Multi-Agent Reinforcement Learning for Computer Agriculture Shared-Irrigation Scheduling Under Groundwater Rights Uncertainty: A Nash-Regret Evaluation

Shared irrigation schemes allocate a common aquifer among competing plots whose groundwater rights are incompletely specified, so that each irrigator's feasible extraction depends on others' choices and on a legal entitlement that may be revised. the present analysis formalises shared-irrigation scheduling as a stochastic game in which agents hold private beliefs over their rights and evaluates multi-agent reinforcement learning (MARL) against a Nash-regret criterion rather than against average reward. Because no field deployment is available, the study is a design-and-operating-characteristics analysis: a before-after-control-impact (BACI) evaluation design is characterised under a declared variance structure with between-cluster SD = 6.0, residual SD = 4.5 and intraclass correlation = 0.64, using 2000 replications per design cell across cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis derives a regret decomposition that separates entitlement uncertainty from strategic uncertainty, states conditions under which independent learners converge to a Nash equilibrium of the induced scheduling game, and reports the power and minimum detectable effect of the BACI design that would be used to evaluate such a scheduler. The contribution is a formal bridge between MARL convergence guarantees and the inferential limits of the agricultural evaluation designs that would test them.