Here's a short story:

was settled by the Ainu, Nivkh, and Orok before recorded history. The "Nihon Shoki", finished in 720 AD, is often said to be the first mention of Hokkaido in recorded history. According to the text, Abe no Hirafu led a large navy and army to northern areas from 658 to 660 and came into contact with the Mishihase and Emishi. One of the places Hirafu went to was called , which is often believed to be present-day Hokkaido. However, many theories exist in relation to the details of this event, including the location of Watarishima and the common belief that the Emishi in Watarishima were the ancestors of the present-day Ainu people. 

During the Nara and Heian periods (710–1185), people in Hokkaido conducted trade with Dewa Province, an outpost of the Japanese central government. From the Middle Ages, the people in Hokkaido began to be called Ezo. Hokkaido, formerly known as Ezochi or . The Ezo mainly relied upon hunting and fishing and obtained rice and iron through trade with the Japanese. 

During the Muromachi period (1336–1573), the Japanese created a settlement at the south of the Oshima Peninsula. As more people moved to the settlement to avoid battles, disputes arose between the Japanese and the Ainu. The disputes eventually developed into a war. Takeda Nobuhiro killed the Ainu leader, Koshamain, and defeated the opposition in 1457. Nobuhiro's descendants became the rulers of the Matsumae-han, which was granted exclusive trading rights with the Ainu in the Azuchi-Momoyama and Edo periods (1568–1868). The Matsumae family's economy relied upon trade with the Ainu. They held authority over the south of Ezochi until the end of the Edo period in 1868. (End of story)

Provide your best guess for the following question. Give ONLY the guess, no other words or explanation.

For example:

Guess: <most likely guess, as short as possible; not a complete sentence, just the guess!>

Here are a few examples of questions and answers:

Question: When did Hokkaido do trading with the Dewa Province?
Guess: During the Nara and Heian periods (710–1185)

Question: When was Hokkaido first noted in history?
Guess: 720 AD, is often said to be the first mention of Hokkaido

Question: By what source?
Guess: According to the text of recorded history

Question: What was the name of that text?
Guess: The "Nihon Shoki",

Question: What does it say about Hokkaido?
Guess: Abe no Hirafu led a large navy and army to northern areas from 658 to 660 and came into contact with the Mishihase and Emishi.

Question: What happened in the Muromachi period?
Guess: the Japanese created a settlement at the south of the Oshima Peninsula.

Question: What time span does that period cover?
Guess: (1336–1573)

Question: What about the Nara period?
Guess: During the Nara and Heian periods (710–1185), people in Hokkaido conducted trade with Dewa Province

Question: What was Hokkaido once called?
Guess: formerly known as Ezochi

Question: What were the people from there called?
Guess: Ezo

Question: When where they first called that?
Guess: From the Middle Ages, the people in Hokkaido began to be called Ezo

Question: How did they source their food?
Guess: hunting and fishing

Question: What about rice?
Guess: obtained rice and iron through trade with the Japanese

Question: What led to the fighting between Japanese and the Ainu?
Guess: Japanese created a settlement at the south of the Oshima Peninsula, disputes arose

Question: What was the outcome from those disputes?
Guess: Takeda Nobuhiro killed the Ainu leader, Koshamain, and defeated the opposition in 1457

Question: What happened to the Edo period?
Guess: Nobuhiro's descendants became the rulers of the Matsumae-han

Question: When did that period occur?
Guess: (1568–1868)

Question: Did anyone trade with the Ainu?
Guess: Matsumae-han

Now answer the following question in the same format.

Question: Why did they trade with them?

they were granted exclusive trading rights with the Ainu