How to Win Friends and Influence People, Truthfully Analysing - - PowerPoint PPT Presentation

How to Win Friends and Influence People, Truthfully

Analysing 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 -
• ptimal 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 mechanism
• 2. Show performance guarantee
• 3. Show monotonicity

Mechanism Design

Weighted Marginal Contribution Sorting

Proportional Share Rule

Example - B=10

1 2 3 4 5 6 7 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-

• ptimal 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.