Tomorrow I’m giving a talk in the econometrics seminar at U.C. Riverside. I was invited to speak on my work on network theory, so I don’t feel too bad about the fact that I’ll be saying only a little about economics and practically nothing about econometrics. Still, I’ve tried to slant the talk in a way that emphasizes possible applications to economics and game theory. Here are the slides:
For long-time readers here the fun comes near the end. I explain how reaction networks can be used to describe evolutionary games. I point out that in certain classes of evolutionary games, evolution tends to increase ‘fitness’, and/or lead the players to a ‘Nash equilibrium’. For precise theorems you’ll have to click the links in my talk and read the references!
I conclude with an example: a game with three strategies and 7 Nash equilibria. Here evolution makes the proportion of these three strategies follow these flow lines, at least in the limit of large numbers of players:
This picture is from William Sandholm’s nice expository paper:
• William H. Sandholm, Evolutionary game theory, 2007.
I mentioned it before in Information Geometry (Part 12), en route to showing a proof that some quantity always decreases in a class of evolutionary games. Sometime I want to tell the whole story linking:
• reaction networks
• evolutionary games
• the 2nd law of thermodynamics
and
• Fisher’s fundamental theorem of natural selection.
But not today! Think of these talk slides as a little appetizer.
