The [game-theory] tag is consistently misused. How do we resolve this?

Question

The game-theory 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.

• Five ask: this game solved, or what's the optimum/winning strategy?
  • Is Circus Maximus solvable? (no other tags)
  • What is the optimal strategy in Quantum Tic Tac Toe? tic-tac-toe
  • Maximum attainable points for a single player in a two player game of Carcassonne carcassonne
  • Is Ultimate Tic Tac Toe solved? tic-tac-toe
  • Hex board game strategy board-game-adaptations board-size
• One asks for the mathematical discoveries about Go. This may be actual game theory.
  • What are the main results in game theory regarding Go? go
• One just asks for a name for a thing that, I am pretty sure, isn't even part of game theory. It's been retagged.
  • What's the name of the theory that the player with the most options has the advantage? (no other tags)

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?

Answer 1

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:

• Is Circus Maximus solvable?
• What is the optimal strategy in Quantum Tic Tac Toe?
• Is Ultimate Tic Tac Toe solved?
• Hex board game strategy
• What are the main results in game theory regarding Go?

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

• Maximum attainable points for a single player in a two player game of Carcassonne might or might not be a combinatorial question (I'm not sure if the stated assumptions are enough to eliminate all the randomness and uncertainty from the game), but if not, is surely is within the scope of classical game theory.
• What's the name of the theory that the player with the most options has the advantage?, while somewhat confusingly written, essentially presents a claim about optimal strategies (namely, that expanding the strategy space for a player cannot reduce the value of the game for said player) and asks whether this claim is a known game-theoretical theorem.

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The real problems with the game-theory 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 game-theory 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.

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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 game-theory. 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?.

Answer 2

Let's create/use three tags for these categories respectively:

• optimization. Three of the first category are about the optimal strategy, and whether a game is solved probably counts too.
• combinatorics or ai. 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".
• terminology. (Already applied in an edit)

Answer 3

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 game-theory 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.