Competition in Mediated-Search based Markets

Example

Shopbot

Capacity:45 Queries

Scanner

Inkjet cartridge

Music CD

product Queries E[min]

20 $5.47

20 $20.95

5 $30.00

total 45 $56.43

• Lower bound $52.86

• Even if had infinite number of stores: $50.00

product Queries E[min]

11 $5.83

15 $21.25

19 $26.50

total 45 $53.58

product Merchants prices

20 ~U($5-$15)

20 ~U($20-$40)

20 ~U($25-$55)

FCFS Alternative Execution1][

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Finding the Optimal Allocation

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Motivating Example

• You want to travel to NY• You are sensitive to price only – you want to

minimize the airfare• There are many airlines you can query for

airfare

Each offering multiple options (fares)• For many people, it is too much to handle…

Search-Based Environments (2)

• You decided to call your travel agent…

• At this point we switched to a mediated environment

Search-Based Environments (2)

• The travel agent can query airfares more efficiently

…Ideally, we’ll have the travel agent query all airlines and get back to us with cheapest airfare

query query query query query query query

Search-Based Environments (2)

• The travel agent can query airfares more efficiently

…Ideally, we’ll have the travel agent query all airlines and get back to us with cheapest airfare

price price price price price price price

Search-Based Environments (2)

• … however each query takes time and the agent’s time is limited

• The search problem – in what order to query and when to terminate the search?

cTAP cIberia cAA cContinentalcUnitedcAlitaliacLOT …Price quote (q) Price quote (q)Price quote (q) Price quote (q) Price quote (q) Price quote (q)Price quote (q)

Hey! This is Pandora’s Problem…

Optimal Solution [Weitzman 1979]• Assign a reservation value to each airline (RV in

terms of cost)

• On each step of the search, pick airline with the smallest reservation value and query for airfare

• If the lowest airfare found so far is lower than lowest reservation value (of non-queried airlines) – terminate search

RV

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If the customer had similar querying expertise, this would be her optimal search strategy

So, do Travel Agents Actually Solve Pandora’s Problem?

• No!• They are self interested – motivated by a

commission they get from airlines• They solve Pandora’s problem taking the

expected commission as the main input• Result is not necessarily the optimal one for

the client

Other Examples (for mediated-search domains)

• Real estate brokers• Car dealers• Search engines (promoting Google ads)

• Comparison shopping agents:– Very structured– Competition dynamics between CSAs

Comparison Shopping Agents (CSAs)

• Shopbots and Comparison Shopping– automatically query

multiple vendors for price information

– Growing market, growing interest

comparison-shopping agents

Comparison Shopping Agents (CSAs)Offline - central DB of prices (daily updated):

DB RequestsUIQuery

Timely Updates

Timely Updates

Timely Updates

Timely Updates

Real-time querying upon receiving a request:

RequestsUI

Query

Query

Query

Query

Real-Time Querying (CSAs)• Ever-increasing frequency of price updates

• Dynamic pricing theories (based on competitors’ prices) [Greenwald and Kephart, 1999]

• “Hit and run” sales strategies (short term price promotions at unpredictable intervals) [Baye et al, 2004]

Assumption: Future CSAs will use real-time (costly) querying

Stable Price Distributions

• Distribution of Prices (reflects the level of competition in the market):– Stable – empirical evidence for persistence of price

dispersion [Baye et al. 2006, Brynjolfsson et al. 2003, Clay et al. 2002]

– No correlation between a merchant’s relative position in the distribution of prices in any two consequent times – empirical evidence for: • Considerable turnover in firms’ relative positions in the distribution

of prices over time; [Baye et al. 2006]

• Significant variation in the identity of the low-price firm for the same product over time [Baye et al. 2006]

• Learning the price distribution of each product over time is possible (past experience, Bayesian update [Rothschild 1974], etc.)

