linq error At least one object must implement IComparable

 Well, you're trying to use SortedSet<>... which means you care about the ordering. But by the sounds of it your Player type doesn't implement IComparable<Player>. So what sort order would you expect to see?

Basically, you need to tell your Player code how to compare one player with another. Alternatively, you could implement IComparer<Player> somewhere else, and pass that comparison into the constructor of SortedSet<> to indicate what order you want the players in. For example, you could have:

public class PlayerNameComparer : IComparer<Player>
{
    public int Compare(Player x, Player y)
    {
        // TODO: Handle x or y being null, or them not having names
        return x.Name.CompareTo(y.Name);
    }
}

Then:

// Note name change to follow conventions, and also to remove the
// implication that it's a list when it's actually a set...
SortedSet<Player> players = new SortedSet<Player>(new PlayerNameComparer());