This paper develops a theory of monopolistic markets for information in environments where buyers interact strategically. A monopolist designs and sells signals about an uncertain state to players engaged in a linear-quadratic game, encompassing settings such as price and quantity competition, financial trading, and public-good provision. The seller's revenue coincides with the aggregate equilibrium value of information, which is endogenously shaped by the strategic interactions. Under strategic complementarity the seller fully reveals the state, whereas under substitutability she optimally distorts or anticorrelates signals and may restrict sales to a subset of players. The analysis also characterizes the efficiency and welfare implications of such markets, showing how information externalities govern whether information is under- or over-provided relative to the social optimum.
This paper characterizes convex information costs using an axiomatic approach. We employ mixture convexity and sub-additivity, which capture the idea that producing “balanced” outputs is less costly than producing “extreme” ones. Our analysis leads to a novel class of cost functions that can be expressed in terms of Rényi divergences between signal distributions across states. This representation allows for deviations from the standard posterior-separable cost, thereby accommodating recent experimental evidence. We also characterize two simpler special cases, which can be written as either the maximum or a convex transformation of posterior-separable costs.
This paper examines how departures from Bayesian updating shape the value of information for subjective expected utility maximizers. Using the ex-ante expectation of interim utilities, it characterizes when one information structure is preferred to another across all decision problems, extending the classic equivalence between dominance à la Blackwell and the mean-preserving spread order on induced posterior distributions beyond the Bayesian benchmark. The analysis identifies non-Bayesian updating as a source of non-instrumental value, and thus of information avoidance. It then introduces two axioms that characterize systematic distortions (de Clippel and Zhang, 2022), a class of updating rules in which each signal’s posterior depends only on its likelihood ratios. Within this class, the paper shows that three properties—the absence of non-instrumental value, the universal optimality of perfectly learning the state, and the desirability of additional information in all decision problems—are equivalent, and it characterizes the distortions under which they obtain. Finally, it highlights a sharp contrast between underreaction and overreaction: while the principle that more information is better can survive under underreaction, it necessarily fails under overreaction. A parallel distinction also emerges under ex-post payoff evaluation, despite important differences in how the two criteria map updating distortions into information value.
We analyze the infinite repetition with imperfect feedback of a simultaneous or sequential game, assuming that players are strategically sophisticated—but impatient—expected-utility maximizers. Sophisticated strategic reasoning in the repeated game is combined with belief updating to provide a foundation for a refinement of self-confirming equilibrium. In particular, we model strategic sophistication as rationality and common strong belief in rationality. Then, we combine belief updating and sophisticated reasoning to provide sufficient conditions for a kind of learning—that is, the ability, in the limit, to exactly forecast the sequence of future observations—thus showing that impatient agents end up playing a sequence of self-confirming equilibria in strongly rationalizable conjectures of the one-period game.
