Back to The Specker Derivative Game (SDG).
The book: Algorithmic Game Theory by Nisan, Roughgarden, Tardos and Vazirani (Cambridge University Press, http://www.cambridge.org/us/catalogue/catalogue.asp?isbn=9780521872829) provides excellent background information on SDG. However, the idea of defining games with derivatives based on combinatorial maximization problems is not touched.
The chapter on Evolutionary Game Theory (chapter 29) is most relevant to SDG, although traditional evolutionary game theory works with infinitely many players. In this world, the players are organisms that meet other organisms from which they buy products (i.e., derivatives) and to which they offer products. The 2 organisms play a fixed, 2 player game. In SDG this amounts to one player creating an instance of the maximization problem and the other creating a solution.
In evolutionary game theory, the money in the account corresponds to the "fitness" of an organisms which helps or hinders the ability of an organism to reproduce. Mutant strategies are studied and the concept of ESS (evolutionary stable strategy) is introduced. An ESS strategy cannot be "overrun" by a mutant strategy.
Thanks to Rajmohan Rajaraman for bringing this book to my attention and to Radu Mardare for introducing me to evolutionary game theory and the connections to SDG.
In
@article{1272536,
author = {Merrilea J. Mayo},
title = {Games for science and engineering education},
journal = {Commun. ACM},
volume = {50},
number = {7},
year = {2007},
issn = {0001-0782},
pages = {30--35},
doi = {http://doi.acm.org/10.1145/1272516.1272536},
publisher = {ACM},
address = {New York, NY, USA},
}
we read:
The principles of science and engineering can be taught
not only by playing games but by designing games.
Our focus is on "designing and implementing robots" to play a game but some effort goes into designing games for robots.
The fun in SDG is a meta-fun: It consists not of playing and experiencing a game but of teaching a robot to play the game and to observe the consequences of the teaching.
Designing artificial markets
http://www.reviews.com/hottopic/hottopic_essay_05.cfm
http://thesocialatom.blogspot.com/2007/02/key-ideas.html