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The tag is a bit messed up at the moment.

Game theory is a well-established field of study of strategic decision making by living beings. It is deeply involved in how people resolve conflicts or get what they want out of each other. A famous example is the prisoner's dilemma. Basically, it's an area of psychology that seeks to understand certain human behaviours. The tag's wiki alludes to this topic as being what the tag is about.

The seven six questions in this tag appear to have absolutely nothing to do with this though - it's not being used for questions about game theory, it's being used for questions about theories about games.

Due to its chronic misuse, these questions should probably be retagged with something else that actually describes what these questions are about. How should we retag them, though?

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    "An important notion in Combinatorial Game Theory is that of solved game (which has several flavors)" en.wikipedia.org/wiki/Combinatorial_game_theory. I still upvoted your question, because I think this is a good exercise in keeping the site clean, even if I disagree with retagging the solved games. – Rainbolt Jun 20 '14 at 13:32
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    Ah! So asking about solved games is part of a branch or relative of game theory, though apparently possibly not part of regular game theory itself. – doppelgreener Jun 20 '14 at 13:49
  • I think all of those questions are relevant to the tag, with the exception of "maximum attainable points", which seems to be more of an optimization problem. – Hao Ye Jun 20 '14 at 19:36
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    @Hao Ye - "Maximum attainable points", where that is the winning criteria, is related in the sense that it implies perfect play by you. – ire_and_curses Jun 21 '14 at 3:44
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    @ire_and_curses: In some situations, it could be related, but as phrased, the question in the thread basically assumes collusion between two players to optimize one person's score, so no strategy is actually involved. It's just an optimization problem constrained by the tileset and scoring rules of the game. – Hao Ye Jun 21 '14 at 16:54
  • @JonathanHobbs I'm not an expert on game theory, but I believe I know enough to say that it's called game theory precisely because it was developed to determine optimal strategies for games (i.e. to solve them). So I agree with other commenters that the tag is appropriate for these six questions. Modern game theory differs from its roots only in the scope of what is considered a "game." – David Z Jun 23 '14 at 20:19
  • I was under the impression it existed to understand human behaviour, and what people could be getting out of certain common zero-sum exchanges that made no sense. Understanding the optimal strategy is only a small part of understanding why the heck people do what they do, like why two prisoners would turn each other in when they could both stay silent and get off free. It's just psychology, not optimisation. – doppelgreener Jun 23 '14 at 22:05
  • There's even some dispute on the Go question about its tag, I just noticed. – doppelgreener Jun 23 '14 at 22:09
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    @JonathanHobbs (2 comments up) I missed your response earlier, but: I don't think that's the case. Understanding human behavior is only one application of game theory, in which it treats interactions among people as games, and even then it only works to the extent that people can be considered rational actors. The psychological analyses you're thinking of actually pick up where game theory leaves off, and allow us to understand why people might not act in accordance with the optimal strategies that game theory predicts. – David Z Jul 3 '14 at 4:42
  • @DavidZ: The biggest distinction between game theory and CGT is that the former considers (mainly) games of luck and imperfect information while the latter considers (mainly) perfect play of mathematical games with perfect information and no random elements. Both theories are interested in optimal strategies. – PJTraill Dec 17 '18 at 2:02
  • @Rainbolt: you quote Wikipedia on CGT rather than on Game Theory, suggesting strongly that solved games are more appropriate to combinatorial-games (which covers CGT) than to game-theory. – PJTraill Dec 17 '18 at 2:05
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Game theory, in its general and original sense, is a branch of pure and applied mathematics that studies the optimal or feasible strategies available to interacting players in various types of formalized decision-making scenarios (which often are, though they do not necessarily need to be, games).

Although a relatively young field of study (less than a century old), game theory has grown to encompass a broad range of subtopics, and has become an important tool (and a subject of study in its own right) within a number of sciences besides mathematics, including but not limited to economics, political science, psychology, biology and computer science. Within this broad field, a number of fairly distict subtopics may be recognized, such as:

  • Combinatorial game theory, which studies sequential games of perfect information, such as Chess, Go or Tic-Tac-Toe. These games are characterized by the property that they include no randomness or hidden information, and thus by the fact that, if all the players follow a perfectly optimal strategy (which must exist, in theory, even if it is not known), the outcome will always be the same.

  • "Classical" game theory, which assumes that all players are fully aware of each others' possible strategies and payoffs, but not necessarily of the specific moves others have chosen to make, and that they all choose their strategy independently to maximize their expected payoff.

  • Cooperative game theory, which allows players to collude and form (more or less) binding coalitions through some kind of enforcement mechanisms.

  • Evolutionary game theory, which replaces the assumption that players rationally choose their strategies with the assumption that they each follow a fixed hereditary strategy which they pass on, possibly with small mutations, to their offspring.

The point to note here is that all these subfields, and many more besides, fall under the broad umbrella term "game theory". In fact, pretty much any mathematical (or quasi-mathematical) analysis of games could be considered a part of game theory, except maybe for games of pure luck (which are traditionally considered to fall under probability theory, although some might see this distinction as more of a historical artifact than an actual qualitative difference).

As for the questions mentioned above, as a mathematician I would regard them all as falling under the scope of game theory, even if some of the answers here may not possess quite the level of mathematical rigor I would usually expect of a formal game-theoretical analysis.

