It sounds like you might be asking about 'The Status Game' by Will Storr, which is non-fiction. If that's the case, there aren't characters in a traditional story sense—the 'key players' are more like ideas, studies, and historical examples the author uses to build his thesis about how humans are driven by status.
He delves into a lot of social psychology, referencing famous experiments like the Stanford prison study and the Milgram obedience tests. So the 'characters' become those researchers and participants, or figures like Napoleon and Shakespeare, used to illustrate points about status-seeking across different cultures. It's less a narrative and more an exploration of human nature through various lenses.
That said, if you mean a different 'status game' story, maybe a novel or a TV show, the title alone is a bit vague—could be anything from a corporate drama to a social media thriller. Without more specifics, it's hard to pinpoint who the key characters would be.