  We consider a peer-to-peer electricity market, where agents hold private
information that they might not want to share. The problem is modeled as a
noncooperative communication game, which takes the form of a Generalized Nash
Equilibrium Problem, where the agents determine their randomized reports to
share with the other market players, while anticipating the form of the
peer-to-peer market equilibrium. In the noncooperative game, each agent decides
on the deterministic and random parts of the report, such that (a) the distance
between the deterministic part of the report and the truthful private
information is bounded and (b) the expectation of the privacy loss random
variable is bounded. This allows each agent to change her privacy level. We
characterize the equilibrium of the game, prove the uniqueness of the
Variational Equilibria and provide a closed form expression of the privacy
price. In addition, we provide a closed form expression to measure the impact
of the privacy preservation caused by inclusion of random noise and
deterministic deviation from agents' true values. Numerical illustrations are
presented on the 14-bus IEEE network.
