The title of The Player of Games has a clever double-meaning. The obvious interpretation is that it refers to the protagonist Gurgeh, and indeed, the title is a translation of a sobriquet he uses as one of his names. However, it can also be interpreted as referring to Special Circumstances. They cleverly set things up so that they could use Gurgeh as a pawn in their "game" to take down the Empire of Azad. This kind of double-meaning is echoed in Use of Weapons, which refers both to the protagonist's ruthless military genius, but also to how the Culture uses him as a weapon to accomplish less than ethical plans.
The game theory concept of the "iterated Prisoner's Dilemma" states that the logically optimum course of action when dealing with a totally unknown entity is to lead off with a minor but benign gesture and then to tailor your responses to mirror the other entity's replies re: cooperation or noncooperation. Now think back to the plot of Excession, and you will realize this is exactly what the Excession was doing. The GSV Sleeper Service even Lampshades this briefly.
When Lededje Y'breq is looking for the avatar of a "disreputable" ship and cruising for sex at the same party (for unrelated reasons), the guy she's talking to mistakenly assumes she wants to havesex with a ship's avatar. Despite being corrected, he then repeats this erroneous assumption to an actual ship's avatar. And while he's surprised, no one seems too terribly bothered by the idea.
Firstly, this suggests that this kind of thing has happened before in the Culture.
And given the later discussion about Special Circumstances and the attitude toward it, it implies that the All Girls Want Bad Boys trope is still alive and well in the Culture, but not limited by gender or even species.
When you consider that Culture citizens are capable of changing sex at will, and that she possesses almost none of the femme fatale traits that would make such a decision useful, and that she is trying to enact serious political change in a medieval world that treats any woman in authority as suspicious/disgusting; it really makes no sense at all in-universe that Vosill in Inversions would have stayed as a woman. So many of the problems that she faces during the course of this book are solely due to the fact that the rest of the Royal court finds a woman doctor to be an appalling concept. A male doctor would have such an easier time of it.
Alternatively, Vosill is hoping that her example will change how women are viewed by the royal court of Haspidus. This is further justified in the epilogue, when Oelph, the narrator, mentions that the king whom Vosill served is succeeded by Haspidus' first ruling queen.
Gender identity still exists in the Culture, just not to the same extent as our society. In The Player of Games, Gurgeh is noted to be an oddity in that he's never changed gender; he doesn't want to be a woman. Maybe Vosill just doesn't want to be a man; given that even Special Circumstances never forces a Culture citizen to do anything against their will, that's all the reason she would need.
We learn in The Player of Games that the Culture is so far beyond our concepts of gender identity and sexuality that they do not even have a pronoun for he, she, his or her in their native language of Marain, instead using a singular term that encompasses every sex including that of aliens and asexuals. They also have no concept of uniforms and have only the barest hint of a formal dress-code for parties. And yet over the course of the series no man is ever stated to wear a dress, skirt, or make-up, despite more than several women doing so, and the long-haired women outweigh the long-haired men by a considerable degree.
How is the first bit any different from various languages in our own Earth already, though??
One of the arguments in favour of Marain that the narrator makes upon its introduction is that language and society go hand-in-hand, the argument being that you can tell most things about a people by how they choose to speak. Every Earth language has the concept of gender built into it even on a minor level, from the notion of objects themselves being masculine or feminine such as in French, to the more esoteric such as Japanese which is a fascinating multi-branching tree like no other. This reflects the fact that gender is and always has been a fundamental part of every human society since the dawn of time. With Marain however, it is meant to be a perfectly gender neutral language that evolved to reflect their perfectly gender neutral society. It's not as simple a concept as merely having no pronouns, it's every layer, from the ground up. To go from that to even the implication that there is gendered clothing is jarring. Of course, the probable reason behind this is the failure of an author who lived in our 1987 being unable to picture his leading man in a dress rather than there being a legitimate in-universe bias.
