So far in this series, we've looked at prayers for ourselves, for which we must find the scriptures to stand on, we must have faith, and we must maintain our primary focus on the Lord. But how does this apply when we are praying for other people? We can't make others do or believe anything. God won't violate our free will, and we can't violate the free will of others in prayer, either. So how does this work?
It depends upon the context.

The default position is that we should be praying for all people at all times (1 Tim 2:1-6, Eph 6:18), as well as for the cities we live in (Jer 29:7). Just as for ourselves, this gives God "legal" entry into the affairs of men, so that He can intervene and do what He wants to do on the earth. The Old Testament priestly blessing was, “'The Lord bless you, and keep you; The Lord make His face shine on you, And be gracious to you; The Lord lift up His countenance on you, And give you peace’” (Numbers 6:23-27). This was what God wanted to do for the children of Israel, and the priests were to invoke this, to give Him permission on earth to do it.

In the New Testament, Jesus made this explicit in Matthew 16:19, and also in Matthew 18:18, when he said to his disciples, "I will give you the keys of the kingdom of heaven; whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven." The spiritual realm is the greater reality compared to the physical. Paul tells us that "we do not look at the things which are seen, but at the things which are not seen. For the things which are seen are temporary, but the things which are not seen are eternal" (2 Cor 4:18). We are to "walk by faith, not by sight" (2 Cor 5:7), using our position of authority in heavenly places through Jesus to change what we see here and conform it to the will of the Father in prayer.

Some examples of effective prayer of one individual for others in scripture:

• In Job 42, God told Job to pray for his friends, so that God could forgive their sin rather than punish them for it (Job 42:8). Clearly this was already God's will, but God still told him to pray for it.
• In Numbers 11, the Israelites disobeyed God and triggered the 'cursing' side of the covenant laid out in the Torah, and consolidated in Deuteronomy 28. But when the people cried out to Moses, and Moses interceded to God for them, the curse stopped (Numbers 11:1-2). God needed a man to ask Him.
• In a similar story, Miriam disobeyed God and triggered the 'curse,' (which now no longer applies to us, thanks to Jesus!), and Moses had to pray for her to be healed as well (Numbers 12:13).
• Moses also interceded for the Israelites after the incident of the golden calf (Ex 32:31-32), so that they would not be destroyed.
• Jesus prayed that Peter's faith would not fail, even before Peter denied him. Because of this, Jesus was confident that Peter would return to the disciples even after he'd stumbled (Luke 22:32). The faith involved was still Peter's, but somehow Jesus' prayer enabled Peter's faith to be revived.
• Paul believed that the prayers of his parishioners would occasion his deliverance, favor, and open doors of opportunity for him that might otherwise have been shut without them (Phil 1:19, 1:22, 2 Cor 1:11).
• Samuel the prophet acknowledged that it was actually a sin to fail to pray for his people.    1Sa 12:23 "Moreover as for me, God forbid that I should sin against the LORD in ceasing to pray for you: but I will teach you the good and the right way."

We pray for others, as individuals, for the same reason that we pray for ourselves: so that God can do what He wants to do on the earth.

How does the prayer of agreement fit into this? Jesus said in Matthew 18:19: "Again, I tell you that if two of you on earth agree about anything you ask for, it will be done for you by my Father in heaven." Why do we need anybody else to agree with us; can't we simply ask and receive all on our own?

I don't totally understand how this works, but I think it's similar to what Solomon said in Ecc 4:12: "a threefold cord is not quickly broken," or to the story of Aaron and Hur physically holding up Moses' arms when he got tired, to ensure that the Israelites achieved victory in battle (Ex 17:8-16). It's why we need the body of Christ to come around us, to bear one anothers' (crushing) burdens, even though we should each carry our own (light) loads (Gal 6:2, 5). It's very possible for one person alone to grow heartsick rather than patient in a long wait (Prov 13:12); that's why we need others to "hold up our arms" in prayer and encouragement. When our own faith is strong, perhaps (this is my speculation), the prayer of agreement is less necessary. It's when we are losing strength or growing heartsick, that the prayer of agreement becomes important.

This may be wh