Evaluation of Constrained Multi-Agent Reinforcement Learning for Computer Agriculture Groundwater Allocation Under Aquifer Drawdown: An Artificial Intelligence Regret Bound for Political Legitimacy of Abstraction Permits

Groundwater abstraction permits in computer agriculture allocate a shared aquifer among competing irrigators, yet the political legitimacy of any allocation rule depends on whether the rule can be shown to converge to a defensible distribution of abstraction rights under drawdown. The framework treats each abstraction permit as a constrained policy in a cooperative Markov game with a shared aquifer state, and characterises legitimacy as the regret of the permit regime relative to a counterfactual social planner who internalises drawdown externalities. The analysis is theoretical: no observational data are used or claimed. The principal result is a regret bound of order O(√(T log N)) for N agents over T allocation rounds under a constrained policy gradient, with an explicit dependence on the aquifer drawdown rate and the permit enforcement capacity of the regulator. The bound implies that legitimacy is not a property of the allocation rule alone but of the rate at which the rule's regret grows relative to the physical depletion of the aquifer.