Simple sybil-proof mechanisms for multi-level marketing

Multi-level marketing refers to a marketing approach in which buyers are encouraged to take an active role in promoting the product. This is done by offering them a reward for each successful referral of the product to other prospective buyers. To encourage potential customers to buy early and to give referrals to influential people, these mechanisms also reward indirect referrals - direct referrals linked to the buyer through other direct referrals. One potential drawback to multi-level mechanisms is that they could allow for sybil attacks. A sybil attack consists of a user purchasing multiple copies of the product under false identities to increase its reward. For example, a user can create two identities, the second with a referral from the first. Then, for each referral made through the second identity both identities would capture some reward. The additional reward captured could be greater than the cost of buying additional product. A sybil at tack is undesirable because it reduces the profits of the seller, since buyers are getting higher rewards than what the seller intended for them to receive. After a sybil attack, an ancestor of the attacker is farther in the referral tree from the children of the attacker. In many reward mechanisms, this means that the ancestor gets less reward from each child, reducing his incentive to make referrals.