Mathematical representation of bias and nudges centered on intangible goods using quantum information theory

Abstract: The purpose of this study is to explore whether the relationship between bias and nudges can be mathematically expressed in terms of quantum information theory, particularly by means of individually customized nudges. Based on the value function of customer satisfaction, which is subject to uncertainty due to the subjectivity of customer evaluations, a model of bias and nudges is proposed that takes into account the environment for intangible goods. Then, by defining an index of nudges from the mathematical properties of the value function obtained from this economic model, a model could be expressed in this study that has a mathematical structure of the same nature as nudges expressed in standard economics, where welfare is impaired by bias from the mathematical structure of the gross social surplus derived as a social welfare function. Moreover, the mathematical structure of the gross social surplus can be made larger than that in standard economics, adding knowledge about the mathematical design of nudges as individually customized customer experiences. This increases the feasibility of the economic model based on quantum information theory and the mathematical design of customized nudges.