optimal marketing strategies over social networks
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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Optimal Marketing Strategies over Social Networks
Jason Hartline (Northwestern),Vahab Mirrokni (Microsoft Research) Mukund Sundararajan (Stanford)
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Network Affects Value
JOHN
VAHAB
JASON
zune
$20 A person’s value for an item depends on others who own the item
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Network Affects Value
JOHN
VAHAB
JASON zune
zune
$30 A person’s value for an item depends on others who own the item
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Examples
Early phone system• Value proportional to #subscribers• Monthly fee doubles every year for first four years
CompuServe• Initially, small sign up fee
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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?
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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
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ContributionsPropose 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
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Problem DefinitionGiven:
a monopolist seller and set V of potential buyersdigital goods (zero manufacturing cost)value of buyer for good vi = 2V R+
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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
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Value with Network Effects
Set B of buyers
If set S of buyers has adopted, viS drawn from distribution FiS.
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Directed Graph Setting
vi(S) = wii + ∑j in S wji
wii
wji
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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?
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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)
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Optimizing Symmetric Casevi(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
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Hardness of General Case?
vi(S) = wii + ∑j in S Wji
Even when weights are known,Maximizing Revenue =Maximizing feedback arc set
Approximation-ratio of 1/2Random ordering achieves approx ratio of 1/2
wii
wij
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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
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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
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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)
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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
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Optimizing over IEDefine 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
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Local Search
Add to S/Delete from S, if F(S) improves
S = {5}
F(S) = 5
Maximizing non-monotone sub-modular functions (Feige et. al., 08)
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Local Search
S = {3,5}
F(S) = 10
Add to S/Delete from S, if F(S) improves
Maximizing non-monotone sub-modular functions (Feige et. al., 08)
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Local Search
S = {2, 3, 5}
F(S) = 11
Add to S/Delete from S, if F(S) improves
Maximizing non-monotone sub-modular functions (Feige et. al., 08)
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Local Search
S = {2, 5}
F(S) = 12
Add to S/Delete from S, if F(S) improves
Maximizing non-monotone sub-modular functions (Feige et. al., 08)
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Recap
We propose model where adoption depends on price, study revenue maximization
Identify Influence and Exploit StrategiesShow they are reasonableDiscuss optimization techniques
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Further Work
Pricing model: set prices once and for all (no traveling salesman)
No price discrimination
Dynamics ?
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Thanks
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