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Secure multiparty protocols proof and why is a necessary condition?

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Is there a strict proof for secure multiparty protocols? What do they serve? I mean some have shown the existence for such protocols, but can I use them in order to substitute a mediator in game theory who sends messages to the players? How can I model a process of $3$ or $4$ players who can play a game wihtout the central mediator and they exchange infroamtion with each other?

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