Dynamic Auctions with Bank Accounts Implementing Bundling in an Online Fashion Vahab Mirrokni 1 Renato Paes Leme 1 Pingzhong Tang 2 Song Zuo 2 1 Google Research 2 Tsinghua University IJCAI, 2016, New York Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 1 / 17
Dynamic Auctions: An Informal Description The seller has a sequence of items to sell to a single buyer. The items arrive over time. At each stage, there is one item for sale. The item will be destroyed at the end of this stage, if not sold. Nobody knows the actual value of the t -th item until the beginning of the t -th stage. Independent valuations, commonly known priors. The seller’s allocation rule and payment rule could depend on past stages. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 2 / 17
An Application: Ads Google/Baidu/Bing sells ad impressions to advertisers. Impressions may come from users’ searches on search engines. (Arrive over time, destroyed immediately if not sold.) The value of each impression varies with (at least) the user’s information (location, time, age, gender, cookies, etc.). Currently, the auctions are rarely conducted dynamically. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 3 / 17
Auction-based and Contract-based Advertising auction-based contract-based dynamic bundling real-time + real-time higher revenue higher revenue lack of competition complicated + high entering cost lower revenue not real-time commitment power We introduce a family of simple dynamic auctions — coined bank account mechanisms to get around these two issues. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 4 / 17
Bank Account Mechanism Seller: selects <z t , q t > Buyer: observes v t based on the balance and reports it to M t Stage Mechanism Selects Reports M t = <z t , q t > Depends on Goto Next Stage Bank Account Decreases Increases Balance Seller: spends s t from Buyer: deposits d t into the bank account the bank account Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 5 / 17
A Toy Example Example One buyer, two stages, i.i.d. valuations: v 1 , v 2 ∼ F . F : Pr[ v = 1] = Pr[ v = 2] = 1 / 2. Bank Account Mechanism Dynamic Auction Seller sets M 1 = posted-price at 1; Stage 1: sell the first Buyer chooses to buy or not, item at price 2 . 5. and deposits 1 . 5, if brought; Stage 2: allocate the second item if and if balance = 1 . 5, Seller spends 1 . 5, only if the first item and sets M 2 = give-for-free; was sold. otherwise, M 2 = not-for-sale. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 6 / 17
Dynamic Bundle Revenue Comparison auction-based dynamic contract-based 2 2 . 5 3 Bank Account Mechanism interpretation: upon Buyer reporting, Seller sells a “dynamic bundle”, item + item(s) item + future benefits static bundle dynamic bundle “future benefits” sold via spends, implemented as discounts in the next stage mechanism. Selling “future benefits” brings the uncertainty of deficits . Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 7 / 17
Constraints on Dynamic Bundles. item + item(s) item + future benefits static bundle dynamic bundle The “future benefits” must satisfy certain properties to ensure the mechanism being incentive compatible (IC) and individually rational (IR). Dominant Strategy IC: no difference with the static environment. This paper: Bayesian IC + interim IR. [Mirrokni, et al. 2016]: Bayesian IC + ex-post IR. [Papadimitriou, et al. 2016]: first paper on this setting, discrete and correlated types, focus on complexity. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 8 / 17
Theorems: overcoming the issues with Bank Accounts Bank account mechanism is extremely simple. Theorem (Optimal revenue is achievable) For any dynamic auction (full history) M, there is a (constructive) bank account mechanism that is as good as M for the buyer and is (weakly) better than M for the seller. Bank account structure identifies trade-offs between revenue and deficits: Theorem (Extra revenue comes from dynamic bundles) The optimal revenue of a bank account mechanism is bounded by the optimal revenue of static/history-independent mechanisms plus its expected spends, E [ � t s t ] . Maximum limits on balance imply trade-offs between revenue and deficits. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 9 / 17
Double-Reserve Auctions Due to time limit, we skip this part. See you in the poster session. More practical subset of auctions: Deterministic allocations. No payment if nothing gets allocated. Extremely simple and easy to describe. Efficiently computable OPT vs nearly optimal heuristic. Empirical evaluation. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 10 / 17
References Mirrokni, Vahab, Renato Paes Leme, Pingzhong Tang, and Song Zuo. “Optimal dynamic mechanisms with ex-post IR via bank accounts.” arXiv preprint arXiv:1605.08840 (2016). Papadimitriou, Christos, George Pierrakosm, Christos-Alexandros Psomas, and Aviad Rubinstein. “On the complexity of dynamic mechanism design.” Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms . SIAM, 2016. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 11 / 17
Thanks for your attend! Thanks! & Questions? Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 12 / 17
Extra Section Dynamic Auctions 1 Bank Account Mechanisms 2 Double Reserve Auctions 3 Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 13 / 17
More practical subset of auctions Some properties are critical in application. Deterministic allocations. No payment if nothing gets allocated. Double Reserve Auction (DRA) At each stage, it runs a posted-price auction. If the item at the previous stage was sold, low posted-price for current stage; otherwise, high posted-price. The DRA is extremely simple and easy to describe. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 14 / 17
Optimal vs Heuristic Theorem (Computation of Optimal Double-Reserve Auction) The optimal double-reserve auction could be computed via a dynamic program. FPTAS for multiplicative revenue approximation. In contrast of the optimal ones, we propose heuristic DRAs, which are easy to construct — only need i) the Myerson reserve and ii) at most two queries to the integration oracle for each stage; nearly optimal for various distributions. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 15 / 17
Empirical Analysis HDR vs. OPT on Exponential Distribution HDR vs. OPT on Lognormal Distribution Revenue & Efficiency 1.0 Revenue & Efficiency 1.6 1.4 0.8 1.2 1.0 0.6 Rev-OPT Rev-OPT 0.8 Eff-OPT Eff-OPT 0.4 0.6 Rev-HDR Rev-HDR 0.4 0.2 Eff-HDR Eff-HDR 0.2 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 Limit L Limit L HDR vs. OPT on Uniform Distribution Revenue & Efficiency 0.5 0.4 0.3 Rev-OPT Eff-OPT 0.2 Rev-HDR 0.1 Eff-HDR 0.0 0.0 0.1 0.2 0.3 0.4 0.5 Limit L Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 16 / 17
Summary Dynamic mechanisms have great potential to improve the revenue of auctions being repeated over time. However, the framework in practice is simply history independent or contract-based. Two major issues for dynamic mechanisms: too complicated, need strong future commitment power. Methodology contribution: “bank account mechanism” solves both of these two issues: simple structure — only need a “bank account”; trade-offs between revenue and commitment power — maximum limit on the balance. More practical mechanism — (heuristic) double-reserve auction. Mirrokni, Paes Leme, Tang, Zuo Bank Account Mechanism IJCAI, 2016, New York 17 / 17
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