It is advantageous for collecting agents in interconnected systems to exchange information (e.g., functions of their measurements) in order to improve their local processing (e.g., state estimation) because of the typically correlated nature of the data in such systems. 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 focuses on a two-agent interactive setting and uses a communication protocol in which each agent is capable of sharing a compressed function of its data. The objective of this paper is to study centralized and decentralized mechanisms that can enable and sustain non-zero 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 are derived analytically and allow a distributed implementation. In contrast, in the decentralized setting, repeated discounted games are shown to naturally enable data exchange (without any central control or economic incentives) resulting from the power to renege on a mutual data exchange agreement. For both approaches, it is shown that non-zero data exchanges can be sustained for specific fidelity ranges even when privacy is a limiting factor. This paper makes a first contribution to understanding how data exchange among distributed agents can be enabled under privacy concerns and the resulting tradeoffs in terms of leakage vs. estimation errors.
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