I have developed a game and I intend to offer it in my friend's website.
His website has a lot of visitors. We discussed the idea, and to make it profitable, his idea is to add banners from Adsense, so we will have metrics and see how many people are actually clicking on ads.
Considering this is his website, and my game uses his logo (brand), how much could he pay me: 10%, 20%, 30%...?
Any suggestions are appreciated
It's impossible to give a solid answer to this question without knowing more information about the site and game in question. At the end of the day it's all going to come down to which one of you is the best negotiator.
As a starting point, I would work out what the relevant costs are going to be for you both. Your costs are going to consist mainly of the time taken to develop and maintain the game, including time spent already, and anticipated time spent in future on providing support and enhancements to the game.
For your friend, costs are going to include any additional resources used up on the server, as well as time spent setting up and administering the game.
Next, you need to consider any additional benefits your friend is going to receive from having this game on his site. If the game becomes popular, then he is going to get an influx of new users to his site. He may therefore receive additional revenue on the back of this, from increased page views on the rest of the site, or from new subscribers to other products and services offered.
Again, it is hard to give an exact figure without knowing the details of the site and the game, but my initial thought would suggest the vast majority of work would be done by yourself in developing and maintaining the game, while all your friend would need to do is set it up, then sit back and occasionally maintain it. It also seems as if he will benefit in other areas, from increased traffic to the rest of the site. A fee of around 80% in your favour would sound more reasonable to me, but again it depends on how well you can negotiate with your friend, and exactly what is involved in the site/game.