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On the Value of using Group Discounts under Price Competition

On the Value of using Group Discounts under Price Competition. Reshef Meir, Tyler Lu, Moshe Tennenholtz and Craig Boutilier. Example. ( 3 , 8 ). Base price : 5$ Price for two clients or more : 2 $. Base price : 4$. Example. ( 3 , 8 ). u1 = 3 – 5 = -2. Base price : 5$

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On the Value of using Group Discounts under Price Competition

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  1. On the Value of using Group Discounts under Price Competition Reshef Meir, Tyler Lu, Moshe Tennenholtz and Craig Boutilier

  2. Example (3,8) Base price : 5$ Price for two clients or more : 2 $ Base price : 4$

  3. Example (3,8) u1 = 3 – 5 = -2 Base price : 5$ Price for two clients or more : 2 $ Base price : 4$

  4. Example (3,8) u1 = 3 – 5 = -2 u1 = 8 – 4 = 4 Base price : 5$ Price for two clients or more : 2 $ Base price : 4$

  5. Example (3,8) (3,0) u1 = 4 u2 = 0 (6,3) u3 = 0 Base price : 5$ Price for two clients or more : 2 $ Base price : 4$

  6. Example (3,8) (3,0) u1 = 4 u2 = 0 (6,3) u3 = 1 Base price : 5$ Price for two clients or more : 2 $ Base price : 4$

  7. Example • No buyer wants to switch vendor (3,8) (3,0) u1 = 4 u2 = 1 (6,3) u3 = 1 4 Base price : 5$ Price for two clients or more : 2 $ Base price : 4$

  8. The LB model (Lu and Boutilier, EC’12) • Every buyer ihas value vijfor each vendor • Every vendor posts a schedule pj= (pj(1), pj(2),…, pj(n)) • If k buyers (including i) select j, the utility of i is ui= vij- pj(k) • A game instance is given by • V=(vij)ij • P= (p1, p2,…, pm) (3,8,5) (6,2,5) (1,8,4) (3,4,7) (0,0,9) (5,5,5) (12,7,7) p2 = (9,7,…,3) p3 = (6,6,…,6) p1 = (8,…,6,..,2,2)

  9. The LB model (Lu and Boutilier, EC’12) • Lu and Boutilier showed that for any V,P there is always a Stable Buyer Partition (SBP) • Denoted byS(V,P) • Maybe more than one SBP • S(V,P) is selected by some coordination mechanism • Pareto-optimal • TU / NTU p2 = (9,7,…,3) p3 = (6,6,…,6) p1 = (8,…,6,..,2,2)

  10. Vendors as players • What prices should the Red vendor post? (3,8) (7,0) (5,5) ? Base price : 4$

  11. Vendors as players • What prices should the Red vendor post? (3,8) (7,0) (5,5) Base price : 5$ Base price : 4$ Revenue = 5$

  12. Vendors as players • What prices should the Red vendor post? • No need for discounts! (3,8) (7,0) (5,5) Base price : 5$ Price for two buyers: 3$ Base price : 4$ Revenue = 6$

  13. Complete information Theorem I: with complete information, vendors have no reason to use group discounts. • This corroborates similar findings in other models (e.g. Anand & Aron’03). • Why would vendors use discounts? • Economies of scale (low marginal production costs) • Marketing effect • Uncertainty over buyers’ valuations

  14. Uncertainty models

  15. Uncertainty models

  16. Uncertainty models

  17. “Groupon competition” Most important slide • Vendors post price vectors P =(p1, p2,…, pm) • Buyers’ types V are set • The stable partition S(V,P) is formed • Utilities are realized or By sampling from D By arbitrary selection from A By the LB model What is the best strategy for vendor j, given p-j ? In particular, would discounts help?

  18. Bayesian model Theorem II. suppose that: • Buyers’ preferences are symmetric • Buyers’ preferences are independent • Other vendors use fixed prices Then vendor j has no reason to use discounts. No longer true if we relax any of these conditions D is i.i.d.

  19. Bayesian model (cont.) Proof outline: • 1 vendor, 1 buyer • 1 vendor, ni.i.d. buyers • m vendors, ni.i.d. buyers V Simulate the n-1 other buyers by sampling from D V Create a new i.i.d distribution D’ for vendor 1: V A distribution on A distribution on

  20. Bayesian model (cont.) • Consider the following (non-i.i.d) example • Suppose that • Then • Best fixed price is • Can do better by posting a prefers vendor 1 0 1 b prefers vendor 2 1 0

  21. Bayesian model Theorem II. suppose that: • Buyers’ preferences are symmetric • Buyers’ preferences are independent • Other vendors use fixed price Then vendor j has no reason to use discounts. No longer true if we relax any of these conditions D is i.i.d.

  22. Bayesian model (cont.) • Consider the following (non-i.i.d) example a prefers vendor 1 0 1 b prefers vendor 2 1 0

  23. Bayesian model Theorem II. suppose that: • Buyers’ preferences are symmetric • Buyers’ preferences are independent • Other vendors use fixed price Then vendor j has no reason to use discounts. No longer true if we relax any of these conditions D is i.i.d.

  24. Strict uncertainty model • We have a similar result: • If buyers are selected from the same set of types, then there is no reason to use discounts • However, if buyers are essentially different, discounts can be useful

  25. Future work • Suppose buyers are correlated • (E.g. by a signal on product quality) • How much can a vendor gain by using discounts? • How to compute the best discount schedule? • Equilibrium analysis • With or without discounts

  26. Thank you! Questions?

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