CRITIC weighting and tripartite game reveal how public buildings can cut energy use

Public institutions—universities, government offices, hospitals, and civic venues—are among the most consequential energy consumers in any economy. They operate at large scale, run energy-intensive systems around the clock, and carry a demonstration weight that private buildings simply do not have. When a university retrofits its campus or a government office upgrades its lighting, the signal ripples far beyond the building envelope. A new study published in Frontiers in Energy Research argues that unlocking this sector’s efficiency potential requires more than better technology: it demands a rigorous way to measure what energy efficiency actually means, and a realistic model of how the stakeholders who must pay for it will behave. The research, led by Wuxiao Chen of State Grid Fujian Electric Power and Yingru Zhao of Xiamen University, combines a statistical weighting method called CRITIC with a tripartite evolutionary game model to evaluate and strategically optimize energy efficiency in public institutions under China’s Carbon Inclusion mechanism.

The motivation is grounded in policy reality. In 2025, China’s National Administration of Government Offices issued a Work Plan for Energy and Resource Conservation in Public Institutions, calling on the sector to align its energy consumption and carbon emissions with the country’s carbon peaking and carbon neutrality goals. Yet the study’s authors point out that existing evaluation standards, management mechanisms, and technical solutions are often inadequate for the demands of a rapidly decarbonizing energy system. Building stock keeps expanding, energy use patterns keep shifting, and energy management has grown more complex as a result. Previous research has tended to focus on isolated technical dimensions—energy consumption and carbon emissions—without a comprehensive, systemic evaluation approach, leaving the energy-saving potential of public institutions poorly identified and efficiency initiatives less effective than they could be.

To close that gap, the team constructed a four-dimensional evaluation system with ten core indicators. The first dimension, energy and resource consumption, tracks per capita comprehensive energy consumption, energy consumption per unit floor area, and per capita water consumption—all cost-type indicators where higher values signal worse performance. The second, advanced guidance, captures the low-carbon transition: carbon emissions per unit floor area, the utilization rate of renewable energy and green power, and the return on investment of technological retrofits. The third, operational management, measures the maturity of energy management systems and the compliance rate of energy efficiency diagnostics for equipment. The fourth introduces scenario-specific indicators tailored to institution type—campus green space coverage and semester-to-vacation energy elasticity for schools, new energy vehicle penetration for government fleets, equipment energy efficiency ratios for hospitals, and heat recovery rates for public venues.

The technical heart of the evaluation is the CRITIC method—Criteria Importance Through Intercriteria Correlation. Unlike purely subjective weighting schemes, CRITIC determines each indicator’s weight from two statistical properties: its contrast intensity, measured by standard deviation across alternatives, and its conflict with other indicators, measured by correlation coefficients. An indicator that varies strongly across retrofit options and remains relatively independent of its peers carries more information and earns a higher weight. The authors normalized the raw evaluation matrix, computed comparative strength and inter-indicator correlations, quantified each indicator’s information content, and normalized the results into final weights. The outcome was striking: technological innovation indicators dominated, with the utilization rate of renewable energy earning the highest weight at 0.258 and carbon emissions per unit floor area close behind at 0.234. In other words, for a university campus, low-carbon technology is not one consideration among many—it is the decisive one.

The framework was tested on a university in Fujian Province, a 600-acre campus serving roughly 30,000 faculty and students, whose current energy system draws about 85 percent of its supply from the municipal grid with natural gas and solar playing supplementary roles. The team modeled the campus as an integrated energy system comprising gas boilers, rooftop photovoltaics, water-source heat pumps, a combined cooling, heating, and power unit with cascade waste heat recovery, electric cooling units, and electric vehicle charging piles, all subject to energy flow balance, carbon emission, and equipment operation constraints. Seven retrofit schemes were evaluated: a comprehensive combination optimized for the highest energy efficiency index; forced scenarios mandating near-maximum deployment of CCHP, photovoltaics, or water-source heat pumps; a management-forced scenario deploying energy management systems campus-wide; a full building envelope retrofit; and a high-efficiency equipment replacement scenario.

The results were unambiguous. The comprehensive retrofit scheme scored highest at 0.907, followed by photovoltaic installation at 0.822 and equipment replacement at 0.797. Forced single-technology scenarios and envelope retrofits lagged well behind, suggesting that while any single measure may optimize certain indicators, comprehensive improvement requires coordinated deployment. Over a 20-year operational period, the comprehensive scheme reduced net present cost by 18.4 percent, annual carbon emissions by 25.2 percent, annual primary energy consumption by 28.1 percent, and annual grid electricity purchases by 34.4 percent—cutting the campus’s dependence on the public grid dramatically. Robustness checks using TOPSIS and the entropy weight method confirmed the ranking of the top schemes, validating the CRITIC-based framework despite minor variations in intermediate positions.

