Rational secret sharing as extensive games

The threat that comes from previously used punishment strategies in rational secret sharing is weakened because the punishment somtimes also causes loss to the punisher himself. In this paper, we first model 2-out-of-2 rational secret sharing in an extensive game with imperfect information, and then provide a strategy for achieving secret recovery in this game. Moreover, we prove that the strategy is a sequential equilibrium which means after any history of the game no player can benefit from deviations so long as the other players stick to the strategy. In particular, when a deviation is detected, the punishment executed by the punisher is still his optimal option. Therefor, by considering rational secret sharing as an extensive game, we design punishment strategies that effectively punish the deviants and meanwhile guarantee punishers' benefit. Hence, these punishments are more credible than previous ones. Except assuming the existence of simultaneous channels, our scheme can have dealer off-line and extend to the t-out-of-n setting, and also satisfies computational equilibria in some sense.