A conversational agentic interface for residential energy digital twins will reduce coalition-based deviations in household energy decision-making by ≥35% when augmented with coalition-stable equilibrium constraints, improving alignment between homeowner, municipal, and aggregator objectives (Bridges: Conversational Agentic Interface × Computing Equilibrium beyond Unilateral Deviation × A Multi-Scale Optimization Framework for Grid-Integrated Electrolysis).

In a simulated multi-household residential energy testbed (N=50–200 households, 1 municipal planner, 1 aggregator), a conversational agentic interface that mediates energy decisions (retrofit timing, EV charging, thermostat setpoints, battery dispatch) while enforcing coalition-stable equilibrium constraints (core-stability / no-profitable-deviation constraints computed via cooperative game theory over the joint action space) will reduce the rate of coalition-based deviations — defined as the fraction of decision epochs in which any subset of stakeholders could unilaterally or jointly improve payoff by deviating from the recommended allocation — by ≥35% relative to a baseline conversational agent using single-objective (non-coalitional) optimization, measured over ≥500 simulated decision epochs, at p<0.05 significance, without degrading individual household cost savings by more than 10% relative to the non-coalitional baseline.

Minimum viable test: a controlled A/B simulation study.

• Arm A (baseline): Conversational agent + single-objective household-level optimizer (myopic cost minimization), no coalition constraints.
• Arm B (treatment): Conversational agent + coalition-stable equilibrium solver (e.g., core computation via linear programming relaxation or Shapley-value-guided allocation with no-deviation constraints) integrated into the digital twin recommendation loop.
• Both arms operate on identical synthetic household population (N=50 baseline cohort, scaled to 200 for stress test), identical price/tariff scenarios (5 scenarios: flat, TOU, dynamic real-time, demand-response event, extreme weather), identical digital twin models.
• Run 500 decision epochs (representing daily decisions over ~1.4 years simulated time) per scenario per arm, 5 random seeds each → 25,000 epoch-runs per arm.
• Primary outcome: coalition-deviation rate (fraction of epochs where ex-post payoff analysis reveals a profitable deviating coalition existed and was not prevented).
• Secondary outcomes: household bill savings, municipal congestion metric (peak-to-average ratio), aggregator profit variance, conversational turn count / user satisfaction proxy (simulated persona satisfaction score).

# Digital Twin + Conversational Coalition Coordinator

for each household h in cohort:
    twin[h] = calibrate_thermal_electrical_model(pecan_street_data[h])

personas = generate_synthetic_personas(n=200, weight_distributions=randomized)

class ConversationalAgent:
    def elicit_preferences(persona):
        dialogue = LLM.converse(persona)
        utility_params = parse_to_structured_utility(dialogue)
        return utility_params  # cost_weight, comfort_weight, emissions_weight

class BaselineOptimizer:
    def recommend(household_utility):
        return solve_MPC(household_utility, grid_constraints=None)

class CoalitionEquilibriumSolver:
    def recommend(all_utilities, municipal_utility, aggregator_utility):
        # joint allocation problem
        allocation = solve_LP(
            objective=weighted_sum(all_utilities, municipal_utility, aggregator_utility),
            constraints=[
                grid_feasibility_constraints,
                no_unilateral_deviation_constraint(all_agents),
                no_coalition_deviation_constraint(subset_sampling=True, k_max=5)
            ]
        )
        return allocation

for scenario in tariff_scenarios:
    for seed in seeds:
        for epoch in range(500):
            prefs = [agent.elicit_preferences(p) for p in personas]
            alloc_A = BaselineOptimizer.recommend(prefs)
            alloc_B = CoalitionEquilibriumSolver.recommend(prefs, muni_util, agg_util)
            deviation_rate_A[epoch] = check_profitable_deviations(alloc_A, prefs)
            deviation_rate_B[epoch] = check_profitable_deviations(alloc_B, prefs)

compute_stats(deviation_rate_A, deviation_rate_B)  # paired test, effect size, CI