This paper uncovers general properties of optimal information structures by exploiting a linear-programming formulation of information design. A critical observation is that an optimum can be found as ``sparse,''i.e., many coordinates of the action-state joint distribution are zero. This implies that, once part of an action-state profile is fixed, there is limited room for the remaining part to fluctuate. As a result, agents'action recommendations are conditionally deterministic in many states, or correlated in a way that allows some agents to infer others'recommendations. The implications of sparsity are illustrated in an adoption problem, where the designer maximizes the number of adopters of an innovation that features network effects. The optimal information structure deterministically recommends full adoption in high states, while it randomizes over nested action profiles in low states, so that whenever an agent is recommended to adopt, she is certain that more optimistic agents also adopt.
Kearns, Roth, and Ryu show that the output agent's error approaches the global predictor's error along sufficiently deep paths with suitable feature coverage, while insufficient depth can prevent aggregation even in large networks.
M. Bateni, Z. Hadizadeh, Mohammadtaghi Hajiaghayi et al.· 0 citations
The results provide a modular framework that can be used to analyze linear bandit algorithms and explicitly connect quality of parameter estimation to optimal regret accumulation.
Arda Güçlü, Subhonmesh Bose, J. Birge· 0 citations
A two-player zero-sum repeated game between a learner and nature whose value identity generates Bayesian updating and an exact accounting of exponential-weights regret at once is given, and supplies the comparator-class variational form that a wide class of concentration phenomena share.
Consider a situation wherein a decision maker sequentially searches for the best alternative among heterogeneous options with an arbitrary search order. The agent partially learns the value of an option when inspecting it. The information structure jointly determines the ex-ante and ex-post value of investigating each...
Peer prediction seeks to incentivize agents to truthfully report an observed signal by rewarding joint sets of reports without observing a ground truth. Following the generalization of information-theoretic mutual information introduced in Kong and Schoenebeck (2019), we call a function of a joint distribution over sig...
Abdellah Aznag, Robin Bowers, Rachel Cummings et al.· 2 citations
Change-of-measure lower bounds show that shared-reward identification is optimal up to one universal logarithmic factor, and that the entire statistical price of removing communication is a multiplicative $\rho^2$ in sample complexity.
Larissa Xu, Jasmine Nguyen, William Chang· 0 citations
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