April 15, 2004

STRANGE Games, Game Theory

by Nick Montfort · , 5:09 pm

Now, to interrupt your regularly scheduled discussion of games (and other things) for a brief dip into evolutionary game theory (EGT), a field that looks at how different strategies can fare against each other, and against themselves, when they repeatedly play games in the von Neumann/Nash sense – and a comment on how game theory relates to game studies.

Ben Packer and I took the nicely implemented JPrison appplet for running EGT games, developed by Laboratoire d’Informatique Fondamentale de Lille, and added a simple, but somewhat flexible, programming language to it: STRANGE, a STRategy lANGuagE. Today in Michael Kearns’ Networked Life class, we had four groups compete to devise strategies under different conditions…

One of the conditions provided some internal structure to the game, which is the link to the topic of the class. (Ben added that capability to JPrison, too.) STRANGE was meant to be easy enough for people will no programming experience to grasp – the class has no prerequisites in this or any other regard – but capable of expressing interesting strategies. It seemed to work at least somewhat on both counts; the experiment went well today, with some interesting shifts of strategy going on.

How game theory (evolutionary or not) relates to game studies is an interesting question; I’m hoping to get to read Jesper’s dissertation and see what he has to say about this. I think it’s more than just a coincidence of names, although the most interesting ways to relate the two fields may not be the obvious ones. I don’t have too much to say about EGT specifically, except to note that the play of individuals and teams in games like JPrison does seem to involve some of the same thinking that goes into mastering SimCity. Perhaps one could develop an interesting EGT-based computer game, just as SimCity demonstrates that you can develop an interesting cellular-automata-based computer game. Perhaps Creatures was an attempt at this?

Katie Salen and Eric Zimmerman have an introductory discussion game theory as it relates to game design in Rules of Play, (pp. 231-246). It’s not couched in the langauge of modern game theory, with discussions of dominant strategies and the concept of Nash equilibrium, the cornerstone of game theory since the 1950s, but then, it is quite a brief introduction. Their claim that “game thoery does not study games as strategically complicated as chess” is only true in part; Joel Watson’s undergrad game theory text Strategy sketches a proof that in chess, either white can guarantee a win, white can guarantee a draw, or black can guarantee a win – there is no other sort of game that chess can be. Their assertion that “game theory does not study psychology directly” and that it deals only with (nonexistent) rational players overlooks recent developments in what Colin Camerer calls, in the title of his recent book, Behavioral Game Theory. Connections to more complex branches of game theory, such as those that study repeated games (e.g., EGT) are also missing in this overview.

I was pleased to see some about game theory in Rules of Play. It’s bold of Katie and Eric to try to draw some connections from this stuffy B-school-associated field (which deals with how players maximize their utililty) to the more aesthetic and social realm of game design (by noting, for instance, the connection between utility and quantifiable outcome). Still, I wouldn’t look on their discussion as exhaustive, but inviting of more thought and writing.