Introduction
This eNote is a translation of my lecture note prepared for a course in the first and second quaters of academic year 2003 at Graduate School, Kochi University of Technology. This is made open in the hope to attract general public to the emerging field of mathematical theory of evolution, that is the evolutionary game theory. (* Translation is done in great hurry, so grammatical and spelling eorrs abound. I will try to correct them in time, and also make overall improvemet to do some justice to the elegant style of the Japanese original:)
There is no prerequisit necessary, although basic knowledge of differential equations would bring readers to the deeper understanding of the matter. I tried to put the technical details to the background as far as possible. What is really required for readers is the mental capacity to accept both serious and light-hearted things, enjoying them together, at the same time to be able to distinguish the two. That is, a brain that thinks and judges. Some experiences in real life that comes with age might help. Love for opera would be very helpful, though not the least essential.
If you acquire interests in the matters discussed here, you are strongly advised to go through texbooks of game theory and dynamical systems theory to familiarize yourself with mathematical aspects which is missing here. Once you get interested, the technical barrieres should be easily surmountable.
Materials presented here are basically the products of original researches by this author, which have been published in research journals in past two years or so. They are presented in casual, irrevalent style, which reflect the authors' desire to compensate for his forced seriousness on the podium. I do intend to compile them is better order, in time, and make them into a publication, probably in the form of a book. So comments and criticisms are very welcome.
From time to time, I might add materials, and modify the texts. So It is advised that you ocasionary do the reloading. A Warning to Safari users: The cash for the safari is too strong that you are unable to reload therewritten pages. You temporrily have to resort to other browsers such as Opera, fairfax and Internet Explorer for proper reloading.
The plan of this note is as follows.
(1) (２) Introduction and preview
(3) (3a) (4) (5) Evolutionary games and altruism
(6) (6a) (6b) (6c) (6d) (6e) Introduction to game dynamical systems
(7) (8) (9) (9a) (9b) Parametric evolutionary systems: Core of this note
(10) (10a) (11) (11a) A Simple model for class society
(12) (13) On system with mixed Nash equilibrium
(14) Summary
(15) References
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