A note on the Replicator Equations of dynamical game theory

✍ Scribed by C. Christopher; J. Devlin

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 189 KB
• Volume: 6
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/0893-9659(93)90119-8

✦ Synopsis

The rteplicator Equations introduced by Maynard Smith and Price [l] are examined in the continuous form given by Taylor and Jonker (21. A simple, explicit classification of the stable classes for three competing strategies is given in terms of the system parameters.

We follow the paper of Zeeman [3], but giving a slightly different derivation of the equations. Given a population in which each member can play one of n+l strategies (i) (i = 0, . . . , n), denote the number playing (i) by Ni. Suppose that an encounter between an individual playing (i) with one playing (j) results in a net pay-off of aij to the first. We hypothesise that the population growth, with a suitably chosen time scale, is given by that is, the per capita growth rate of Ni is proportional to the average pay-off of strategy (i). Writing Nil cr, Nk = Xi, we have