In Rabin and Ben-Or, their basic assumption is that each participant can broadcast a message to all other participants and that each pair of participants can communicate secretly. Hence, they design a protocol of communication that is called verifiable secret sharing protocol (VSSP), and show that any multiparty protocol, or game with incomplete information, can be achieved if a majority of the players are honest.
As we know from game theory the players have some signal that is state dependable, say $s_i(\omega)$ for every player $i$, where $\omega$ is the state of the world. Usually, they are making some extra assumptions about the signals and sometimes they assume that they are normally distributed and independent or at least they follow some specific probability distribution. In the case of cryptographic protocols, the underlying assumption for the pdf is the uniform one as far as I am concern, so can we assume differently yes or no and why?
Also, since the agents share their secrets and lets say that the majority of them are rational with good intentions (in essence honest). So, I assume that each player $i$ shares her signal with the other players $j\ne i$, so as they can compute the joint pdf. Is this function a Boolean function?