The institutional analysis and development framework: A mathematical representation in water arena

Institutions are human-designed systems facilitating structured interactions to achieve specific objectives. The Institutional Analysis and Development Framework (IAD), introduced by Elinor Ostrom, is a valuable tool for analyzing these systems. This study formulates a mathematical representation of the IAD within an operational context related to water demand and supply services. It demonstrates that structuring institutional (sub)systems entails a cost driven by external factors and interactions. Such a cost functions as an outcome within the scope of the IAD. This outcome can be mathematically expressed based on the components of the action arena and exogenous variables within a given context and over a distinct timeframe. This concept provides a theoretical basis for computationally evaluating and comparing different system states across varying (sub)system structures.