Specifically, the following questions ask about optimal (or quasi-optimal) strategies of sequential games of perfect information, and are thus clearly within the scope of combinatorial game theory:

The remaining two questions may not be about combinatorial game theory, but do seem to fall under the scope of classical game theory:


The real problems with the tag here, IMO, are two-fold:

  1. several of the questions are simply not very good questions, or, even if the questions might be potentially interesting, are poorly asked; and

  2. even the game-theory questions that are reasonably well asked seem to rarely get good answers on this site, presumably because we don't have many mathematicians (or people from related fields) here to answer them.

Honestly, I suspect that several of these questions would've been better asked at math.SE, or possibly at MathOverflow. That said, I can also imagine valid game-theory questions that might get better answers here (e.g. because they required extensive knowledge of a particular board or card game that most mathematicians would be unlikely to have), so I'm not quite ready to say that the tag simply shouldn't exist here. But it is, IMO, sort of borderline.

Anyway, to summarize, I don't think there's anything wrong with the use of the tag on these questions. There might be other things wrong with them, but those issues should be resolved by editing or closing the questions, not by retagging.


Ps. We do also have several questions that are clearly about game theory in the mathematical sense, even if they're not (currently) tagged with . A few examples I found are Does a winning strategy exist for Don't Break the Ice? and Are there guaranteed winning strategies for Quarto?.

  • As of 2018-12-17 we have combinatorial-games, whose tag-info makes it clear that it is mean for CGT. I have applied it to the questions for which it is said above to be appropriate, and removed the game-theory. – PJTraill Dec 17 '18 at 1:25
  • @PJTraill I have voted to reject all of your suggested edits. The consensus from this meta post is that no change is necessary to the tags. If you still think that the tagging should be changed, you can reopen the discussion here or with a new Meta post, but please do not initiate a retagging without community consensus. – BJ Myers Dec 17 '18 at 2:08
  • @BJMyers: Sorry: I see that I misread this answer: I saw the line clearly within the scope of combinatorial game theory and missed the conclusion don't think there's anything wrong with the use of the game-theory tag. I agree that my retagging conflicted with that conclusion, but I do feel (a) that the conclusion was based on a situation where we did not yet have combinatorial-games and (b) the distinction between CGT and classical Game Theory is real and useful, even if CGT is part of Game Theory in the broadest sense. But it is now way past my bed-time so I must stop for now. – PJTraill Dec 17 '18 at 2:20
  • @PJTraill There was a Meta post in 2017 requesting a "combinatorial-game-theory" tag - it seemed generally rejected, having a -2 score before it was automatically deleted. The combinatorial-games tag was created by the same user that proposed the cgt tag, and he/she applied that tag to the only two questions that had it. So the whole creation of that tag was really without community consensus either. – BJ Myers Dec 17 '18 at 2:26
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    I recognize the difference between the two tags, but I think that for this site it is really splitting hairs to try to distinguish between them. The kinds of questions (and probably question answerers) to whom this distinction matters are probably better suited for Mathematics. – BJ Myers Dec 17 '18 at 2:27
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Let's create/use three tags for these categories respectively:

  • . Three of the first category are about the optimal strategy, and whether a game is solved probably counts too.
  • or . I'm not sure about these two tags, actually, but the resources linked on this answer (like this one and this one, and the book On Numbers and Games) are explicitly about combinatorial game theory, which is game theory as much as physics is mathematics - heavily involves it, but a pure mathematician isn't going to be the best person to ask about particle interactions and decay, for instance. If tags are about "connecting experts with questions", we wouldn't be doing a very good job tagging a question for combinatorial game theory experts with just "game theory".
  • . (Already applied in an edit)
  • optimization and terminology sound OK, but neither combinatorics (quite) nor ai is ideal for CGT, for which for some time we have had combinatorial-games. ai would be appropriate to AI techniques such as neural networks (as used by AlphaGo), which are not CGT. combinatorics would apply to a broader field of mathematical techniques such as counting and classifying various sorts of patterns; these might also apply to some non-CGT questions, though I suppose on a Games-site most combinatorics will be CGT. – PJTraill Dec 17 '18 at 1:35
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I have a simpler solution. Change the definition of the tag.

While you are correct that Game Theory has a very specific meaning as relates to Math we do not need to be bound by that here.

At this site we should use so that it has a consistent meaning to us, the users of B&CG. We don't have much need for a tag dedicated to the math meaning of the term. Folks looking for answers in that vein should be directed to math.stackexchange.com

I think the usage of the tag is pretty OK as it stands now. Splitting one low usage tag into three tags doesn't seem overly useful.

  • Game theory is psychology. It's combinatorics which covers maths, or combinatorial game theory. – doppelgreener Jun 26 '14 at 7:16
  • Also I'm only suggesting splitting it in two - the last one was already retagged away, and then re-retagged as just a general terminology question, which we already have plenty of. Optimisation is simple enough, and probably has broader use here - I'm just not sure about the one that seems to genuinely be about combinatorial game theory. – doppelgreener Jun 26 '14 at 7:45
  • As of 2018-12-17 this is quite unnecessary, as we have had combinatorial-games for some time, and this is intended for CGT; I have applied it to several of the questions where it was more appropriate than game-theory. – PJTraill Dec 17 '18 at 1:27

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