Abstract
The study of Rational Secret Sharing initiated by Halpern and Teague regards the reconstruction of the secretin 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.
Yvo Desmedt thanks the Jonsson Endowment. He is also an Honorary Professor at University College London. A part of this research was done while Yvo Desmedt was visiting The University of Auckland, partially supported by Marsden Fund grant 3706352.
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- 1.
Sometimes the acronym SMC is used.
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Desmedt, Y., Slinko, A. (2019). Realistic versus Rational Secret Sharing. In: Alpcan, T., Vorobeychik, Y., Baras, J., Dán, G. (eds) Decision and Game Theory for Security. GameSec 2019. Lecture Notes in Computer Science(), vol 11836. Springer, Cham. https://doi.org/10.1007/978-3-030-32430-8_10
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