The 2030 Agenda for Sustainable Development, adopted in 2015, outlines 17 SDGs aiming for global prosperity and well-being. While many countries have implemented plans to achieve these goals, challenges remain due to various political and economic factors, underscoring the need for synergistic international action as highlighted by the IPCC. The Paris Agreement further emphasizes international cooperation, focusing on strengthening scientific knowledge, fostering community cooperation, and providing capacity-building support. Despite widespread recognition of the importance of international cooperation, quantitatively measuring this cooperation across the multifaceted SDGs has been challenging. Previous research often focuses on isolated national efforts without capturing the dynamic interplay of international collaboration. This study addresses this gap by introducing a novel synergy-based framework for quantitatively measuring international cooperation towards SDGs, detailing individual country contributions (positive or negative). The G7, comprising Canada, France, Germany, Italy, Japan, the UK, and the US, serves as a case study due to their status as advanced economies and their stated commitment to SDG collaboration, although studies suggest incomplete integration of SDGs into domestic policies and inter-member relations. The COVID-19 pandemic highlighted the need for a shift towards more socially equitable and environmentally sustainable economies within the G7. The synergy-based framework helps provide a deeper understanding of how policy decisions affect countries' SDG progress, enabling both current policymaking and retrospective analysis for continuous improvement.

Existing literature highlights the importance of international collaboration for achieving the SDGs but lacks a robust quantitative approach to assess the level of cooperation among nations. Studies predominantly focus on individual national efforts and commitments to specific targets, neglecting the dynamic interactions and collective impact of international cooperation. The need for a quantitative method to measure interactive and cumulative efforts among countries working towards shared goals has been widely acknowledged. This research bridges that gap by introducing a synergy-based framework.

This study utilized data from the Our World in Data database for 42 SDG indicators (economic (SDGs 1-9) and environmental (SDGs 12-15)) spanning 2000-2020. All indicators were normalized to a range of 0-1. The methodology involved three key components: 1. **Quantifying Oscillation in SDG Indicators:** Domestic Changes (DC) were calculated as the distance between consecutive yearly indicator values for each country. Foreign Changes (FC) were calculated as the distance between the average indicator values of all G7 countries in consecutive years. 2. **Calculating Synergy:** Synergy for each year was calculated by subtracting FC from the sum of DC for all countries and dividing by the number of countries. A sign function determined the synergy's direction (positive if aligned with the indicator's expected direction, negative otherwise). 3. **Quantifying Individual Country Contributions:** Contribution of each country to the overall synergy was calculated as the percentage change in domestic change from year to year, divided by the yearly synergy and its sign. This reflects each country's positive or negative contribution to overall G7 synergy. The R programming language was used for data processing, synergy calculation, and figure generation.

The analysis revealed synchronized domestic changes in economic indicators across G7 countries, reflecting a close relationship. Oscillations were observed during the 2008 financial crisis and the 2020 COVID-19 pandemic. Environmental indicators showed significant fluctuations among countries, with notable instability in Japan (2011 Tohoku earthquake), France, and Germany. Gross synergy analysis across all SDG indicators demonstrated a fluctuating trend around zero, with positive synergy prevailing over the period. Economic synergies were significantly affected by the 2008 and 2020 crises. Environmental indicators showed mostly positive but small synergies, suggesting the need for more collaboration. Analysis of individual country contributions revealed positive contributions to economic indicators across all G7 members, with Canada having the highest overall positive contribution for GDP growth. In contrast, environmental indicators revealed disparities, with Canada and Germany showing significant negative synergy contributions, while France and Italy showed positive contributions. The median synergy contributions indicate that all G7 countries positively contributed to economic growth, while their performance on environmental indicators was mixed, with some countries showing negative contributions. The differences in contributions highlight the need for strengthened collaboration among G7 countries in addressing climate change and preserving biodiversity.

The findings highlight the existing strengths and weaknesses in G7 cooperation on SDGs. The strong economic synergy reflects a cohesive approach to economic development but the disparities in environmental performance underscore a critical need for increased collaborative efforts. The framework employed effectively quantifies the level of cooperation among G7 countries towards achieving the SDGs. While the study identifies these strengths and challenges, the absence of quantitative data for socio-dimensional aspects of the SDGs limits the scope of analysis.

This study presents a novel quantitative framework for assessing international collaboration on SDGs, applied to the G7. The findings reveal a strong economic synergy but highlight significant discrepancies in environmental performance, emphasizing the need for enhanced G7 collaboration to tackle climate change and biodiversity loss. Future research could expand the scope to include socio-dimensional indicators and additional countries or regions.

The study's scope was limited to the G7 countries and a selection of economic and environmental SDG indicators. The absence of data for socio-dimensional aspects prevented a comprehensive assessment of all SDG dimensions. The analysis relied on available data, which might have limitations in terms of accuracy and completeness. The time frame (2000-2020) may not fully capture long-term trends and the impacts of recent global events beyond 2020.