In Agile, the grand bargin with the project sponsor is to deliver "best value" at a fixed cost in trade for latitude to evolve the scope details. The concept is like pick of the litter: "the most valuable deliverables" from among all the possible deliverables.
Of course: who says it's "best"? Answer: the customer, or the one holding the customer's proxy.
At each iteration, the customer goes through the backlog and reprioritizes and may invent new things. New things are all put in a backlog stack. The totality of the stack is compared to remaining time and budget. (Mix in a little technical debt to add seasoning to the backlog) At some place in the backlog stack you draw the line--actually, the line gets redrawn at every iteration if anything changes, which it will. Above the line, things get delivered; below the line: there's always V2.0!
At the end of the project, the customer has picked the best value from the backlog. Anything not done is of lesser value than those that were picked.
So what's best effort? Best effort has been around a long time. All cost-plus-fixed-fee (CPFF) contracts are legally 'best effort'. The contractor's responsibility is to apply best effort to the defined scope (defined by the customer in the SOW and specifications); if it doesn't get done, then the sponsor has a decision: bring more money, or terminate the effort. The contractor has no obligation to finish on his own dime.
To the uninitiated, best effort sounds crazy, but actually it works quite well to get difficult jobs done; but it's not the same bargain as made in Agile. The best effort bargain is to bring the best and brightest to the problem and work as responsibly as possible, but at the end of the day, the sponsor is on the hook for the money to finish.
So, where's the rub? It's in the opportunity cost. For the contractor, the fee (profit) is fixed; the contractor can't get richer on a better job, nor poorer on a bad job. In other words, it's economically regulated from the contractor's point of view. Nobody can get "Facebook rich" on best effort like they could on best value.