Two-sided communication is different from sender-receiver games since both parties possess private information, have opportunities to communicate it, and have the ability to influence the chosen alternative. It is also different from cheap-talk games as the messages have payoff-relevant consequences (e.g., changing the default alternative implies delay to changing it back). It is different from a direct revelation mechanism because the message set is restricted, implying the need for multiple communication rounds. Nevertheless, because the set of equilibrium outcomes coincides across many communication systems, this allows for very general results. One feature of equilibria that we construct is that the deviations from equilibrium behavior are punished by the other player becoming a ``dictator".
