Optimal coupling of rewards beyond one-dimensional bias curves

Determine how reward schedules should be optimally coupled when agents’ biases are supported on a two-dimensional region rather than on a one-dimensional curve, and establish whether coupled-reward principles scale to more complicated environments.

Background

The paper constructs coupled reward schedules for two agents whose biases lie on a known, strictly decreasing one-dimensional curve. The difference between the agents’ actions then identifies their bias pair, allowing the reward schedule to correct incentives and make the human’s loss arbitrarily small. The authors explicitly note that this construction relies on the lower-dimensional support restriction. When biases instead vary over a two-dimensional region, the action difference generally cannot identify both biases, so the optimal design of coupled rewards and the scalability of the approach remain unresolved.

References

Of course, biases might, in practice, be supported on the two-dimensional plane so the reward schedule can no longer be designed to achieve the first-best outcome. We think an interesting open problem is how reward should be optimally coupled then---and more broadly whether such principles might scale to more complicated environments.

— Mechanism Design for Alignment and Control  (2609.01595 - Bergemann et al., 1 Sep 2026) in Section 5, roman example “Competition through coupled rewards” (Section 5.2, following Proposition 5.1)