Is there an algorithm in literature to compute an efficient (pareto optimal) and envy-free cake cutting when there are only $n=2$ players and a mediator?
Huh? I cut, you choose. Why do we need a Mediator?
Take a look at:
or the description of Crawford Divide and Choose as described in the book Equity: In Theory and Practice, by H. Peyton Young, Princeton U. Press.