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Respond to the question: Function maximized in Nash Equilibrium?

06/10/2002 06:01 AM by Burkhard C. Schipper; Re: Re: Function maximized in Nash Equilibrium?

This is a reply to Man-Chung Ng's reply on my message "Function maximized in Nash Equilibrium?"

Thanks for the reference. This paper you suggest uses indeed category theory in a much more sophisticated way than I do. Therefore I am grateful of becoming aware of it. However, the question ask and answered by Vassilakis is I think quite a bit different.

As far as I diguested Vassilakis (1992), he looks at much bigger questions such as whether games and solution concepts can be obtained as limit of their subobjects, or whether we can resolve infinite regress problems. I just look at a small question of constructing a simple function that is maximized in Nash equilibrium in strategic games. Indeed I do not see yet a direct connection to my note except for the basic tools I use. However, this can be also due to my ignorance since I do not understand his paper yet.

By the way, there is another paper on game theory using category theory by Laptisky or similar in International Game Theory Review. However, I couldn't get hold of it till now.

Yet, there is another paper by Keiding on category theory applied to Social Choice in one of the first issues of Mathematical Social Science.

On top of it, some researchers on categorical logic (I think Andrea Schalk or similar) used games and categories of games. That's all I know about category theory and game theory. [Manage messages]

05/17/2002 07:28 PM by Man-Chung Ng;

The idea in your short paper is not new at all. Solution concepts can be obtained as some kind of limit. Spyros Vassilakis has worked on similar problems ten years ago. I suggest that you may take a look at one of his papers, "Some [View full text and thread]

05/13/2002 09:22 AM by Burkhard C. Schipper; Function maximized in Nash Equilibrium

Is there any work on the characterization of a function that is maximized in pure-strategy Nash equilibria (if they exist) for any strategic game with countable action space? I don't mean potential functions, weighted potential [View full text and thread]