Mechanism Design for Privacy-Preserving Information Sharing in Oligopoly Competition

Information sharing among competing suppliers can improve decisions under demand uncertainty, but it may also intensify strategic interaction by aligning firms' beliefs. We study a Cournot oligopoly in which a platform designs an information-sharing mechanism using participation-contingent access, external platform information, and privacy-preserving noise. The central privacy-design challenge is that noise has two opposing effects: it limits how much a firm's report improves rivals' information, but it also reduces the value of the posterior signal released by the platform. In symmetric duopoly, privacy protection alone cannot implement sharing without an external platform signal. More generally, privacy can induce firms that would otherwise not share to participate only when combined with external platform information, which preserves an informational benefit independent of competitors' reports. The $n$-firm case adds a distinct force: under reciprocal access, non-participants lose access to the pooled signal generated by others, so a baseline sharing region may exist even without privacy protection or platform signals. We characterize this sharing-feasible region and show how external information and privacy noise expand it beyond the reciprocal-access baseline. We further provide conditions under which full sharing, rather than partial participation, is the unique participation equilibrium. Finally, we show that privacy noise is valuable as an implementation tool but costly for welfare, so the platform chooses the least distortionary privacy level that implements full sharing, and privacy-induced sharing improves total surplus only when participation gains outweigh informational losses.