Games restricted by simplicial complexes and an application to vertiport cooperation

Abstract

This article deals with the study of a simplicial complex and its properties as restrictive information in the context of a cooperative game. By analyzing the maximal partitions of the coalitions formed in the game, a connection between simplices and coalitions is established. This provides a clear understanding of the structure of coalitions and how they are formed. The main contribution of this paper concerns an axiomatization of a value for simplicial complexes given a game, and an application. The results obtained promise to broaden our understanding of coalition dynamics and optimal strategies in cooperative interaction situations. A new value for games restricted by a simplicial complex is proposed and also an axiomatization of this value is given. The application of the value is shown by an example where we propose a strategy to share the costs of vertiport-owning firms via a cooperative game and the simplicial complexes formed by the action areas of the vertiports.