Two agents needs to prove a common knowledge by means of answering a question, without revealing the answer if the other party doesn’t know the answer.
Real world example: Two strangers arrive at a residential building door, protected by a pin code. If one enter the code, the other sees it wether he had previous knowledge of it or not. So they must prove to each other they both know the code without revealing the answer. If they both reveal the right answer, all good. If they both reveal wrong answers, all good. But if one reveals the right answer and the other don’t, one party has gained knowledge.
Has this dilemma been framed in game theory ?
Closest I could find is zero knowledge proof (ZKP) which is I assume part of it, but not exactly a dilemma.
Cheers!
Start by considering the case where one person knows and the other doesn't. To prevent the other person from gaining information, the first person would have to tell a code at random. Since neither person knows the status of the other person, when both people know, they still each tell a code at random. Therefore, no matter what happens, both people tell a code at random.