View
214
Download
0
Category
Tags:
Preview:
Citation preview
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][
N
abaxE N
Finding the Optimal Allocation
NNN xFxxxPxF 11,,min 1
y
NN
NNN
dyyyfxE
xFxNfdx
xdFxf 11
capacityNNNts
dyyfyfyfyMiny
NNN
321
321
..
321
y
NNN
y
N
y
N
y
NNNN
dyyfyfyfy
dyyyfdyyyfdyyyfxExExEMin
321
321
321
321321
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
q
ii dqqfqRVc0
)(
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
Seller Ns
qMc 11,
)(qf
)(qf
)(qf
Price quote (q)
Price quote (q)
qMc 22 ,
qMcss NN ,
Price quote (q)
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
ii RqPqM
iiii dqqfRqPqMc )(xf
Price quote (q)
Commission given a quote q Buying probability given a quote q
CSA’s expected Revenue
sN
ssss
s
s
sNsN
ss
sNsN
s
iiii
s
q
NNNN
N
kkN
R
NN
RRqM
N
i R
iiii
i
kki
RRqM
RqPqM
Ni
dqdqdqqfcqfqfqf
dqdqdqqfcqfqf
dqqfcqPqMRRV
11max
11
max
2211
1
2 max
111max
2211
11111111
1
211
1211
2111
)(max
)(max
,,
iiii qPqMqPqMqPqM ,,,maxmax 222111 where:
terminating search on first trial
terminating search after querying the i-th seller
querying all sellers
Seller’s Perspective
• Mi(q) affects:– Order by which seller is queried– Probability that seller is chosen– Net revenue
1RV 2RV 3RV 4RV 5RV
Mi
Greater net revenue if buyHigher chance of being queriedHigher chance of being selected
Seller’s Perspective (2)
0
)()()()(q
purchaseselected dqqfqMqqPqPprofitE
1RV 2RV 3RV 4RV 5RV
Chance of being queried, and that the price quote actually selected to be returned to the user
Buyers’ Perspective
• CSA strategy results with a distribution of price returned to buyer: G(q), g(q)
0q
returned dqqqgqE
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,
. . .Mc, Mc, Mc, Mc,
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
R
q
dqqfRPqPMc0
)()()(
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)
N
RMF
N
RFyF
RF
M
dyyfRF
RF
RF
yFMdyyfRPyPMc
R
y
N
R
y
NNR
y
0
0
11
0
1
11)()()(
Increase in N requires increase in R
Analysis (cont.)
RF
dyyfyMPc
RVRFdyyfyMPcRV
R
y
R
y
0
0
)()(
1)()(
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)
RFRF
dyyfRF
yFMc
RF
dyyfyMPc
RV
R
y
NR
y 0)(1)()(
0
1
0
N
RMF
RF
yF
N
RMFdyyf
RF
yFM
R
y
NR
y
N
00
1
1)(1
Mean Price to Buyer
• Notice Sellers revenue is E(price)-M
R
y
NR
y
NR
y
N
R
y
NR
yN
R
y
N
dyRF
yFdyyFdyyFR
dyyFyyFdyyyfpriceE
000
0
0
0
1)(1)(
)()(
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
Mc, Mc, Mc, Mc,
+ = q
R
y
N
dy
MNcyF
priceE0
1
N
N
a
1
Increases in N
2 3 4 5 6 7 8 9 100.01
0.012
0.014
0.016
0.018
0.02
0.022
0.024
0.026
0.028
0.03
# of competing CSAs
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.
Recommended