  Data collecting agents in large networks, such as the electric power system,
need to share information (measurements) for estimating the system state in a
distributed manner. However, privacy concerns may limit or prevent this
exchange leading to a tradeoff between state estimation fidelity and privacy
(referred to as competitive privacy). This paper builds upon a recent
information-theoretic result (using mutual information to measure privacy and
mean-squared error to measure fidelity) that quantifies the region of
achievable distortion-leakage tuples in a two-agent network. The objective of
this paper is to study centralized and decentralized mechanisms that can enable
and sustain non-trivial data exchanges among the agents. A centralized
mechanism determines the data sharing policies that optimize a network-wide
objective function combining the fidelities and leakages at both agents. Using
common-goal games and best-response analysis, the optimal policies allow for
distributed implementation. In contrast, in the decentralized setting, repeated
discounted games are shown to naturally enable data exchange without any
central control nor economic incentives. The effect of repetition is modeled by
a time-averaged payoff function at each agent which combines its fidelity and
leakage at each interaction stage. For both approaches, it is shown that
non-trivial data exchange can be sustained for specific fidelity ranges even
when privacy is a limiting factor.
