  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.
