influence 

influence - n 
a power to affect persons or events especially power based on prestige etc; "used her parents' influence to get the job" 
a cognitive factor that tends to have an effect on what you do; "her wishes had a great influence on his thinking" 
the effect of one thing (or person) on another; "the influence of mechanical action" 

wordplays

Influence is the power to have an important effect on someone or something. If someone influences someone else, they are changing a person or thing in an indirect but important way.

Sometimes a person who influences another doesn't intend to have any effect, but sometimes they are using influence to benefit themselves. An example of a personal benefit or advantage would be the use of political influence. Influence is also a verb, from Latin influere to flow in.

vocabulary.com