Foreword to this Website

Game theory can be of considerable use to evolutionary biologists, especially behaviorists. Originally developed as a tool to predict rational human economic behavior, it has been successfully applied to many evolutionary problems. Game theory is useful in understanding situations where the fitness consequences of an individual's behavior depends in part on the types and frequencies of behaviors exhibited by other animals in the population.

This site provides an introduction to evolutionary game theory. It is aimed primarily at undergraduates with a serious interest in animal behavior and evolution. I have tried to make the material accessible to any student with a good facility in algebra. Portions of the site dealing with the "war of attrition" do contain some calculus but I have taken care to explain the calculations in detail for students who have not yet studied calculus.

Besides undergraduates, I hope that the site will be of interest to others including graduate students. I am especially hopeful that other instructors might find unique ways to use the simulations that are freely available at this site and that they will make their efforts generally available to others.

Much of the text parallels the early chapters of John Maynard-Smith's 1982 book Evolution and the Theory of Games. To that, I have added additional reference materials aimed at students not yet well grounded in evolution and the use of modeling techniques with some additional material thrown in to introduce frequency dependence. Since my interests are in communication, most of the examples will relate to this area.

The games discussed at this site are limited to a few examples of the type that Maynard Smith (1982) refers to as pairwise contests. Although probably not the most common type of contest in nature, they are the most commonly discussed (see note) when students first learn about game theory.

I hope that this site will give the student a good introduction to game theory and will complement the excellent treatments available in a number of behavior texts.

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What is Unique About this Site?

What is unique (to my knowledge) about this site and what takes it beyond the textbooks is itsinteractive approach to learning game theory. This is achieved by:

• Interactive simulations, which allow students to explore game theory. Using these simulations, students can:
  • Quickly explore hypotheses as to the effects of relative costs and benefits of behaviors on equilibrial frequencies (the concept of the Evolutionary Stable Strategy).
  • See how populations characterized by different types of behavioral strategies and different initial strategy frequencies evolve over many generations. These sorts of calculations are usually not done by students because they are highly tedious.
  • Note although the simulations eliminate the need for the students to go through the tedium of calculating game theory results, a thorough explanation of the calculations is presented to aid in gaining a complete understanding of the game theory.
• Extensive use of hyperlinks in the explanatory text. This allows the student to rapidly move between related concepts or review previous material.
  • The text contains review and thought type questions with hyperlinked answers and/or further questions.
  • Finally, the simulations and hypertext are used together to lead the student through the process of relating abstract (and simplified) game simulation models to actual animal behavior. As part of this process the student should be better able to understand the use and limitations of abstract models in scientific research.

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To the Student

General Information About Using this Site: If you are not familiar with the basics of game theory, then you will probably get the most out of this site if you work your way through the various pages and simulations sequentially. The correct sequence is listed top to bottom in the navigation frame on the left. If you are familiar with game theory, you can proceed directly to the links to the simulations but please take the time to read about how they work first.

Navigation: There are many links on this site and as a result, navigation can get to be a bit complicated. Please keep in mind the following:

• The main hypertext sections of this site work from within a frameset layout. This is the layout you are presently using.
• The left frame of the browser window is a navigation tool. Please note that it is broken into subdirectories; these are listed as links at the top of the navigation frame.
• The right frame of the browser window will contain most of the hypertext. Generally, you will move from one frame to the next using the navigation frame on the left.
  • Each frame has its own contents links; these are at the top.
  • I have made a concerted effort to make it easy for you to move from one link back to where you were. You are probably aware that pressing the "Back" button on a browser takes you to the last active link. If that link is at the top of a long text section and you have read down a ways and then pressed a link, hitting "Back" will not necessarily return you to your previous place.
    • Whenever I have thought that this would be a problem, I have tried to get around it by placing a link that will take you back to where you were! Use this return link whenever you find it instead of the "Back" button on your browser.
    • Here is an example of this feature: press here for a quick demo.
  • When a link needs to take you to another page of review or whatever, an entirely new window will open.
    • This window will not appear as a frame; it will simply be a new window.
    • It will cover the frameset you are presently viewing.
    • When you are done reading the material of interest, simply close the window.
    • The frameset you were using will become visible again in the same place. WARNING: once again, hitting "Back" from the new window will probably take you to a different place than you were (to your last visited link).
    • Note: you could keep the window open and navigate back to the frameset, but I suspect that you will soon have many windows opened and you will have trouble finding your way around. So closing popup windows is a good idea -- you can always open them again!
    • Here is a demo -- press this link to see an informational window, then close it.

The Simulations: I cannot emphasize too much that you will not get much out of the simulations unless you understand how they work. Thus, if you are not familiar with game theory, you should study the hypertext materials and be certain that you can calculate (manually) the payoff matrices and solve for pure and mixed ESSs. You should use the simulations to:

• demonstrate what you have learned,
• do thoughtful "What if" experiments where you attempt to discover more about the models and finally
• get an idea how a population would evolve in a particular game situation (this sort of thing is very tedious to calculate by hand).

I wish you good luck, hope this site benefits you and I would encourage your helpful feedback on this site by using the feedback form (which can be found at the bottom of the navigation window).

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Maynard Smith, J. 1982. Evolution and the Theory of Games. Cambridge Univ. Press.

Copyright © 2004by Kenneth N. Prestwich College of the Holy Cross, Worcester, MA USA 01610 email: kprestwi@holycross.edu About Fair Use of these materials Last modified 4 - 29 - 04

Endnote: While pairwise contests are discussed most often in animal behavior courses, they are probably not the most common type of biological competitive interactions that are amenable to game theory. Maynard Smith (1982) points out that "playing the field" is probably a more common type of interaction. pairwise models are important in animal behavior however for the obvious reason that pair wise contests over resources are quite common, often dramatic, and perhaps also because that is how humans often seem to prefer to view competitions!

Demo Link: You would find some review material, answer to a question, or wise observation here. When you are done reading it, press the link below to get back to where you were (if you hit "Back" instead of this link it will take you to the last link you visited).

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