Towards a Fair Allocation of Rewards in Multi-Level Marketing
  An increasing number of businesses and organisations rely on existing users for finding new users or spreading a message. One of the widely used "refer-a-friend" mechanisms offers an equal reward to both the referrer and the invitee. This mechanism provides incentives for direct referrals and is fair to the invitee. On the other hand, multi-level marketing and recent social mobilisation experiments focus on mechanisms that incentivise both direct and indirect referrals. Such mechanisms share the reward for inviting a new member among the ancestors, usually in geometrically decreasing shares. A new member receives nothing at the time of joining. We study fairness in multi-level marketing mechanisms. We show how characteristic function games can be used to model referral marketing, show how the canonical fairness concept of the Shapley value can be applied to this setting, and establish the complexity of finding the Shapley value in each class, and provide a comparison of the Shapley value-based mechanism to existing referral mechanisms. 
Talal Rahwan, Victor Naroditskiy, Tomasz Michalak, Michael Wooldridge,   Nicholas R Jennings
cs.GT