Degree-based assignation of roles in ultimatum games on scale-free networks

► In most previous studies of ultimatum games on graphs, two linked individuals are endowed with the equal opportunity to act the game roles (proposer or responder). ► However, there may be not such absolute equality in real social systems. ► We in this paper propose a simple model of ultimatum game, in which a simple regime for assignation of the game roles are introduced. ► In the interaction between individuals the ultimatum game roles are assigned based on the social connectivities of participators (degree-based).