The General Setting of Mediated Search

Seller 1

Seller 2

Buyer1

Buyer 2

Buyer Nb

CSA 1

CSA 2

Seller Ns

CSA Nc

Multi-buyer, multi-seller, multi-CSA

The Setting - Buyers

Seller 1

Seller 2

Buyer1

Buyer 2

Buyer Nb

CSA 1

CSA 2

Seller Ns

CSA Nc

• Periodically request price-comparison service from single/several CSAs (sequentially / in parallel)• May offer monetary incentive to CSAs• Interested in minimizing the total expense

The Setting - Sellers

Seller 1

Seller 2

Buyer1

Buyer 2

Buyer Nb

CSA 1

CSA 2

Seller Ns

CSA Nc

• Queried by CSAs and return price quote• May offer monetary incentive to CSAs (e.g., if buyer directed

to their web-site, if buyer buys eventually the product)

• Interested in maximizing the net profit

The Setting - CSAs

Seller 1

Seller 2

Buyer1

Buyer 2

Buyer Nb

CSA 1

CSA 2

Seller Ns

CSA Nc

• Receive requests from buyer and query sellers according to incentives offers• Subject to a search cost• Interested in maximizing net profit

Possible Analysis

• Numerous analysis directions (seller side, buyer side, CSAs’ perspective, any combination)

• To be presented:– Focus on the CSA’s search, where monetary

incentives offered only by sellers– Results for homogeneous environments– Illustration of some non-intuitive characteristics of

equilibrium based on specific distribution function

Self-Interested CSA

CSA

modeling CSA competitionP(q)

Price quote (q)Seller 1

Seller 2

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Reduction to Pandora’s Problem[Weitzman 1979]

• CSA assigns a reservation value to each seller (RV in terms of revenue)

• On each step, pick seller with the highest reservation value and query for price

• If the highest expected commission found so far is greater than highest reservation value (of non-queried sellers) – terminate search

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Price quote (q)

Commission given a quote q Buying probability given a quote q

CSA’s expected Revenue

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terminating search on first trial

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Seller’s Perspective

• Mi(q) affects:– Order by which seller is queried– Probability that seller is chosen– Net revenue

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Seller’s Perspective (2)

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Buyers’ Perspective

• CSA strategy results with a distribution of price returned to buyer: G(q), g(q)

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Remember: buyer is not paying any commission

Equilibrium Analysis

• Equilibrium is a stable set {M1 , M2 , … , MN}• Complex!!!– For some distribution functions direct calculation

is precluded– Changes in incentives affect the order according to

which the CSAs search -> reconstructing the equation

Fortunately, some interesting characteristics of the model can be shown with simple settings…

Homogeneous Environment Equilibrium

• Assumptions:– All CSAs share same search cost c– All sellers offer same fixed commission M– CSAs are not limited by a finite decision horizon

infinite number of sellers (justified by dynamic pricing theories and entrance of new sellers)

• Simplify analysis, yet enable demonstrating important effects of model

Mc,

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Analysis (CSA’s point of view)

• Sellers are identical -> same reservation value (R) – can now be expressed in terms of prices

• Probability of buying at price q (P(q)) = probability that none of the other CSAs returned a lower quote

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Analysis (cont.)

• Probability of buying at price q (P(q)) = probability that none of the other CSAs returned a lower quoteP(y)=(1-F(y)/F(R))^(N-1)

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Analysis

Proposition: In equilibrium, the expected net benefit of each CSA (E[comission-search_costs]) is zero

So what is the incentive to search? Market makers can compensate CSAs if they improve overall market performance (even requiring the CSAs to get a single quote will push them to optimal behavior)

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• Notice Sellers revenue is E(price)-M

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Analysis (2)Proposition: As the number of competing CSAs increases, the expected minimum quote increases Proof according to Equilibrium equations:

A very non-intuitive market behavior!However, since CSAs end up with zero net-revenue anyhow, the increased competition results with “less” search (and higher quotes)Meaning, more price quotes but with greater average

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competing CSAs - seller's expected revenue

competing CSAs - minimum quote received (buyer’s cost)

minimum quote (Seller’s revenue)with self operated CSA

buyer's expected expensewith self operated CSA

$

q ~ U(0,1)M=0.01C=0.0003

Difference is the commission paid

Minimum of sample of size E[total querris]

So, Who loses here?(and what dynamics are formed?)

• Offering a commission, sellers fully subsidize search costs• If this subsidy transferred completely to buyers, the latter

would improve performance and sellers would worsen theirs• Nevertheless, the multi-CSA scenario suggests several agents

search in parallel (instead of one agent searching sequentially) - overall search process less efficient

• Thus despite the spending on subsidizing, seller agents benefit from the search inherent inefficiencies

• In a similar manner, despite the inefficiencies of the search, buyer agents benefit from having CSAs perform the search for them for free

Important result for market design!

Conclusions

• A multi-competitive CSAs framework that can improve overall performance

• Several counter intuitive results– Effect of competition– Effect of subsidizing search costs

• Analysis directly addresses a reality in which artificial agents are the main players (inherently more rational and less computationally bounded than people) - substantial potential for implementation in the real world.