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Optimal Marketing Strategies over Social Networks

Optimal Marketing Strategies over Social Networks. Jason Hartline (Northwestern), Vahab Mirrokni (Microsoft Research) Mukund Sundararajan (Stanford). JOHN. JASON. Network Affects Value. $20. A person’s value for an item depends on others who own the item. VAHAB. zune. JOHN. JASON.

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Optimal Marketing Strategies over Social Networks

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  1. Optimal Marketing Strategies over Social Networks Jason Hartline (Northwestern),Vahab Mirrokni (Microsoft Research) Mukund Sundararajan (Stanford)

  2. JOHN JASON Network Affects Value $20 A person’s value for an item depends on others who own the item VAHAB zune

  3. JOHN JASON Network Affects Value zune $30 A person’s value for an item depends on others who own the item VAHAB zune

  4. Examples Early phone system Value proportional to #subscribers  Monthly fee doubles every year for first four years CompuServe Initially, small sign up fee

  5. Standard Influence Models (See [Kempe+03], its citations) Probability of adoption depends on who else has item No dependence on price Maximize adoption: Which k players would you give item away to?

  6. Standard Optimal Pricing Set B of buyers No network effect or externalities Value vi drawn from distribution Fi Revenue(p) = p(1 - F(p)) pi* is optimal price, Ri is optimal revenue

  7. Contributions Propose model where adoption is based on price and network effects Study Revenue maximization Identify a family of strategies called influence and exploit strategies that are easy to implement and optimize over

  8. Problem Definition Given: a monopolist seller and set V of potential buyers digital goods (zero manufacturing cost) value of buyer for good vi = 2V R+

  9. Problem Definition (cont.) Assumptions: buyer’s decision to buy an item depends on other buyers who own the item and the price seller does not know the buyer’s value function but instead has a distributional information about them

  10. Value with Network Effects Set B of buyers If set S of buyers has adopted, viSdrawn from distribution FiS.

  11. wii Directed Graph Setting wji vi(S) = wii + ∑jin S wji

  12. Marketing Strategy Seller visits buyers in a sequence and offers each buyer a price Order and price can depend on history of sales Seller earns the price as revenue when buyer accepts Goal: maximize expected revenue Marketing Strategy: sequence of offer to buyers and the prices that we offer Question: algorithmic techniques?

  13. Upper Bound on Revenue viS drawn from distribution FiS Player specific revenue function Ri(S)Ri(S) is monotone ∑i Ri(B/i) is an upper bound on revenueOptimal price no longer optimal(myopic optimal price)

  14. Optimizing Symmetric Case vi(S) drawn from distr. Fk(k=|S|) Define: p*(#bought, #remain), E*(.,.) E(k, t) = (1 - Fk(p))[p + E*(k+1, t-1)]         +      Fk(p)[E*(k,t-1)] optimal price is myopic Initial discounts or freebies are reasonable

  15. wii Hardness of General Case? wij vi(S) = wii + ∑jin S Wji Even when weights are known, Maximizing Revenue = Maximizing feedback arc set Approximation-ratio of 1/2 Random ordering achieves approx ratio of 1/2

  16. Influence and Exploit(IE) Give buyers in set I item for free.  Recall freebies by symmetric strategy Visit remaining buyers in random sequence,offer each(adaptively) myopic optimal price Motivated by max feedback arc set heuristic and optimal pricing

  17. Diminishing Returns We assume Ri(S) is submodular Ri(S) - Ri(S/j) >= Ri(T) - Ri(T/j), if S is a subset of T Studies indicate this is reasonable assumption

  18. Easy 0.25-Approximation Building I: Pick each buyer with probability ½Offer remaining myopic optimal price Sub-modularity implies: Pick each element in set S with prob. p,then: E[f(S)] >= p f(S)

  19. Monotone Hazard Rate Monotone Hazard Rate: f(t)/(1-F(t)) is increasing in t Buyers accepts offer with non-trivial probability Can be used to improve the bounds to 2/3 Satisfied by exponential, uniform and Gaussian distributions Nice closure properties

  20. Optimizing over IE Define Revenue(I) Lemma: If Ri s are submodular, so is revenue as a function of influence set. But, it is not monotone Use Feige, Mirrokni, Vondrak, to get a 0.4 approximation

  21. Local Search S = {5} F(S) = 5 Add to S/Delete from S, if F(S) improves Maximizing non-monotone sub-modular functions (Feige et. al., 08)

  22. Add to S/Delete from S, if F(S) improves Local Search S = {3,5} F(S) = 10 Maximizing non-monotone sub-modular functions (Feige et. al., 08)

  23. Add to S/Delete from S, if F(S) improves Local Search S = {2, 3, 5} F(S) = 11 Maximizing non-monotone sub-modular functions (Feige et. al., 08)

  24. Add to S/Delete from S, if F(S) improves Local Search S = {2, 5} F(S) = 12 Maximizing non-monotone sub-modular functions (Feige et. al., 08)

  25. Recap We propose model where adoption depends on price, study revenue maximization Identify Influence and Exploit StrategiesShow they are reasonableDiscuss optimization techniques

  26. Further Work Pricing model: set prices once and for all (no traveling salesman) No price discrimination Dynamics ?

  27. Thanks

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