Markets for (concealable) information

We study markets in which imperfectly informed experts occasionally receive signals about an unknown state and sell their expertise to decision makers. Experts care both about profits and about influencing decisions toward a preferred action. Potential customers have heterogeneous idiosyncratic biases favoring a particular action, but they also value matching their action to the true state. We show that, in a monopoly market with uniformly distributed decision maker biases, an expert has no incentive to filter information, even when biased. However, when decision maker biases are not uniformly distributed, filtering becomes an instrument of influence, and the optimal filtering depends on whether the distribution is moderate or polarized. Similarly, if influence requires securing a majority rather than maximizing overall support, the monopolist trades off profits against the probability of gaining the required majority. In a duopoly, we characterize how purchasing decisions depend on expert biases and signal quality. The total amount of information purchased can be non-monotonic in the preferences of decision makers. By contrast, when experts do not value influence and disclose truthfully, any equilibrium requires that decision makers either purchase from both experts or from none. Our results shed light on information provision in media markets and, more broadly, on competition among biased experts seeking to influence decisions.