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

Most previous studies concerning ultimatum games in structured population assume either that the game roles are assigned randomly between linked individuals or that the game is played twice in an interaction, alternating the roles of proposer and responder. We develop a model in which individuals play the role of proposer with probabilities according to the degree. Specifically, players of two types are considered: (A) pragmatic agents, who do not distinguish between the different roles and aim to obtain the same benefit, and (B) agents whose aspiration levels and offers are independent. We investigate the evolution of altruistic behavior in pure populations with two different effective payoffs: accumulated payoffs and normalized payoffs. It is found that, for type B individuals, if the low-degree individuals can act as proposers with larger probabilities, the average value of offers reaches a higher point, irrespective of whether accumulated or normalized payoffs are used for strategy updating; for type A individuals, the two calculation methods for payoff lead to different outcomes