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Competition in Mediated-Search based Markets

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Example Shopbot Capacity: 45 Queries Scanner Inkjet cartridge Music CD productQueriesE[min] 20$5.47 20$20.95 5$30.00 total45$56.43 Lower bound $52.86 Even if had infinite number of stores: $50.00 productQueriesE[min] 11$5.83 15$21.25 19$26.50 total45$53.58 productMerchantsprices 20~U($5-$15) 20~U($20-$40) 20~U($25-$55) FCFSAlternative Execution

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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…

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Search-Based Environments (2) You decided to call your travel agent… At this point we switched to a mediated environment

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Search-Based Environments (2) The travel agent can query airfares more efficiently … Ideally, well have the travel agent query all airlines and get back to us with cheapest airfare query

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Search-Based Environments (2) The travel agent can query airfares more efficiently … Ideally, well have the travel agent query all airlines and get back to us with cheapest airfare price

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Search-Based Environments (2) … however each query takes time and the agents time is limited The search problem – in what order to query and when to terminate the search? c TAP c Iberia c AA c Continental c United c Alitalia c LOT … Price quote (q) Hey! This is Pandoras Problem…

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

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So, do Travel Agents Actually Solve Pandoras Problem? No! They are self interested – motivated by a commission they get from airlines They solve Pandoras problem taking the expected commission as the main input Result is not necessarily the optimal one for the client

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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

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Comparison Shopping Agents (CSAs) Shopbots and Comparison Shopping – automatically query multiple vendors for price information – Growing market, growing interest comparison- shopping agents

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Comparison Shopping Agents (CSAs) Offline - central DB of prices (daily updated): DB Requests UI Query Timely Updates Real-time querying upon receiving a request: Requests UI Query

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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

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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 merchants 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.)

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The General Setting of Mediated Search Seller 1 Seller 2 Buyer1 Buyer 2 Buyer N b CSA 1 CSA 2 Seller N s CSA N c Multi-buyer, multi-seller, multi-CSA

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The Setting - Buyers Seller 1 Seller 2 Buyer1 Buyer 2 Buyer N b CSA 1 CSA 2 Seller N s CSA N c Periodically request price-comparison service from single/several CSAs (sequentially / in parallel) May offer monetary incentive to CSAs Interested in minimizing the total expense

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The Setting - Sellers Seller 1 Seller 2 Buyer1 Buyer 2 Buyer N b CSA 1 CSA 2 Seller N s CSA N c 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

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The Setting - CSAs Seller 1 Seller 2 Buyer1 Buyer 2 Buyer N b CSA 1 CSA 2 Seller N s CSA N c Receive requests from buyer and query sellers according to incentives offers Subject to a search cost Interested in maximizing net profit

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Possible Analysis Numerous analysis directions (seller side, buyer side, CSAs perspective, any combination) To be presented: – Focus on the CSAs 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

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Self-Interested CSA CSA modeling CSA competition P(q) Price quote (q) Seller 1 Seller 2 Seller Ns Price quote (q)

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Reduction to Pandoras 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 Price quote (q) Commission given a quote qBuying probability given a quote q

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CSAs expected Revenue where: terminating search on first trial terminating search after querying the i-th seller querying all sellers

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Sellers Perspective M i (q) affects: – Order by which seller is queried – Probability that seller is chosen – Net revenue MiMi Greater net revenue if buy Higher chance of being queried Higher chance of being selected

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Sellers Perspective (2) Chance of being queried, and that the price quote actually selected to be returned to the user

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Buyers Perspective CSA strategy results with a distribution of price returned to buyer: G(q), g(q) Remember: buyer is not paying any commission

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Equilibrium Analysis Equilibrium is a stable set {M 1, M 2, …, M N } 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…

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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...

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Analysis (CSAs 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 quote P(y)=(1-F(y)/F(R))^(N-1) Increase in N requires increase in R

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Analysis (cont.)

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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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Mean Price to Buyer 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 += q Increases in N

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q ~ U(0,1) M=0.01 C=0.0003 Difference is the commission paid Minimum of sample of size E[total querris]

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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!

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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.

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