Lattice Games and the Economics of Aggregators

RAIN Seminar, Stanford

Lattice Games and the Economics of Aggregators

Joint work withPatrick Jordan, Uri Nadav, Kunal Punera, Andy Skrzypacz

George VargheseUCSD and Yahoo Research

Outline• 1. Why aggregators?

• 2. Modeling Aggregators

• 3. Strategies and satisficing strategies

• 4. Other Results

• 6. Tools: a pay-as-you go along content market?

1 :WHY AGGREGATORS?

1 .The Evolution of Browsing by Topic - Directories

David and Jerry Guide to the Web

The Evolution of Browsing by Topic – Portals

The Evolution of Browsing by Topic – Aggregators

Mac Scour

What is an aggregator?

• Aggregator: a web site that collects and organizes and content from various sources including web sites, and possibly adds (especially editorial) content of its own

Middle ground between super-specialization (ultimatepersonalized search) and one size fits all

• Choice & editorial comment often gives the aggregator a distinct voice or slant.

Three ways people find information• Search: Know what you want (Google),

– No voice, no bias, pollution by SEO and spam

• Social recommendation : see what your friends like (Facebook) – Voice and bias, but no coherence around a topic.

• Aggregation: Know topic of interest, enjoy bias (AllthingsD) – Voice and bias, and coherence around topic

• Thesis: Extrapolating from the long tail (Ebay, NetFlix) we posit more specialized aggregators will arise.Tension between specialization to cater to users & capturing

a big enough market. Can we capture this in an economic model?

2 :TOWARDS A MODEL

Model Goals

• Capture reality as far as possible : mathematical model of a sociological phenomenon (rise of aggregators)

• Answer questions:– What incentives do aggregators have?– Why do aggreators enter some spaces and not others?– At what point does specialization prevent entry?

• Suggest market opportunities to cater to aggregators.

Once upon a time

8M People interested in news and sports

4M: only politics

6M only sports

2M: news with conservative slant

Lattice of taste sets underlying the story

2M

4M

6M

8M

Sports, General news,

Conservative news

General news, Conservative news

Conservative news

Sports

Lattice of subsets of user tastes. Subsets not shown have no weight. Parents not sum of child weights!

Aggregators pick lattice nodes, users pick “closest” aggregator based on Jacquard

Distance

2M

4M

6M

8M

S, GN, CN

GN, CN

CN

S

P1

P2P3

Jaccard distance between two sets: 1 – Resemblance, Resemblance = Intersection/Union

U1(S,CN)

U2(S)

A Game Between Aggregators• Extensive form game: Players (i.e., aggregators) enter

sequentially and get one move to choose a lattice node.

• Users are assigned to the closest (in Jaccard distance) single aggregator. In case of ties, two variants:– First Mover takes ties. First mover gets all ties– Equal Ties: All aggregators with equal distance split users

• Aggregator Profit = Number of assigned users – fixed cost F

• Questions: What are good strategies for entry? Are there Nash Equilibria? Even better Subgame Perfect Nash Equilibria?

Model limitations?

• Multiple player moves? Completely retooling a web site is equivalent to starting as a new player.

• Users choose multiple aggregators not one? Model a user as a probabilistic agent that chooses different taste sets with defined probabilities. Our model applies if revenue is expected number of users

• Variable not Fixed cost? costs may depend on number of users served. Can be modeled by subtracting variable cost from node revenue before placing node in lattice.

Differences from standard economic models?

• Euclidean distance versus Jaccard distance: Location Games Hoteling (1929); Ansari, Economides, Steckel (1998). Believe Jaccard models content disparities and nuances better

• Prices and competition for prices: We have none as most aggregators are paid for by advertising and “eyeballs”

• Fixed cost regardless of size of content (seems reasonable for virtual goods)

3 :TOWARDS A STRATEGY

AB (0.9M)

ABC (0.1M)

Fixed cost F = 1M

BC (0.8M)

A (0.3M) C (0.3 M) B (0.2 M)

Player 1

Player 2Player 3

If Player 1 aspires too high, Player 1 can be undercut. suggests, players should descend to a frontier

AB (0.9M)

ABC (0.1M)

Fixed cost F = 1M

BC (0.8M)

A (0.3M) C (0.3 M) B (0.2 M)

Player 1

First Attempt: Player 1 picks highest revenue lattice node in frontier

frontier

B (3)

ABC (Revenue = F - 1)

Fixed cost = F

BC (F - 2)

frontier

Player 1

Player 2

Picking higher cardinality sets can lead to being undercut. Pick highest revenue among lowest cardinality sets!

