Before you guys have a discussion like this you really have to define what you mean when you refer to women "playing games." From your responses to each other it is obvious that several of you have entirely different things in mind as your definition of women "playing games" and that is why you're so conviced that a different reaction is called for.
Three games women play include:
1. Playing hard to get by being less available than you'd like.
2. Giving attention to other guys to make you jealous.
3. Treating you like a doormat (aka "giving you sh1t") to see if you allow it.
All three of these games serve the same goal of testing your neediness level--like a bat sending out sonar waves to get a sense of where the cave walls are, she is "pinging" you to get feedback on how badly you want or need her.
But the first two games are very different from the third.
Regarding number three, you can and should call her on it.
If she is treating you like a doormat then ALLOWING it conveys neediness. It says you don't dare to stand up for yourself because you're afraid that if you do, you might lose her. So regarding situation three, you should call her on it because doing nothing is what conveys neediness and then you would "fail the test".
Games one and two are the exact reverse of game three. If she is playing hard to get or if she's spending time with other guys to make you jealous, then the mere fact that you NOTICE it as something she's "doing to you" and the fact that you're upset by it (upset enough to "call her on it") is what conveys neediness and you lose.
Instead of needing her so much, what you really need is to have enough success with women in general so that her playing hard to get or her giving attention to other guys doesn't ruin your day, doesn't upset you and make you feel like she's "giving you sh1t", and doesn't fill you with an angry urge to "call her on it".
The tricky thing is that when you really like a woman then for you situations one and two can end up feeling like situation three, even though they are very different.
From your own subjective point of view the first two games can end up feeling like she is "giving you sh1t" just because they're the opposite of what you'd like to see from her. From your point of view having her make you jealous or having her acting aloof and unavailable can feel like "sh1t" and yet it's very different from a true instance of her "giving you sh1t" (treating you like a doormat). After all, if you're not in a relationship you have no claim over her and she is perfectly free to be unavailable or uninterested in you, or more interested in other guys. You can't bully a woman into wanting you by simply "calling her on it" whenever she isn't showing as much interest in you as you'd like.
So the challenge is to recognize those situations where you win by calling her on it versus those situations where you win by NOT being (or at least not seeming) the least bit bothered by what she is doing.
For the camp that favors "calling her on it" I will grant you this: if a woman is playing games to see if she can upset you, then simply keeping silent isn't necessarily going to convince her that her games failed. Women are very perceptive and if a guy is silently stewing over a woman's behavior then more often than not, a woman will know from his tense expression, his fidgetty mannerisms, his emotionally distant tone, and so on that he is upset. Can't YOU tell if a woman is upset when you ask her "what's wrong?" and she snaps back, "oh nothing!"
That is why making a playful comment about a woman's game playing behaviors can sometimes be an effective way to convey the fact that she hasn't succeeded at her game. After all, if her behavior were really upsetting you, you'd find it difficult to talk about it without some sort of irritation creeping into your voice. That is why most guys opt to say nothing at all. But if you can make a comment about her behavior in a playful way, and your voice doesn't contain the slightest trace of annoyance or sarcasm, that can be a very powerful way to communicate the fact that her behavior doesn't faze you in the least.
If you do take the approach of making a playful comment to show that her behavior doesn't bother you, understand that it should be limited to those aspects of her behavior that are extremely obvious. Things that anyone else would notice and pay attention to. Because there are some things a guy would not even NOTICE unless he were pathetically insecure. For instance, if you joke about the way you saw her looking at some guy the other day, it doesn't matter how playful you are in commenting about it, the mere fact that you're noticing and remembering things like that will reek of neediness and no amount of playfulness will cover that up.
Finally, I should add that for the most part, all of this pertains to women who have reason to be unsure of where they stand with you. Once you and she are in a relationship where there is a reasonable basis for you both feeling more trust with each other, then you don't want to be constantly playing these games with each other because that will undermine the trust the two of you share.
Why would a woman continue playing hard to get or continue trying to make a guy jealous even after she's in a relationship? For one thing, she could be doing it for a good reason--maybe she's desperate to see some show of affection from a husband who is far too distant and aloof with her. Or, she could be so insecure and needy herself that she compulsively fishes for reassurance that the guy needs her as much as she needs him. Or, she could be doing it to gain power in the relationship--trying to create the impression that he needs her more than she needs him so she'll be able to leverage off his insecurity to easily control him.
If you are in a relationship with a woman and she is continuing to play these games then you may want to discuss it with her, but you have to do it very carefully because if you simply "call her on it" that can end up making her feel rewarded for playing those games. Remember--she plays those games because she is fishing for signs that you need her, and if you get visibly upset about what she's doing it makes her feel like she succeeded. So instead of simply being upset and focusing on how it makes YOU feel, help her to understand how that sort of game playing is reducing the chances for both of you to enjoy a relationship based on mutual trust.
DeepBlue