Evaluation alone, however, cannot explain why efficiency projects stall or succeed. Energy efficiency improvement in public institutions is inherently a strategic interaction among three parties: the government, which formulates policy and provides subsidies; integrated energy service providers, or IESPs, which implement projects and trade carbon credits; and the public institutions themselves, which decide whether to undertake retrofits. The study constructed a tripartite evolutionary game model in which each party chooses between active and passive strategies, with payoffs derived directly from the physical energy flows and carbon accounting of the integrated energy system. The public institution’s energy-saving benefit is computed from the difference in energy procurement costs before and after retrofit, while the IESP’s carbon trading revenue is defined by the total verified emission reduction multiplied by the unit carbon price—strictly coupling economic strategy to physical operations.

Stability analysis of the replicator dynamic equations, using the Jacobian matrix and Lyapunov’s first method, revealed that the game system stabilizes at only two evolutionary equilibrium points. Numerical simulations over 50 evolutionary time steps showed that the carbon trading price is the critical lever. Using case parameters, the team calculated the exact subsidy-free carbon price threshold required to trigger IESP participation at 71.29 RMB per ton. Below that threshold—at 70 RMB per ton—the government declines to enforce incentive policies, the IESP refuses to implement the project, and the educational institution pursues the retrofit autonomously because its realized benefits outweigh the modification costs. Above the threshold—at 80 RMB per ton—the IESP actively implements the project and offers incentives to the participating institution, which reciprocates by undertaking the retrofit, even though the government remains passive.

Sensitivity analysis on initial willingness and key parameters added further nuance. Regardless of the government’s initial probability, its strategy invariably converged to non-intervention, indicating that subsidies function primarily as early-stage accelerators rather than permanent supports. Higher initial willingness among all parties correlated with faster convergence to the stable cooperative state. Variations in the magnitude of government subsidies and IESP incentives exerted no significant influence on evolutionary speed during stabilization, suggesting these financial levers are guiding and auxiliary mechanisms within the framework. Most critically, the perceived cost of retrofitting dramatically affected the rate of evolution: lower perceived costs accelerated convergence, but if perceived costs exceeded expected energy-saving benefits, the system rapidly shifted toward a non-cooperative equilibrium characterized by withdrawal from the project.

The study’s practical implications are considerable. Rather than applying uniform policies, the authors recommend that policymakers use this case-based calculation methodology to determine institution-specific dynamic policy triggers: subsidies should be activated when the carbon price falls below the institution-specific mark and systematically phased out once the market price exceeds it, minimizing redundant fiscal expenditure. IESPs, for their part, should establish dynamic carbon pricing response and incentive adjustment mechanisms, and promote models such as energy management outsourcing that lower the technical barriers for public institutions undertaking retrofits. The authors acknowledge two limitations: the empirical results rest on a single university case, and the deterministic game model may not fully capture the stochastic volatility of real energy and carbon markets. Future work should validate the framework across hospitals, government agencies, and public venues, and integrate stochastic evolutionary game frameworks—potentially by introducing Gaussian white noise into dynamic pricing parameters—to enhance robustness. For now, the message is clear: measuring efficiency rigorously and modeling stakeholder behavior realistically are twin prerequisites for turning public buildings into engines of decarbonization.

Subject of Research: Energy efficiency evaluation and stakeholder strategy optimization in public institutions using CRITIC weighting and evolutionary game theory

Article Title: Evaluation and strategic optimization of public institution energy efficiency: a hybrid framework combining CRITIC weighting and tripartite evolutionary game

Article References: Chen, W., Xiong, Y., Zhang, C., Cai, Y., Jiang, Z., Xu, Z., Yang, K., Xie, S., & Zhao, Y. (2026). Evaluation and strategic optimization of public institution energy efficiency: a hybrid framework combining CRITIC weighting and tripartite evolutionary game. Frontiers in Energy Research, 14, Article 1794357. https://doi.org/10.3389/fenrg.2026.1794357

Image Credits: AI Generated

DOI: 10.3389/fenrg.2026.1794357

Keywords: public institutions, energy efficiency, CRITIC weighting, evolutionary game theory, carbon trading, integrated energy systems, building retrofits, IESPs, government subsidies, carbon inclusion, renewable energy, decarbonization