We study rationality in protocol design for the full-information model, a model characterized by computationally unbounded adversaries, no private communication, and no simultaneity within rounds. Assuming that players derive some utility from the outcomes of an interaction, we wish to design protocols that are faithful: following the protocol should be an optimal strategy for every player, for various definitions of "optimal" and under various assumptions about the behavior of others and the presence, size, and incentives of coalitions. We first focus on leader election for players who only care about whether or not they are elected. We seek protocols that are both faithful and resilient, and for some notions of faithfulness we provide protocols, whereas for others we prove impossibility results. We then proceed to random sampling, in which the aim is for the players to jointly sample from a set of m items with a distribution that is a function of players' preferences over them. We construct protocols for m ≥ 3 that are faithful and resilient when players are single-minded. We also show that there are no such protocols for 2 items or for complex preferences.