How to Win Friends and Influence People,
TruthfullyAnalysing Viral Marketing Strategies
Original paper: "How to Win Friends and Influence People, Truthfully: Influence Maximization Mechanisms for Social Networks" by Yaron Singer
Presented by: Jean-Rémy Bancel, Lily Gu, Yifan Wu
Influence, Cont.
Last week:
● Real data: Twitter/Facebook● Empirical evaluation of influence
Today: graphs, optimizations, greedy algorithms and
mechanism design
Outline
Problem Description & Motivation
Past Research
Singer's Mechanism Design
Experiments & Results
Problem Description
To promote a product with limited budget, who to target/convert?
Problems to solve:● Elicit cost to convert a customer● How "conversion" propagates through the
network.● Optimize the influence given the budget
This is a very open question that has (too) many moving part
Knowledge of the Network?
● Could you get it?○ Who's the principle? Ad platform or product
companies
● Accurate representation?○ Types of graph
■ Yelp, Amazon vs Facebook G+○ vs Physical network?
■ does it matter?
● Dealing with the size○ Related to cost as well
Revealing cost
● Could you ask?○ Are they truthful?○ If not, how to reveal by implicit choices?
● Why not use the take-it-or-leave-it approach (posted price)?
● What is the cost anyways? ○ Time? Reputation?
Activation
● One time chance?
● Always positive? ○ No modeling for negative effects, is it linear etc.?
● What does this influence even mean?○ Ads vs word of mouth
■ Why should your friend post an ad without compensation?
■ Is it money or opinion?
Clarifying the Research Goals
Truthful
Budget Feasible
Computationally Efficient
Bounded Approximation
Social Network
A social network is given by:
Past Research - Diffusion Models
● Choosing influential sets of individuals - optimal solution is NP-hard.
● Submodular Model ○ Linear Threshold○ Independent Cascade
● Game Theory Model
Submodularity
We consider a set X with |X|=n. A set function on X is a function .
Game Theory Model
For each player i in the network, we define:○ action: A or B○ utility function:
Coverage Model
Model
Coverage Function
Coverage Model
Coverage Model
● Too simplistic? No propagation● Why using it?
The coverage function is submodular
Goal
● Design an incentive compatible mechanism○ incentive compatible = truthful○ mechanism = algorithm + payment rule
● Input○ Graph / Social network structure○ Reported costs○ Influence function○ Budget
● Output○ Subset of agents○ Payment vector
Incentive Compatible Mechanisms
● Result:○ Monotone○ Threshold payments
● Myerson's Characterisation, 1981○ seller's optimal auction○ direct revelation mechanism○ preference uncertainty and quality uncertainty○ monotone hazard rate assumption○ virtual surplus
Monotonicity and Threshold Payments
Design Schedule
1. Design an approximation mechanism2. Show performance guarantee3. Show monotonicity
Mechanism Design
Weighted Marginal Contribution Sorting
Proportional Share Rule
Example - B=10
1 2 3
4
5
67
0
9
8
2
3.1 5
0.7
4
3
4
2
7
6
S C f
1 2 6
1,4 2.7 7
Optimal?
Performance Guarantee
Breaking Monotonicity
.91
.6
4
9
Performance Guarantee
Fixing Monotonicity
Algorithm
Monotone?
Details of the Condition
Algorithm
Summary
What about payments?
Extending to Voter Model
Random Walk○ e.g. PageRank
Reduce to the coverage model○ Calculated the number of nodes to be influenced
with the transition matrix
● Advertise for a travel agency● Ad method: posting a message with
commercial content in their Facebook page● Need to specify $$$ and # of friends on FB● Reward
○ Each worker who participated in the competition was paid
○ the workers who won the competition received a bonus reward at least as high as their bid.
MTurk Experiment, Setup
No Correlation!i.e.: OK to plug in to random node
Facebook graph
● Partial○ degree distribution (as opposed to real degree)
● Steps○ Limited to 5 (10% IC), 10 (1% IC), and 25 (LT)
● Uniform pricing○ Here it chooses the best uniform price by an near-
optimal approximation (a stronger assumption)
Application:● Does it (really) work? ● How long is each cycle● Need data and ground truth
Theory:● Is efficient auction the most optimal?
○ Bulow-Klemperer's research● The models? Negative reviews?
○ We've taken them for granted for this paper
Related/Future Research
Thanks & Questions
Fun Fact Singer (the author) will be joining Harvard as an Assistant Professor of Computer Science in Fall 2013.
