Denis Kaiser summarizes Anselm of Canterbury's satisfaction theory of atonement.
Denis Kaiser, The Doctrine of Atonement According to Peter Abelard: A Literary and Historical Analysis (Norderstedt, Germany: GRIN Verlag, 2008), 30-32
Anselm of Canterbury (1033-1109) develops his satisfaction theory in his Cur Deus Homo. According to this theory God’s justice must be satisfied by humanity to reconcile to God. The relationship between God and man is based upon a divine law. Men have transgressed that law and stand guilty before God. He is offended by human sin, and sin robs God of the honor which He is due. His honor needs vindication, either by punishment or satisfaction. God’s mercy prompted Him to seek it in the way of satisfaction. Since man is not able to bring about the required satisfaction, only God can provide it. Sin, being an infinite offense against God, required a satisfaction equally infinite, one that God alone could provide. Yet the satisfaction had to be at once human and divine. This answered the question: Why did God become a human being? Only a God-man would possess the ability (as God) as well as the obligation (as human being) to pay the required satisfaction to God. That is why Christ died to pay the penalty that God’s justice requires for human transgression of the law and Christ fulfills the law to the utmost. Atonement is the reparation or satisfaction made to the divine justice because of the injury sin has caused. God is the object of Christ’s atoning work, and He is reconciled through the satisfaction made to His justice. However, it is not so that God’s attitude is changed by the death of Christ. The God who demands satisfaction is the God who himself makes the satisfaction in the person of Jesus Christ. The merit earned by Christ becomes available for men. He further emphasized that Christ’s death served as an example to men of how they should bear their own sufferings. Christ redeemed the whole world from sin and eternal death by his voluntary death. The devil exercised great power over man but he had no legal claim over him. That is why neither God nor man owed the devil anything. So Christ’s death was not a ransom paid to the devil. Anselm criticizes the idea that the devil had the right assigned to him by God to punish men with death. God did not have to respect such rights, and He did not deceive the devil.