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: http://ideas.repec.org/p/pad/wpaper/0022.html 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. 

