It is often said that interpretivist theory does not, in principle, reject quantitative methods. That said, how could an interpretivist defend using a quantitative method (e.g., statistical model; game theory) as part of their research if they admit that conceptualizing human behavior by way of deductive models and categorical correlations is to fundamentally misunderstand the nature of human subjects? And, why would an interpretivist choose to employ a quantitative method if they admit that the objects of their investigation and the tools by which their investigation is carried out share the same social context?
Insisting upon a human interpretation to put a result in context does not reduce the value of the result itself. Interpretations of statistics are still interpretations, after all. The objection is to considering the result as a meaningful object on its own, outside a context that integrates all of the social constructions that might have pushed the results in one direction or another. The supposedly objective method is not irrelevant, it is just no more relevant than other sources of ideas. All sources can be integrated into an overall explanation.
Clinical psychologists of a basically interpretivist bent often use scored instruments, especially projective media, to derive a starting point for searching out ideas about their clients that might be hidden by the client during communication. They just do not accept that the instrument necessarily 'says' something definite. After all, the fact that someone gives answers similar to those given by people with a given way of interpreting the world can mean you are one of those people. But it can also mean that you have been trained or influenced to consider those kinds of answers more acceptable, or that you have an unusual way of taking the world it that produces the same patterns for some other reason.
Various kinds of ascetics, for instance can come across as depressive if you look at how many hours a night one sleeps, what one's food intake is, how one moves through space, and other objective measures, and even opinions about the world and other people. An instrument will score them that way. But you can just look at them and see that a different frame of reference is in order. That does not mean that an objective measure might never tell you someone is depressed when they pretend otherwise in public because they have been trained to not get others down. It means that you have to actually think, despite the fact you have a supposedly objective instrument.
I'd say if it's used with judgement; governments after all uses censuses to plan schooling provision, for example - which seems sensible; whereas using statistical means to judge the value of scientific theories, or literature seems wrong-headed to me; though there maybe other ways in which this may be useful - for example trawling through law records, or gathering economic data.
Game theory, is used in economics, and it seems a useful explanatory schema in perhaps throwing some light on economics; but one can only judge this, if one already knows a something about economics.