This study investigates how the commitment of firms under competition influences environmental sustainability investment, pricing decisions, and profits of firms. We consider a stylized model where two firms compete in the market and examine three scenarios: (1) both firms commit, (2) only a single firm commits, and (3) neither firm commits. Interestingly, we find that commitment to sustainability investment by all firms results in the lowest sustainability investment in the industry. However, when a commitment is only made by one firm, sustainability investment in the industry can be the highest. Compared with under the no commitment scenario, a committed firm obtains a higher profit regardless of whether the commitment is also made by the competitor, but the competitor may become more profitable than the committed firm when it does not make a commitment. Although commitment by all firms yields the largest profits, it is the least effective from the entire societal perspective, resulting in both the lowest social welfare and the lowest sustainability investment. Instead, commitment by a single firm or no commitment can be the most effective for the entire society. We also discuss the implications of the investment efficiency of sustainability and consumer taste preference.

The K-means algorithm, widely used in cluster analysis, is a centroid-based clustering method known for its high efficiency and scalability. However, in realistic situations, the operating environment is susceptible to contamination issues caused by outliers and distribution departures, which may lead to clustering results from K-means that are distorted or rendered invalid. In this paper, we introduce three other alternative algorithms, including K-weighted-medians, K-weighted-L ² -medians, and K-weighted-HLs, to address these issues under the consideration of data with weights. The impact of contamination is investigated by examining the estimation effects on optimal cluster centroids. We explore the robustness of the clustering algorithms from the perspective of the breakdown point, and then conduct experiments on simulated and real datasets to evaluate their performance using new numerical metrics. The results demonstrate the effectiveness of the proposed K-weighted-HLs algorithm, surpassing other algorithms in scenarios involving both contamination issues.