Mediators enable comparisons players cannot credibly perform themselves [causal]
A mediator can consummate certain communications while blocking off certain facilities for memory. (In this regard he serves a function that can be reproduced by a computing machine.) He can, for example, compare two parties' offers to each other, declaring whether or not the offers are compatible without revealing the actual offers. He is a scanning device that can suppress part of the information put into it. He makes possible certain limited comparisons that are beyond the mental powers of the participants, since no player can persuasively commit himself to forget something.
XREF: Connects to game theory and mechanism design — the mediator as a trusted third party who can process information without full disclosure, relevant to trustless computation and MPC (secure multi-party computation) literature.
Thomas C. Schelling, The Strategy of Conflict, loc. 335