The evolutionary analysis of the ultimatum game based on the net-profit decision

• The ultimatum game model based on the net-profit decision is proposed.
• Kindness rather than fairness increases the average payoff of the whole population.
• Kind and fair players survive by forming compact isolated clusters.

In an ultimatum game where competitive pressures and alternating roles exist, we suppose that players make their decisions based on the net profit of their own. Here we conduct a behavioral experiment in a selection examination, and then we establish a model and study the evolution of strategies on square lattices. In this model, we specify a player’s strategy with two parameters: offer level α∈[0,1)α∈[0,1) and net profit acceptance level β∈[−1,1)β∈[−1,1). Evolutionary results show that individuals characterized by fairness (α→0.5)(α→0.5) and moderate kindness (β<0β<0, β→0.0β→0.0) prevail over other individuals. Further analysis demonstrates that individuals’ kindness rather than fairness increases the average payoff of the whole population. Moreover, we conclude that the emergence of kindness is promoted by the spatial structure, and eventually the evolutionary advantage is gained by kindness.