How to Win Friends and Influence People, Truthfully
Transcript of How to Win Friends and Influence People, Truthfully
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.