male that would not signal as the unit of time. For a non-unit \(q_1\), the fitness

https://static-content.springer.com/image/art%3A10.1007%2Fs13235-014-0108-0/MediaObjects/13235_2014_108_IEq8_HTML.gif

and

https://static-content.springer.com/image/art%3A10.1007%2Fs13235-014-0108-0/MediaObjects/13235_2014_108_IEq9_HTML.gif

, the females’ threshold \(\theta \) and the males’ strategies

https://static-content.springer.com/image/art%3A10.1007%2Fs13235-014-0108-0/MediaObjects/13235_2014_108_IEq11_HTML.gif

would just be multiplied by \(q_1\). We do not do that to keep better track of the dimension of the variables involved.

The fact that \(x\) and \(x'\) in Eq. (2) of [4] belong to a Banach space makes it very difficult to give a meaning to \(M(x',x)\) and to the integral: the symbol \(\mathrm {d}x'\) cannot stand for the Lebesgue measure which does not exist in a Banach space.

For both models, we also investigated the case where the limiting factor for the males is their potential reproduction rate.

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Title: Evolutionary Dynamics of the Handicap Principle: An Example
Author: Pierre Bernhard
Publication date: 01-06-2015
Publisher: Springer US
Published in: Dynamic Games and Applications / Issue 2/2015
Print ISSN: 2153-0785
Electronic ISSN: 2153-0793
DOI: https://doi.org/10.1007/s13235-014-0108-0

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