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The standard definitions in game theory read "normal form game" and "extensive form game", or "game in normal form" and "game in extensive form".

Is there a lack of "of a" in the following phrase, in the place of the blank:

Example of a normal/extensive form _______ game with probabilistic players?

So, could we say:

Example of a normal/extensive form of a game with probabilistic players.

Would you write that? Or is omitting "of a" a better variant?

Example of a normal/extensive form game with probabilistic players.

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  • It's worth pointing out that you haven't given us a full sentence to work with – none of these are complete sentences. The technical language doesn't help. It really depends on if there is such a thing as a normal/extensive form game, or if there are merely normal/extensive games, and you're referring to something like one of those.
    – J.R. ♦
    Commented Dec 18, 2014 at 9:15
  • Yes, the standard definitions in game theory read "normal form game" and "extensive form game", or "game in normal form" and "game in extensive form". Let us consider the two sentences as descriptions under a figure.
    – Jan Pax
    Commented Dec 18, 2014 at 9:24
  • You might want to add some of that background information into your question with an edit. The more readily understandable your question is, the more likely you are to get an answer. If your question is too confusing, people are more likely to gloss over it and find another question to answer instead.
    – J.R. ♦
    Commented Dec 18, 2014 at 9:28
  • May I delete the entire question?There is no one here familiar with game theory which makes the task impossible.
    – Jan Pax
    Commented Dec 18, 2014 at 9:32
  • That's up to you, but that's also a rash assessment. The question has been open for less than half an hour; who knows if any game theory experts frequent ELL? Also, I think the question could be a good one if you simply took a few minutes to explain the grammatical constructs. Some people might appreciate an opportunity to learn a little something about game theory while helping you understand English better.
    – J.R. ♦
    Commented Dec 18, 2014 at 9:37

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"Normal form" is a noun phrase, which can also be used adjectivally. For the non-mathematicians in the room, it refers to a restricted class of objects with nice properties but which is equivalent to the whole class. For example, a normal form for fractions is that you express the numerator and denominator in least terms. So 2/4, 3/6 and 5/10 are all perfectly good fractions but the normal form would be 1/2. You'd typically use the normal form because it's easier to prove things about.

Because "normal form" is a noun phrase, both options are correct, though they have slightly different nuances. If you talk about "normal form games", you're talking about the class of all games in normal form. So, if you say "An example of a normal form game" the suggestion is that the reader should look at the class of all games that are in normal form, and choose one. But if you say "An example of a normal form of a game", the suggestion is that the reader should look at the class of all games, choose one and then convert it into normal form before continuing to think about it. If I were writing the caption to a figure that showed a game in normal form, I'd prefer "An example of a normal form game", since you chose that example from the class of normal form games, rather than choosing any old game and normalizing it.

By the way, you could also consider hyphenating "normal form" when it comes before the noun: for example, "This normal-form game is in normal form."

In the comments to the question, there is made the analogy to "A difficult game" versus "*A difficult of a game", with the clear conclusion that "A normal form game" is the only correct option. This analogy doesn't actually work because "difficult" is an adjective, not a noun phrase. The analogous options would be "A difficult game" versus "A difficult version of a game": both are correct.

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  • I think you misread my comment. I never suggested the version without of a was the only grammatical option, but given the OP's mention of the exclusively attributive use of the noun phrase, it seems that in the context given by the OP there is nothing wrong with the omission of of a, which certainly seemed to be the main concern in the question.
    – oerkelens
    Commented Dec 18, 2014 at 10:01
  • "Normal form of an extensive game" is acceptable for me. But I meant "(we give examples of) a normal and extensive form games", where normal is not meant normal to its extensive counterpart.Is in this case "normal and extensive form of a game" acceptable?
    – Jan Pax
    Commented Dec 18, 2014 at 13:48
  • "a normal and extensive form games" doesn't work because you're mixing singular and plural. This new example is one where I don't feel I know enough game theory to give confident advice.
    – David Richerby
    Commented Dec 18, 2014 at 13:55
  • So how do you express yourself, when there are two types of games (here normal and extensive, which are finer then normal, carrying more information about a game, or say,e.g.dictates sequence of moves, while in normal game you have just a matrix and both players choose simultaneously his strategy by selectin row or column), and you want to give an example of both?And extensive form are trees at which nodes the players act by choosing an outgoing edge.
    – Jan Pax
    Commented Dec 18, 2014 at 14:01
  • In a figure caption, something like "Examples: a normal form game and an extensive form game." In running text, it's a bit awkward to say that you're giving one example of each of two different things; something like "We give two examples: a normal form game and an extensive form game" works well or "We give an example of a normal form game and of an extensive form game."
    – David Richerby
    Commented Dec 18, 2014 at 14:04
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You wrote in a comment:

Yes, the standard definitions in game theory read "normal form game" and "extensive form game", or "game in normal form" and "game in extensive form".

So, the expressions normal form and extensive form are used attributively. In that case, there is absolutely no reason to add anything between the attributive and the noun.

Instead of normal form you could place any adjective, for instance difficult. Your example would become:

Example of a difficult _______ game with probabilistic players?

Now, ask yourself if you would feel anything is missing in the gap.

Now, ignoring the given context, and stepping outside the given specific subject, it is absolutely possible, of course, to read the given phrase as if normal form is not attributive. This is the way most people would read it that are not used to the specific vocabulary of normal form and complex form games.

In that case, of course the version without of a is missing something. This would be equivalent with:

That is one hell () question.
That is a special () kind person.
That is a complex form (*) game.

In those cases, of or of a needs to be added. That is of course, assuming that we are not talking to people that expect to hear about normal form games!

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