Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) said that the Messenger of Allah (peace and blessings be upon him) "forbade shighar (exchange marriage)", and "shighar is that a man arranges his daughter's marriage with another man on the condition that the other gives him his own daughter in marriage, with no dowry (mahr) between them"; but Yahya did not mention the other man.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14134
Nafi' said that Sayyiduna Abdullah bin Umar (may Allah be pleased with them both) said that the Messenger of Allah (peace and blessings be upon him) "forbade shighar". I asked Nafi': What is shighar? He said: A man marries another man's daughter and his own daughter is married to that man, with no dowry between them; and he marries another man's sister and his own sister is married to the other, without dowry.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14135
Sayyiduna Abu Hurayrah (may Allah be pleased with him) said that the Messenger of Allah (peace and blessings be upon him) forbade shighar, and Ibn Numayr added: "Shighar is that a man says to another man: Marry your daughter to me and I will marry my daughter to you; and marry your sister to me and I will marry my sister to you."
(b) Abdah narrates from Ubaydullah: "and there is no dowry between them."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14136
Sayyiduna Jabir bin Abdullah (may Allah be pleased with him) said that the Messenger of Allah (peace and blessings be upon him) forbade "shighar", and shighar is that the private part of one woman is the dowry for the other woman.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14138
Abd al-Rahman bin Hurmuz al-A'raj (may Allah have mercy on him) said that al-Abbas bin Abdullah bin Abbas (may Allah be pleased with them both) married his daughter to Abd al-Rahman bin al-Hakam, and Abd al-Rahman bin al-Hakam married his daughter to him, and they also set a dowry. Sayyiduna Mu'awiyah (may Allah be pleased with him) wrote to Marwan (may Allah have mercy on him) to separate them, because this "is the shighar which the Messenger of Allah (peace and blessings be upon him) forbade".
Hadith Referenceالسنن الكبرى للبيهقي / كتاب النكاح / 14140