Abstract
In the conventional definition of a normal-form game, payoffs can only be dealt with in real values, and thus non-quantifiable payoffs cannot be dealt with mathematically and rigorously. Therefore, a generalized normal-form game is defined such that non-quantifiable payoffs can be treated mathematically and rigorously. Furthermore, the mathematical significance of this definition and its practical significance in the field of business are also discussed. However, although the mathematical and practical significance of the definition is discussed, its relevance to the business field is not. Therefore, in this study, I delved into the significance of the payoff function in the definition of a generalized normal-form game and discussed its relevance in the field of business. As a result, it was found that the set of players can be classified by the payoff function of the generalized normal-form game, that is, the players are grouped by the payoff function and can be interpreted as forming a single decision-making entity as one player. Furthermore, I successfully mentioned the relevance of the mapping of power and interest grids in stakeholder analysis used in business analysis and the classification by the generalized normal-form game with payoff functions.
