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.