The benefits of participants in the game may affect their willingness to participate in the game, and this willingness may be influenced by others. Based on this, we integrate the game willingness into the ultimatum game and establish an asymmetric coupling mechanism for the interdependent networked game, where the game willingness is adaptively adjusted by the change of payoff. A comparative study is conducted, which verifies that the adaptive adjustment mechanism considering game willingness can significantly improve the level of fairness. The simulation results further show that the extent of increase (decrease) of game willingness has a significant effect on fairness, while the evolutionary game results have a certain correlation with the coupling strength. In addition, the evolutionary dynamics of game willingness is explored and it is concluded that a lower average level of game willingness is conducive to the emergence of fairness.