We use reciprocal verbs and reflexive pronouns such as each other to describe actions that happen mutually. (We can also use one another in these sentences.)
Verbs that follow this pattern are agree, argue, chat, debate, disagree, discuss (something), fight, joke, quarrel and reach an agreement.
We can also describe these actions using the pattern below:
plural noun + verb + among + plural reflexive pronoun
Therefore, these two sentences have the same meaning:
Here are some more examples:
However, in sentences with non-reciprocal verbs, changing -selves for each other changes the meaning.
Compare: