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Abstract: We study competitive data markets in which consumers own their personal data and can trade it with intermediaries, such as e-commerce platforms. Intermediaries use this data to provide services to the consumers, such as targeted offers from third-party merchants. Our main results identify a novel inefficiency, resulting in equilibrium data allocations that fail to maximize welfare. This inefficiency hinges on the role that intermediaries play as information gatekeepers, a hallmark of the digital economy. We provide three solutions to this market failure: establishing data unions, which manage consumers' data on their behalf; taxing the trade of data; and letting the price of data depend on its intended use. 

We propose and demonstrate a general method to calibrate the frequency-dependent response of selfcompensating noble-gas–alkali-metal comagnetometers to arbitrary spin perturbations. This includes magnetic and nonmagnetic perturbations such as rotations and exotic spin interactions. The method is based on a fit of the magnetic field response to an analytical model. The frequency-dependent response of the comagnetometer to arbitrary spin perturbations can be inferred using the fit parameters. We demonstrate the effectiveness of this method by comparing the inferred rotation response to an experimental measurement of the rotation response. Our results show that experiments relying on zero-frequency calibration of the comagnetometer response can over- or underestimate the comagnetometer sensitivity by orders of magnitude over a wide frequency range. Moreover, this discrepancy accumulates over time as operational parameters tend to drift during comagnetometer operation. The demonstrated calibration protocol enables accurate prediction and control of comagnetometer sensitivity to, for example, ultralight bosonic dark-matter fields coupling to electron or nuclear spins, as well as accurate monitoring and control of the relevant system parameters.