There seems to be a huge discrepancy in what people refer to when they speak of "game theory". I tend to think of it as including, among other things:

*Combinatorial*game theory dealing with certain games of perfect information, i.e., things like the Sprague-Grundy theory of (terminating, perfect information) impartial games, but also partizan games*à la*Berlekamp, Conway and Guy, and more (e.g., not necessarily terminating games where non-termination is counted as a draw).Questions of determinacy: Martin's proof of Borel determinacy, for instance, is probably more commonly classified as being part of set theory, but it seems odd to me not to (also) consider it part of game theory.

Games with application to model theory, like semantic games, Ehrenfeucht-Fraïssé games, etc.

Differential game theory.

Various questions of algorithmic computability or complexity linked to some of the above.

...and probably much more that I've never even heard about (quantum game theory?).

On the other hand, if we look at this online course (by Jackson, Leyton-Brown and Shoham) that is simply called "game theory", it is obvious from the syllabus that their focus is much narrower:

Week 1. Introduction: Introduction, overview, uses of game theory, some applications and examples, and formal definitions of: the normal form, payoffs, strategies, pure strategy Nash equilibrium, dominated strategies.

Week 2. Mixed-strategy Nash equilibria: Definitions, examples, real-world evidence.

Week 3. Alternate solution concepts: iterative removal of strictly dominated strategies, minimax strategies and the minimax theorem for zero-sum game, correlated equilibria.

Week 4. Extensive-form games: Perfect information games: trees, players assigned to nodes, payoffs, backward Induction, subgame perfect equilibrium, introduction to imperfect-information games, mixed versus behavioral strategies.

Week 5. Repeated games: Repeated prisoners dilemma, finite and infinite repeated games, limited-average versus future-discounted reward, folk theorems, stochastic games and learning.

Week 6. Coalitional games: Transferable utility cooperative games, Shapley value, Core, applications.

Week 7. Bayesian games: General definitions, ex ante/interim Bayesian Nash equilibrium.

Evidently they don't intend to teach about the various things I mentioned above.

Now this presents the unfortunate problem that I don't know how to refer to this particular sub-branch of game-theory-in-the-wide-sense, or, alternatively, if we reserve the term "game theory" to this game-theory-in-the-narrow-sense, how to rename game-theory-in-the-wide-sense. I've thought of calling it "Nashian game theory", but I don't want to be caught making up names for branches of mathematics that I'm in no way a specialist of, at least not without some kind of asking about.

Sadly, neither the Wikipedia article (which sort-of favors using "game theory" in the wide sense) nor the AMS classification (which is really unclear as to what goes into 91Axx — do we seriously think that "Games involving topology or set theory" should be part of "Game theory, economics, social and behavioral sciences"?) seem to have an idea as to what game-theory-in-the-narrow-sense might be called.

So, can someone suggest less ambiguous terminology, and possibly a map of the layout of game theory (how the different sub-domains stand in relation to each other)? I'm also curious to know how wide the intersections are (some descriptions seem to suggest that combinatorial game theory and Nashian(?) game theory are almost a partition, but the picture is probably much more complex).

Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels(where he proves that chess is determined), so that would make combinatorial game theory older than the von Neumann–Morgenstern book. (contd.) $\endgroup$ – Gro-Tsen Mar 9 '16 at 21:154more comments