The Gemara discusses the enforceability of an agreement to submit to arbitration and whether a party may retract before judgment is issued. The discussion turns on when binding consent is established, not on whether the document named both parties explicitly.
מַתְנִי׳ אָמַר לוֹ: ״נֶאֱמָן עָלַי אַבָּא״, ״נֶאֱמָן עָלַי אָבִיךָ״, ״נֶאֱמָנִים עָלַי שְׁלֹשָׁה רוֹעֵי בָּקָר״. רַבִּי מֵאִיר אוֹמֵר: יָכוֹל לַחְזוֹר בּוֹ, וַחֲכָמִים אוֹמְרִים: אֵינוֹ יָכוֹל לַחְזוֹר בּוֹ. אָמַר רַב יְהוּדָה אָמַר שְׁמוּאֵל: מַחְלוֹקֶת בְּ״מָחוּל לָךְ״, אֲבָל בְּ״אֶתֵּן לָךְ״ – דִּבְרֵי הַכֹּל יָכוֹל לַחְזוֹר בּוֹ. וְרַבִּי יוֹחָנָן אָמַר: בְּ״אֶתֵּן לָךְ״ – מַחְלוֹקֶת. תָּא שְׁמַע, דְּאָמַר רָבָא: מַחְלוֹקֶת בְּ״אֶתֵּן לָךְ״, אֲבָל בְּ״מָחוּל לָךְ״ – דִּבְרֵי הַכֹּל אֵין יָכוֹל לַחְזוֹר בּוֹ.
MISHNA: If one litigant says to the other: My father is trusted to adjudicate for me, or: Your father is trusted to adjudicate for me, or: Three cattle herders, who are not proficient in halakha, are trusted to adjudicate for me, all of whom are disqualified from serving as judges, Rabbi Meir says: The one who made the offer can retract it, and the Rabbis say: He cannot retract it, but must accept their verdict. Rav Yehuda says that Shmuel says: The dispute between Rabbi Meir and the Rabbis is with regard to a case where the claimant had said to the defendant: The money I claim you owe me is forgiven you if my father or your father rules as judge to that effect, and the claimant subsequently wishes to retract his offer. But in a case where it is the defendant who said: I will give you what you claim if that is the ruling of this judge, everyone agrees that he can retract his offer. And Rabbi Yoḥanan says: The dispute is with regard to a case where the defendant said: I will give you what you claim if that is the ruling of this judge. The Gemara suggests: Come and hear a resolution from that which Rava says: The dispute is with regard to a case where the defendant says: I will give you, but in a case where the claimant says: The money I claim you owe me is forgiven you, everyone agrees that he cannot retract his offer.