Realistic versus Rational Secret Sharing
This work addresses the issue of secret reconstruction failure in rational secret sharing for scenarios involving non-rivalrous goods, which is incremental as it extends prior game-theoretic models.
The paper tackles the problem of rational secret sharing by modeling it as part of a larger game where the secret enables access to a common good, finding that when the good is non-rivalrous and non-excludable, many natural Nash equilibria exist, unlike the rivalrous case studied by Halpern and Teague.
The study of Rational Secret Sharing initiated by Halpern and Teague regards the reconstruction of the secret in secret sharing as a game. It was shown that participants (parties) may refuse to reveal their shares and so the reconstruction may fail. Moreover, a refusal to reveal the share may be a dominant strategy of a party. In this paper we consider secret sharing as a sub-action or subgame of a larger action/game where the secret opens a possibility of consumption of a certain common good. We claim that utilities of participants will be dependent on the nature of this common good. In particular, Halpern and Teague scenario corresponds to a rivalrous and excludable common good. We consider the case when this common good is non-rivalrous and non-excludable and find many natural Nash equilibria. We list several applications of secret sharing to demonstrate our claim and give corresponding scenarios. In such circumstances the secret sharing scheme facilitates a power sharing agreement in the society. We also state that non-reconstruction may be beneficial for this society and give several examples.