Final answer:
The child who isolates himself and refuses to play with others is likely experiencing 'basic anxiety' according to Karen Horney's psychoanalytic social theory, as this aligns with her 'moving away from people' coping style.
Step-by-step explanation:
In Karen Horney's psychoanalytic social theory, she discussed the concept of basic anxiety as a critical force in personality development. According to Horney, basic anxiety arises from early childhood experiences of feeling alone and isolated. When considering the options provided in your question, a child isolating themselves and refusing to play with others may be expressing a coping mechanism of 'moving away from people.' This is one of the three coping styles Horney identified, characterized by detachment and isolation as a way to handle anxiety.
Consequently, the correct answer here is (a) Basic anxiety. This style of coping is characterized by detachment and isolation, which aligns with a child isolating himself and refusing to play with others.