The Random Beacon proposal suggests a scheme where K-of-N signatures are used to sign a random number. It suggests that the only way for a random number to be corrupted if all
K signers are corrupt; it takes only one honest signer to make the signature valid.
My question is: why would there be a honest signer? Game theoretically, if the value of the random number is high enough, it makes rational sense that the
K signers make a deal to corrupt the random number and split the reward between themselves - i.e., it takes one interested party to bribe all the others, making all signers dishonest. Why should an outsider trust one of the
K signers is honest?