Optimal Information Provision for Strategic Hybrid Workers

TL;DR

This paper investigates how a strategic central planner can optimally signal information about an uncertain infectious risk to influence remote or in-person work decisions, using tailored signaling mechanisms to maximize desirable outcomes.

Contribution

It develops optimal signaling strategies for both stateless and stateful objectives, including a linear programming approach for the latter, advancing information design in strategic settings.

Findings

Optimal signaling partitions the parameter space into at most two intervals.

The linear program effectively computes optimal signals for stateful objectives.

Information design improves outcomes compared to no or full information benchmarks.

Abstract

We study the problem of information provision by a strategic central planner who can publicly signal about an uncertain infectious risk parameter. Signalling leads to an updated public belief over the parameter, and agents then make equilibrium choices on whether to work remotely or in-person. The planner maintains a set of desirable outcomes for each realization of the uncertain parameter and seeks to maximize the probability that agents choose an acceptable outcome for the true parameter. We distinguish between stateless and stateful objectives. In the former, the set of desirable outcomes does not change as a function of the risk parameter, whereas in the latter it does. For stateless objectives, we reduce the problem to maximizing the probability of inducing mean beliefs that lie in intervals computable from the set of desirable outcomes. We derive the optimal signalling mechanism and show that it partitions the parameter domain into at most two intervals with the signals generated according to an interval-specific distribution. For the stateful case, we consider a practically relevant situation in which the planner can enforce in-person work capacity limits that progressively get more stringent as the risk parameter increases. We show that the optimal signalling mechanism for this case can be obtained by solving a linear program. We numerically verify the improvement in achieving desirable outcomes using our information design relative to no information and full information benchmarks.