Allowing unmediated communication in a two-person double auction dramatically enlarges the set of equilibrium outcomes. It then consists of all allocation rules that are equilibrium outcomes of games in which all traders have the power at the end to veto proposed trades. All the allocation rules so characterized are equilibrium outcomes of a single game in which the traders exchange messages once before bidding in a double auction. These outcomes are all obtained by equilibria in which the traders truthfully tell each other their values. Adding a mediator achieves no further outcomes. © 1989.
Matthews, S. A., & Postlewaite, A. (1989). Pre-play communication in two-person sealed-bid double auctions. Journal of Economic Theory, 48(1), 238–263. https://doi.org/10.1016/0022-0531(89)90126-9