  Procuring flexibility services from energy consumers has been a potential
solution to accommodating renewable generations in future power system.
However, efficiently and securely coordinating the behaviors of diverse market
participants within a privacy-preserving environment remains a challenge. This
paper addresses this issue by introducing a game-theoretic market framework for
real-time energy balancing. The competition among energy consumers is modeled
as a Generalized Nash Game (GNG), which enables the analysis of their strategic
decision-making. To mitigate the market power exerted by active energy
consumers, we employ a supply function-based bidding method in this market
design. We incorporate physical constraints to ensure the secure operation of
the distribution network. Previous approaches to steering consumers towards the
Generalized Nash Equilibrium (GNE) of this game often necessitate the sharing
of private information, either in full or in part, which may not be practically
feasible. To overcome this limitation, we propose a preconditioned
forward-backward algorithm, with analytical convergence guarantees, that only
requires participants to share limited, non-private sensitive information with
others. Finally, numerical simulations on the enhanced IEEE 33-bus test case
validate the effectiveness of our proposed market mechanism and algorithm.
