An MSc in AGT (Algorithmic Game Theory) INBAL TALGAM-COHEN My - PowerPoint PPT Presentation

An MSc in AGT (Algorithmic Game Theory) INBAL TALGAM-COHEN

My Background MSc from Weizmann Institute (advised by Uri Feige) PhD from Stanford (advised by Tim Roughgarden) Postdoc at Hebrew & TAU (hosted by Noam Nisan and Michal Feldman) Joined Technion in October 2018 Algorithmic game theorist from the start ◦ Lawyer in past life... INBAL TALGAM-COHEN - AN MSC IN AGT 2

Why I Love AGT You can: ☺ Find a new way to apply theoretical CS to classic economic models underlying modern markets ☺ Prove a communication complexity lower bound solving a decade-long open problem ☺ Advise government policy makers or industry leaders ☺ Collaborate across disciplines … all in a day’s work! INBAL TALGAM-COHEN - AN MSC IN AGT 3

Research Proposal in CS Theory Read papers ◦ In AGT, also consider applications Identify a problem Get an initial handle on the problem Write proposal [Then stay open-minded] INBAL TALGAM-COHEN - AN MSC IN AGT 4

Plan for Rest of the Talk Introduce the research area of market design (& industry connections) ➢ Research topic 1: simple, approximately-optimal algorithms auctions ➢ Research topic 2: a surprising connection between complexity and markets ➢ Research topic 3 (time allowing): as-fair-as-possible resource allocation Step back: common theme INBAL TALGAM-COHEN - AN MSC IN AGT 5

What is Market Design? INBAL TALGAM-COHEN - AN MSC IN AGT 6

Resource Allocation A fundamental combinatorial problem Input: Resources, agents with different values for resources Output: An allocation of the resources among the agents Objective: (Approximately) optimize welfare [Roy’s talk] / revenue / fairness / … Challenges: ◦ Computational complexity – studied in classic CS theory ◦ Agents are self-interested – studied in classic economic theory INBAL TALGAM-COHEN - AN MSC IN AGT 7

Example Objective: Maximize welfare Challenge: Self-interested agents distort information □ = $2 □ = $12 △ = $1 △ = $1 2 Agent Resource □ = $10 □ = $10 △ = $0 0 △ = $0 Agent Resource INBAL TALGAM-COHEN - AN MSC IN AGT 8

Market Design Markets/ Market Algorithms/ mechanisms Design optimization Theory of allocating Theory of aligning Theory of optimizing a resources among self-interests with centralized objective self-interested agents centralized objective by (like welfare) with private information engineering the market subject to constraints INBAL TALGAM-COHEN - AN MSC IN AGT 9

1-Slide History of Market Design 1960s-80s: 1990s-00s: Now & future: Theoretical New needs New theory foundations and solutions Nobel prizes: Computerized, Economics and Mirrlees- Vickrey’96 online markets game theory Hurwicz-Maskin- Myerson’07 transform resource join forces Shapley- Roth’12 allocation with CS theory INBAL TALGAM-COHEN - AN MSC IN AGT 10

Market Design in the Industry Online ad Matching E- Cloud Network Crowd- auctions platforms commerce computing protocols sourcing INBAL TALGAM-COHEN - AN MSC IN AGT 11

Research Topic 1: Simple, Approximately-Optimal Auctions [Roughgarden-T.C.-Yan] [Eden-Feldman-Friedler-T.C.-Weinberg] INBAL TALGAM-COHEN - AN MSC IN AGT 12

Objective: Welfare There exist simple optimal auctions ◦ Maximize welfare even though agents are self-interested 8 price = 5 3 5 “2ndPrice” auction INBAL TALGAM-COHEN - AN MSC IN AGT 13

Objective: Revenue Even with single agent and resource, unclear how to price Necessary assumption: value drawn from distribution 𝐺 △ = ? △ = $10 Agent Seller INBAL TALGAM-COHEN - AN MSC IN AGT 14

Optimal Price Depends on 𝐺 𝐺(𝑤) 1 0.99 99% purchase 0.99 at price=1 𝑤 price=1 price=99 100 INBAL TALGAM-COHEN - AN MSC IN AGT 15

Beyond Single Agent, Single Resource Multiple agents ◦ eBay buyers ◦ Wireless carriers like AT&T Multiple resources ◦ Items on eBay ◦ Spectrum licenses Auctions are the standard tool for resource allocation in these settings INBAL TALGAM-COHEN - AN MSC IN AGT 16

Multiple Items Agent may: ◦ want a single item (“unit - demand”) ◦ have an additive value over items ◦ have a submodular value over items [Roy’s talk] 𝑤 1 ∼ 𝐺 ◦ … 1 𝐺 1 … 𝐺 𝑘 … 𝐺 𝑛 INBAL TALGAM-COHEN - AN MSC IN AGT 17

Multiple (Symmetric) Agents 𝐺 1 … … 𝑤 𝑗𝑘 ∼ 𝐺 𝑘 𝐺 𝑘 … … 𝐺 𝑛 INBAL TALGAM-COHEN - AN MSC IN AGT 18

