A note on one-shot public mediated talk

Lehrer and Sorin (1997, Games Econ. Behav. 20, 131–148) use a one-shot public mediated talk model to show that, given any probability distribution on the outcomes of a finite normal-form game, there exists a public mediated talk mechanism that simulates that distribution, provided the probabilities on outcomes are rational numbers. It is shown here that a minor amendment of the very same model allows a much stronger conclusion: any distribution on the outcomes, whether the probabilities are rational numbers or not, can be obtained as the outcome of a one-shot public mediated talk mechanism.