Figure 1. The average offer level p, acceptance level q, and the average payoff w of the population as functions of the parameter α at the equilibrium state.

The population is structured by the scale-free networks. The degree-based role assignment regime is invoked to determine whoever acts as the proposer. The larger the α is, the more likely the individuals of larger degrees serve as the proposers. Moderate fairness and gentle asking rate stabilize whenever low-degree individuals gain more chances to be proposers. However, the Nash Equilibrium solution of the Ultimatum game is recovered whenever advantage skews towards the large-degree individuals. Other parameter: m = 3, m₀ = 3, the population size N = 1000, selection intensity β = 10, δ = 0.005.