Strongly polynomial-time algorithm for optimal contract computation

Determine whether computing a revenue-optimal contract in the discrete principal–agent model with limited liability (actions and outcomes specified by costs, rewards, and a technology matrix q) admits a strongly polynomial-time algorithm, possibly under additional regularity assumptions such as the monotone likelihood ratio property (MLRP) or first-order stochastic dominance (FOSD).

Background

The survey shows that optimal contracts can be found via linear programming and therefore in weakly polynomial time. However, whether linear programming itself admits a strongly polynomial algorithm is a classic open problem. This raises a natural computational question specifically for the optimal contract problem: can its special structure (or added regularity such as MLRP/FOSD) yield a strongly polynomial-time algorithm?

Answering this would clarify the exact computational complexity of designing optimal contracts and potentially improve practical solvability in large-scale environments.