• Algorithms affect stable allocations of collaborative benefits or costs • Improving an algorithm can result in a worse allocation of costs or benefits • Consultants can extract benefit from a collaboration by having a good algorithm The characteristic function of a cooperative game typically results from a decision making process involving optimization. In practice, players have individual algorithms to solve the underlying optimization problem, which differ in quality. Therefore, the quality of the algorithm affects the characteristic function. We define the value of an algorithm as the benefit to the player, e.g. a cost reduction. We provide conditions under which an improvement in the algorithm quality yields a benefit, but also show that surprisingly an improved algorithm might be disadvantageous. Our model naturally admits a representation of a consultant, specialized in algorithms while not directly facing the underlying optimization problem. We present conditions under which a profit for the consultant is guaranteed, but also show that only a limited number of consultants can simultaneously make a profit. We illustrate our findings by means of numerical experiments on 580800 instances with an underlying pickup and delivery problem.

• Propose a model to assess efficiency with endogenous material flow coefficients. • We show how to estimate the proposed model and apply it to study pollution cost. • Illustrate the methodology on 33 OECD and BRICS countries from 2001 to 2019. • We provide interesting insights on available options to scale down CO2 emissions. Departing from traditional approaches that treat carbon dioxide ( CO2 ) emissions as a bad output, therefore relying on the weak disposability assumption, this paper considers CO2 emissions as a cost to minimise, thus preserving the materials balance condition. In particular, we extend the pollution cost approach (Coelli et al., 2007) by evaluating peer countries on their carbon intensity per total energy consumption, in addition to their energy use. The proposed methodology is then applied to estimate the extent to which a selection of 33 OECD and BRICS countries can reduce their CO2 emissions, given their gross domestic products and populations over the 2001–2019 period. Our results indicate that the period mean reduction potential for CO2 emissions of 60 % (i.e. an efficiency level of 40 %) can be decomposed into a 33 % reduction in energy intensity and a 40 % decrease in the carbon intensity of energy (i.e. efficiencies of 67 % and 60 %, respectively).