Social Networks: Advertising, Pricing and All That

Zvi Topol & Itai Yarom

Agenda

• Introduction– Social Networks– E-Markets

• Motivation– Cellular market – Web-services

• Model

• Discussion

Social Networks

• Set of people or groups that are interconnected in some way

• Examples:– Friends – Business contacts – Co-authors of academic papers– Intermarriage connections– Protagonists in plays and comics – …

Social Networks (Continued)

Social Networks - Applications

• Information diffusion in social networks

• Epidemic spreading within different populations

• Virus spreading among infected computers

• WWW structure

• Linguistic and cultural evolution

• Dating, Jobs, Class reunions

• …

Social Network (continued)

• Popular books:

Properties of Networks

• Diameter of the network: – Average geodesic distance– Maximal geodesic distance

• Degree distributions– Regular graphs– Binomial/Poisson – Exponential

• Clustering/Transitivity/Network Density– If vertex A is connected to vertex B and vertex B is connected to

vertex C, higher prob. that vertex A is connected to vertex C– Presence of triangles in the graph– Clustering coefficient :

verticesof triplesconnected #

network in the triangles# x 3C

Properties of Networks (continued)

• Degree correlations – preferential attachment of high degree vertices/low degree vertices

• Network resilience/tolerance – effects on the network when nodes are removed in terms of– Connectivity and # of components– # of paths– Flow– …

• …

Small World Models

• Milgram conducted in the 60s a controversial experiment whose “conclusion” was 6 degrees of separation – “small world effect”

• In their study Watts and Strogatz validated the effect on datasets and showed that real world networks are a combination of random graphs and regular lattices (low dimensional lattices with some randomness)

• Barabasi et al showed that the degree distribution of many networks is exponential

E-Markets

• E-commerce opens up the opportunity to trade with information, e.g., single articles, customized news, music, video

• E-marketplaces enable users to buy/sell information commodities

• Information intermediaries can enrich the interactions and transactions implemented in such markets

E-Markets Examples

• Stock market (Continuous Double Auction)– Agents can outperform humans in unmixed markets and

have similar performance in mixed markets (of humans and agents) [1]

• Price posting markets– Cyclic price wars behavior occurs [2]

• What are the roles that agents can take in those markets?– Agent can handle large amount of information and never

get tired

[1] Agent-Human Interactions in the Continuous Double Auction, Das, Hanson, Kephart and Tesauro, IJCAI-01.

[2] The Role of Middle-Agents in Electronic Commerce, Itai Yarom, Claudia V. Goldman, and Jeffrey S. Rosenschein. IEEE Intelligent System special issue on Agents and Markets, Nov/Dec 2003, pp. 15-21.

Motivation

• Ubiquitous markets scenarios:– Cellular phones– Web services

• Applications:– Sale on demand– Advertising

Model

• Social Network where:– A is set of rational economic agents– E is set of edges connecting agents, representing

(close) social connections

• SN is weighted according to the function – Where T is a trust domain, usually T = [0, 1]– We look at trust as a partial binary relation, i.e.

– Let , then an edge e connecting both agents is in E iff

EASN ,

TEw :

),( ji aat

TAAt :Aaa ji ,

Model (continued)

• A seller s would like to use the Social Network to sell his product and bears a marginal cost function for production of

• We look at a repeated game, at the beginning of which he approaches a set of recommenders from SN and acts according to the following protocol:

C

Model(continued)

1. Seller: approaches potential recommenders

2. Recommender: sends list of recommended friends to seller

3. Seller: receives list of recommended customers (friends) and pays according to the function

4. Seller: approaches list of recommended friends

5. Customer (friend): decides whether to purchase the product

6. Recommenders: further remunerated according to

7. Seller: updates internal model of social network structure

)(1 rf

)(2 brf

Bootstrapping Details

• An initial scale-free network

• No prior knowledge of seller about the structure of the network

• Initial recommenders are picked randomly

Model (continued)

• The system updates the social network:– If a recommended agent buys the product, then the

recommender’s trustworthiness is increased by and the recommender is paid by the seller.

– If a recommended agent decides not to buy the product, then the recommender’s trustworthiness is decreased by

– Two not previously connected agents who both buy the product, have probability to be connected in the next time step.

1b

2b

Discussion

• Buyers want to identify the money maker recommenders

• Friend of a friend recommendation (different depths along the chain)

• Learning of Social Network behavior

• Relevant research