In a variety of distributed systems including critical infrastructure networks* such as the Smart Grid, information sharing and data exchanges are essential for reliable and sustained operation. However, despite its importance, data sharing in such systems is stymied, due to the lack of a framework that addresses the competitive interests and information leakage concerns of the various data generating agents. This leads to a new competitive privacy problem amongst the agents that captures the tension between sharing data to ensure network reliability (utility/benefit to all agents) and withholding data for profitability and privacy reasons. For a specific problem of distributed linear state estimation, recent results on tradeoff between estimate fidelity and leakage of private state data as a result of sharing data are presented for a two agent network model which demonstrates the optimality of one-shot information exchange. The applicability of such one-shot interactions for a larger network of agents is briefly discussed.