Yes, Nao and Akiyama are Both working TOGETHER
I'm not really sure what kind of title I can give this post without it being a spoiler, because I've seen a lot of hate about Nao claiming: 'We Won!'
Now yes, I can see how that's a bit pretentious, and it would have made more sense if she just told Akiyama: 'You Won!' because that is how it worked out on paper anyway. Akiyama is technically the sole winner of the Minority Game and put in the most work.
But I think it's incredibly unfair to give Nao no credit whatsoever.
Firstly, Nao was the one who went and talked to the other Players. She also figured out the most likely safe Players to form their team and actually recruited them.
She also came back to the game location the next day and actively gave Akiyama valuable information that allowed him to Win.
But above all else- She was actively trying.
I'm not saying that she did a better job than Akiyama. But she wasn't Useless.
Sure, she was wrong when she suspected No. 15. She was technically wrong to bring in the people she did as well. But in doing so, she allowed Akiyama and X to have a one on one confrontation that caused the cheque to be returned.
And at the end of the day, even if you don't end up accomplishing anything, the fact that you're still trying to win is amazing.
Since a lot of Liar Game haters seem to love Cote, I do honestly have to ask, when you compare the first 7 Episodes of Cote to the first 7 Episodes of Liar Game, is it even comparable in terms of the mind games?
And do you honestly prefer Kouneji- Someone who CAN win but chooses not to and is an annoyance to the Class because he seems then as too weak to even try- To Nao- Someone who Might not do well under pressure, but is doing an amazing job at putting in effort and doing her absolute best to try and help herself and Akiyama Win and actively save as many Players as she can.