General Frontier Descent (first mover game)

• Descend: Descend lattice in all directions till one reaches a node all of whose descendants all have subtree revenue less than F.

• Choose: Pick maximum revenue among all lowest cardinality nodes in frontier.

• Recurse: Remove frontier node and all descendants and then recurse for next player.

3 :RESULTS

Simon versus Nash• Satisficing: Make a positive payoff (break even) as long as

subsequent players also do (Akin to Simon for strategies)

• Nash: Do as well as possible assuming subsequent players are also trying to do the same thing. Often hard

• Approximate Nash: Try and get an approximation to the Nash Equilibrium. Often hard.

• We can prove that:– Frontier descent is a satisficing algorithm– Frontier descent is polynomial time O(N log N ) versus O(N!)

AB (0)

ABC (F-1)

Fixed cost F

BC (3)

A (F + 2) C (1)

frontier

B (F+ 1)Player 1

Player 2

Player 3

Frontier descent is not guaranteed to find an equilibrium. Better for Player 1 to choose ABC

AB (0)

ABC (0)

Fixed cost F = 80

BC (0)

A (59) C (60) B (60)

CD (0)

D (59)

Frontier descent is a losing strategy for the equal ties game! Sharing can lead to future undercutting

Player 1Player 2 Player 3

Summary of Results• First Mover and Equal Ties have SNPEs in pure strategies

• First Mover has a polynomial time satisficing strategy

• Equal Ties has no satisficing strategy

Fixed cost F = 80

A (60) C (60) B (60) D (60)

AB (0) BC (0) CD (0) Player 3

Player 2

Player 1

3 cases: Player 1 enters on singletons, doubletons, and ABC: in all cases, A loses money in Equal Ties

EF (1000)

AF (1000)

CD (1000)

DE (1000) BC (1000)

AB (1000)F (80) A (80)

E (80)

D (80)

B(80)

C (80)

Fixed cost F = 1100

Snowflake conjecture: Exists equal tie instances with unbounded revenue but no player enters game

5 :MARKET OPPORTUNITIES?

Tools for aggregators: a market opportunity?

• Frontier descent suggests that as fixed cost F goes down , more aggregators will enter in more specific niches.

• A vendor that can reduce the cost of doing business F can open the floodgates . . . and reap a rich reward.

• Aggregators today add some original content but mostly a pastiche of other sources. Many either point to source or use “fair use” to show content snippets.

• It would be a better user experience to legally include the borrowed content. How to do this for small aggregators?

We suggest a pay-as-you-go revenue sharing content market to fill this need

ContentProvider

ContentProvider

ContentProvider

Content Market

Aggregator

Comparison to Ad Markets

• Similar in philosophy: empowers small players without recourse to lawyers and negotiators.

• Similar in payment based on clicks except this is true revenue sharing (click -> ad revenue -> content revenue)

• Different in that one can sell same piece of content to any number of aggregators but ad impressions are limited.

• So how should prices be set? By competition between content providers. By reverse auctions? New models needed?

Textual Summary (and research questions)

• Aggregator s: portals long tail of aggregators magazines– Empirical measurements of trends?

• Model: Location game on lattice with Jaccard distance– Other economic settings?

• Strategy: For First Mover Games: Frontier Descent– Better poly time algorithms that come closer to an SPNE?

• Satisficing: Break even as long as other players also do so.– Useful for other games?

• Content Market: Pay as you go along for small aggregators.– How to set prices? How to search market for content?

AB (0.9M)

ABC (0.1M)

BC (0.8M)

A (0.3M) C (0.3 M) B (0.2 M)

Player 1

frontier

SPNEsatisficing

Pay as you go along content markets

Apparent Contradiction• Showed there exists SPNE for equal ties but no satisficing

strategy.

• But Satisficing can be considered a NE with the sign bit of the normal payoff function (positive versus negative only)

• There is an SPNE for the sign game but this does not imply a satisficing strategy (reverse implication is true)

• But in examples like 4 nodes A, B, C, D with 60 each and fixed cost = 80, there is an SPNE (Player 1: AB, Player 2: CD) but there is no Satisficing Strategy because subsequent players can deviate from best response as long as they get positive payoffs.