You wish to wish the wish you wish to wish but if you wish the wish your friend will not wish to wish then your friend will not wish the wish you wish to wish What could be the possible wishes?
The wish that could be a possible wish is every wish in the world besides the friend's wish that you wished you would wish your friend would not wish to wish and that you wished to wish. Since you wish something your friend does not wish, and without further info. that is the only possible answer.
Logically, the wish could have been, "I wish no else would make this wish but me," assuming the wish came true.
Another possibility could be: "I wish my friend will not make this same wish."
But then there is the problem of context: If your friend wishes "I wish my friend will not make this same wish," is it the same as you wishing "I wish my friend will not make the same wish?" The 'I' and 'my friend' differ in each of these cases.