Good text to start studying topological games?
Solution 1:
Here are some suggestions. I'm afraid they do not fit exactly to your requirements; but I hope this will help anyway. I apologize in advance if you already know all of that.
0 Of course, Kechris and Oxtoby are great.
1 Concerning topological games like Banach-Mazur, and applications to Banach space theory, you could have a look at the following (and the references therein)
- Julian P. Revalski: The Banach-Mazur Game: History and Recent Developments, http://www1.univ-ag.fr/aoc/activite/revalski/Banach-Mazur_Game.pdf
- Jiling Cao and Warren B. Moors: A survey on topological games and their applications in analysis, http://www.rac.es/ficheros/doc/00232.pdf
- Ratislav Telegársky: Topological games: On the 50th anniversary of the Banach Mazur game, Rocky Mountain J. Math., Volume 17, Number 2 (1987), 227-276. http://projecteuclid.org/euclid.rmjm/1250126541
2 Concerning AD and these kinds of things:
Besides Kechris' book, there are lots of things in the older book by Moschovakis.
Maybe the following article by Mycielski (after all, AD is his axiom): Jan Mycielski: Games with Perfect Information (Chapter 3 in Handbook of Game Theory with Economic Applications), doi:10.1016/S1574-0005(05)80006-2, https://www.math.upenn.edu/~ted/210F10/References/GameTheory/Chapter3copy.pdf
3 Concerning the difference between strategies and tactics, try the following paper by Debs:
- Gabriel Debs, Stratégies gagnantes dans certains jeux topologiques, Fund. Math., Volume: 126, Issue: 1, page 93-105, 1985. https://eudml.org/doc/211611, http://matwbn.icm.edu.pl/ksiazki/fm/fm126/fm12618.pdf
4 Incidentally, the best reference is perhaps Dens' "thèse d'état" entitled convexes compacts et jeux topologiques (but I didn't read it!)
5 A more specialized thing, which I suspect you may enjoy reading:
- Gary Gruenhage: The Story of a Topological Game, Rocky Mountain J. Math., Volume 36, Number 6 (2006), 1885-1914, http://projecteuclid.org/euclid.rmjm/1181069351