A mediator, whether imposed on the game by its original rules or adopted by the players to facilitate an efficient outcome, is probably best viewed as an element in the communication arrangements or as a third player with a payoff structure of his own who is given an influential role through his control over communication. But a mediator can do more than simply constrain communications—putting limits on the order of offers, counter-offers, and so forth—since he can invent contextual material of his own and make potent suggestions. That is, he can influence the other player's expectations on his own initiative, in a manner that both parties cannot help mutually recognizing. When there is no apparent focal point for agreement, he can create one by his power to make a dramatic suggestion.

XREF: Connects to coordination games and focal point theory in Schelling's framework; mediator as a mechanism for resolving coordination failures.

Thomas C. Schelling, The Strategy of Conflict, loc. 334