The issue with the football manager example is thus: the football manager doesn't force the football players to take advice from him (i.e., if one of the players truly and utterly doesn't believe in his plays, then he will simply quit, as opposed to being thrown in jail in the example of the citizen not following advice (i.e. law) from the state.)  Though I agree that there will always be leaders in this world, for this implies there are some people who are more intelligent or wise or skillful than others (which I believe to be entirely true), they must remain as leaders to be counted as leaders; once a supposed leader imposes himself onto his subjects, he then becomes a ruler.  Certainly societies will have leaders who recommend courses of actions, but if these people are truly fit for such advice, they will naturally accrue a following, rather than forcing people to follow as is the case now (after all, if it's good advice, it would be voluntary, assuming people have rational self-interest which I believe they do.)  As per my political philosophy: so long as it is voluntary.

Anyhow, on the matter of cooperative-competitive relationships: I have such a relationship with my best friend, he and I are writers.  We share advice on the ways we do things because we want to improve; however, we also compete to show one another that this or that can be done better.  It's a benign relationship at best, certainly not the typical view of competition, and there are certainly more writers in the marketplace than just he and I that we must compete against, but I'm a peaceful fellow myself so that's about all there is from me  We can scale this relationship between businesses: two businesses exist in a small area--let's say, within the same suburb--and each sell basics for everyday life, such as bathroom and kitchen supplies, basic groceries, medicine, etc.  They cooperate by agreeing not to impede upon each other's businesses; they won't burn each other's stores down, try to steal each other's customers, and won't make nasty untruthful snarks about the other.  However, they also compete: to gain business, they each must provide something better that the other doesn't, whilst ensuring they offer these as the lowest possible price.  If one tries to charge too much, the other undercuts them and gains business; if the other tries to sell an inferior product, the customers have an alternative to turn to.  If they both attempt it (i.e. price fixing), a third business sprouts up and everyone flocks to them.  They agree to compete and cooperate, just as athletes would in the Olympics; they do not attack each other so that they can get an advantage, they cooperate and compete; just as rival bands would (well, perhaps the milder ones), they do not smash each other's instruments or break the drummer's fingers, they instead compete and cooperate.

We don't always do it tho; you and I cooperate with our talks, but I'm not entirely sure we compete; perhaps if our political ideas differed and we were actively trying to accrue a following into either camp, we'd compete, but I'd rather we got along  Anyway, that's not to say that competition can't eventually disappear; if that business mentioned before did such a tremendous job that the other businesses could not compete at all, then that business becomes a monopoly, but of a different sort we're used to: this monopoly offers the greatest service for the lowest prices, and makes it impossible for others to compete, at least in the area (I doubt a corporation can keep this kind of service and price going universally, but that's just my take on it; it'd be wonderful if this were possible but I have my doubts.)

I do agree somewhat with your assertion of Libertarians and Anarchists of America; I don't think people will naturally and voluntarily agree that certain individuals will be able to keep their stake of power over areas of land.  I think, without the use of force, this land will be much more divided and even among people (what good is land if nobody will agree to work on it?--what good is ownership if none agree to your owning it?), and places of work will not necessarily have an owner, but perhaps, as you mentioned, a leader, and people would then take a much more even cut of the profit, thereby squashing the class divide (mostly; that's not to say some people won't strike it rich with their products, i.e. Notch and Minecraft, but in general people will be much wealthier than before.)