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.
We study information aggregation in the networked learning model introduced by Kearns, Roth, and Ryu (SODA 2026). There is a fixed distribution over $d$ features and a common label. Agents learn in topological order on a directed acyclic graph. Each observes a subset of the features and its parents'predictions, fits a...
M. Bateni, Z. Hadizadeh, Mohammadtaghi Hajiaghayi et al.· 0 citations
Linear bandits model sequential decision-making problems with noisy rewards that are linear in the decision variable, where an agent must simultaneously learn about an unknown parameter that governs the mean rewards, while maximizing (expected) rewards over time. Two prominent algorithmic families--upper confidence bou...
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
Cooperative teams often need to agree on the best few options rather than simply accumulate reward, and they must do so while each member sees only a fragment of the team's collective experience. We study this as top-$K$ joint-arm identification in multi-agent multi-armed bandits: at every round $M$ agents simultaneous...
Larissa Xu, Jasmine Nguyen, William Chang· 0 citations
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