Major Open Problem How to maximize revenue from selling multiple items? Optimal auction design: [Laffont-et-al ’ 87, McAfee-McMillan ’ 88, Armstrong ’ 96, Manelli-Vincent ’ 06, Hart- Reny ’ 12, Cai-et-al ’ 12, Daskalakis-et-al ’ 13, Giannakopoulos-Koutsoupias ’ 14, Haghpanah-Hartline ’ 15, Devanur-et-al ’ 16 … ] Approximately-optimal auction design: [Briest-et-al ’ 10, Chawla-et-al ’ 10, Alaei ’ 11, Hart-Nisan ’ 12, Li-Yao ’ 13, Cai- Huang ’ 13, Babaioff-et-al ’ 14, Yao ’ 15, Rubinstein-Weinberg ’ 15, Chawla- Miller ’ 16 … ] INBAL TALGAM-COHEN - AN MSC IN AGT 19

Major Open Problem How to maximize revenue from selling multiple items? Our contribution: alternative approach based on competition What’s known after 3 decades: ◦ Optimal auctions incredibly complex even for 2 items ◦ Known approximations impractical (strong assumptions, lose too much) Intuition: Cannot maximize revenue item by item ◦ Bundling required (exp. many prices) ◦ Randomization required (inf. many prices) INBAL TALGAM-COHEN - AN MSC IN AGT 20

Our Result First idea: What if we run the welfare-maximizing auction? ◦ Simple ◦ But too far from revenue-optimal (e.g., single agent) Second idea: What if we run it with extra competing agents? ◦ Key question: How many would we need? ◦ Benchmark: Revenue-optimal auction Approach inspired by [Sleator- Tarjan’84, Bulow - Klemperer’96] INBAL TALGAM-COHEN - AN MSC IN AGT 21

Our Result With mild extra competition, revenue “ reduces to ” welfare Theorem: 𝑛 items, agents with i.i.d. values drawn from 𝐺 1 , … , 𝐺 𝑛 𝔽 [ 2ndPrice revenue] ≥ 𝔽 [ OPT 𝐺 𝑛 revenue] 1 ,…,𝐺 with 𝑜 + linear (𝑛, 𝑜) agents with 𝑜 agents INBAL TALGAM-COHEN - AN MSC IN AGT 22

Our Result: Special Case Revenue-optimal auction (depends on 𝐺 1 , … , 𝐺 𝑛 , complex) ≈ Welfare-optimal auction with extra agents (oblivious to 𝐺 1 , … , 𝐺 𝑛 ) 𝐺 1 … 𝐺 𝑛 𝑛 … INBAL TALGAM-COHEN - AN MSC IN AGT 23

Advantage 1: Simplicity “ In practice, auction designers place a tremendous value on the simplicity of an auction ’ s design Simplicity helps attract participants into the auction Hardly anything matters more ” [Milgrom ‘ 04] ➢ Extra agents – plausible ➢ Our results also translate to standard approximation guarantees INBAL TALGAM-COHEN - AN MSC IN AGT 24

Advantage 2: Robustness “ The statistics of the data we observe shifts rapidly ” [Google Research white paper] “ Precise [distributional] knowledge is rarely available in practice ” [Bertsimas-Thiele ’ 06] ➢ For multiple items, even perfect knowledge of the distributions doesn ’ t help INBAL TALGAM-COHEN - AN MSC IN AGT 25

Result statement: 2ndPrice with 1 + 𝑛 agents ≥ OPT with 1 agent Proof Steps Upper-bound expected revenue of OPT from item 𝑘 1. … … Lower-bound expected revenue of 2ndPrice from item 𝑘 2. … … Relate the bounds by coupling values for 𝑛 items with values of 𝑛 agents 3. ◦ Use “ principal of deferred decision ” for the coupling INBAL TALGAM-COHEN - AN MSC IN AGT 26

Research Topic 2: A Surprising Connection Between Complexity and Markets [Roughgarden-T.C.] INBAL TALGAM-COHEN - AN MSC IN AGT 27

Resource Allocation, Decentralized Demand Demand □ = $2 Marketplace = △ = □ △ = $1 Price=$2 Price=$1 Demand Agent □ = $10 = □ Over-demand Demand △ = $0 = Supply Price=$1 Price=$0 Agent INBAL TALGAM-COHEN - AN MSC IN AGT 28

Market Equilibrium Definition: A pair (allocation, prices) such that ◦ every agent is allocated her demand given the prices ◦ the supply clears Equivalently: Given the prices, the allocation simultaneously maximizes ◦ every agent ’ s utility (value minus payment) ◦ the total revenue → Equilibrium allocations maximize welfare INBAL TALGAM-COHEN - AN MSC IN AGT 29

Market Equil. – A Fundamental Concept ADAM SMITH’S INVISIBLE HAND ALAN TURING ’ S INVISIBLE HAND? INBAL TALGAM-COHEN - AN MSC IN AGT 30

Market Equilibrium: Does it Exist? Existence guaranteed with item prices if agents value items as substitutes Major open problem: When else is existence guaranteed? I.e., for which classes of valuations and prices? ◦ [Gul-Stacchetti ’ 99, Milgrom ’ 00, Parkes-Ungar ’ 00, Sun-Yang ’ 06, Teytelboym ’ 13, Ben-Zwi ’ 13, Sun-Yang ’ 14, Candogan ’ 14, Candogan-Pekec ’ 14, Candogan ’ 15 … ] INBAL TALGAM-COHEN - AN MSC IN AGT 31