On Daf 2a, we learn that our Mishna is R. Akiva who learns walled cities from time of Yehoshua. On 2b R. Yehoshua differs and has walled cities from the days of Achashverosh. Per Pesachim 112a some hold he was the son of R. Akiva - holding that this is the case how is he arguing on his father on the timing of what is a walled city? Rashi specifically notes here that R. Yehoshua didn't hear the Gezeira shava that's used in our Mishna from his rabbi so he can't use it. (Perhaps this just disproves that he is R. Akiva's son.)
Moshe Shalom, Brooklyn, NY
The Mishnah is Rebbi Akiva because the Megilah is read on Adar 11-15 because of "Zman, Zmanam, Zmaneihem" but the Chachamim read only on 14-15.
Basing on Yehoshua bin Nun's time or on Achashveirosh's time is another issue which Rebbi Akiva does not relate to (at least not openly). So Rebbi Yehoshua ben Karchah could argue on the standard opinion of the Mishnah.
All the best,
Reuven Weiner