Realistic versus Rational Secret Sharing

TL;DR

This paper explores how the nature of the shared resource affects rational secret sharing strategies, showing that non-rivalrous, non-excludable goods lead to multiple equilibria and societal benefits.

Contribution

It extends rational secret sharing analysis to non-rivalrous, non-excludable goods, revealing new equilibria and societal applications beyond rivalrous scenarios.

Findings

Multiple Nash equilibria exist for non-rivalrous, non-excludable goods.

Secret sharing can facilitate power sharing in society.

Non-reconstruction can be beneficial in certain social contexts.

Abstract

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.