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

▶
an msc in agt
SMART_READER_LITE
LIVE PREVIEW

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

May 30, 2023 599 likes •1.13k views

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)

slide-1
SLIDE 1

An MSc in AGT (Algorithmic Game Theory)

INBAL TALGAM-COHEN

slide-2
SLIDE 2

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

slide-3
SLIDE 3

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

slide-4
SLIDE 4

Research Proposal in CS Theory

INBAL TALGAM-COHEN - AN MSC IN AGT 4

Read papers

  • In AGT, also consider applications

Identify a problem Get an initial handle on the problem Write proposal [Then stay open-minded]

slide-5
SLIDE 5

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

slide-6
SLIDE 6

What is Market Design?

INBAL TALGAM-COHEN - AN MSC IN AGT 6

slide-7
SLIDE 7

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

slide-8
SLIDE 8

Example

Objective: Maximize welfare Challenge: Self-interested agents distort information

INBAL TALGAM-COHEN - AN MSC IN AGT 8

□ = $10 △ = $0 2 □ = $10 △ = $0 □ = $2 △ = $1 □ = $12 △ = $1 Agent Agent Resource Resource

slide-9
SLIDE 9

Market Design

INBAL TALGAM-COHEN - AN MSC IN AGT 9

Market Design Markets/ mechanisms Algorithms/

  • ptimization

Theory of optimizing a centralized objective (like welfare) subject to constraints Theory of aligning self-interests with centralized objective by engineering the market Theory of allocating resources among self-interested agents with private information

slide-10
SLIDE 10

1-Slide History of Market Design

INBAL TALGAM-COHEN - AN MSC IN AGT 10

1960s-80s: Theoretical foundations Nobel prizes: Mirrlees-Vickrey’96 Hurwicz-Maskin-Myerson’07 Shapley-Roth’12 1990s-00s: New needs Computerized,

  • nline markets

transform resource allocation Now & future: New theory and solutions Economics and game theory join forces with CS theory

slide-11
SLIDE 11

Online ad auctions Matching platforms E- commerce Cloud computing Network protocols Crowd- sourcing

Market Design in the Industry

INBAL TALGAM-COHEN - AN MSC IN AGT 11

slide-12
SLIDE 12

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

slide-13
SLIDE 13

There exist simple optimal auctions

  • Maximize welfare even though agents are self-interested

“2ndPrice” auction

Objective: Welfare

INBAL TALGAM-COHEN - AN MSC IN AGT 13

8 3 price = 5 5

slide-14
SLIDE 14

Even with single agent and resource, unclear how to price Necessary assumption: value drawn from distribution 𝐺

Objective: Revenue

INBAL TALGAM-COHEN - AN MSC IN AGT 14

△ = ? △ = $10 Agent Seller

slide-15
SLIDE 15

Optimal Price Depends on 𝐺

INBAL TALGAM-COHEN - AN MSC IN AGT 15

𝐺(𝑤) 𝑤 1 100 0.99 price=1 price=99 99% purchase at price=1 0.99

slide-16
SLIDE 16

Beyond Single Agent, Single Resource

INBAL TALGAM-COHEN - AN MSC IN AGT 16

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

slide-17
SLIDE 17

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]
  • …

INBAL TALGAM-COHEN - AN MSC IN AGT 17

𝐺

1

𝐺

𝑘

𝑤1 ∼ 𝐺

1

… … 𝐺

𝑛

slide-18
SLIDE 18

Multiple (Symmetric) Agents

INBAL TALGAM-COHEN - AN MSC IN AGT 18

… 𝑤𝑗𝑘 ∼ 𝐺

𝑘

… 𝐺

1

𝐺

𝑘

… … 𝐺

𝑛

slide-19
SLIDE 19

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…]

Major Open Problem

INBAL TALGAM-COHEN - AN MSC IN AGT 19

How to maximize revenue from selling multiple items?

slide-20
SLIDE 20

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)

Major Open Problem

INBAL TALGAM-COHEN - AN MSC IN AGT 20

How to maximize revenue from selling multiple items? Our contribution: alternative approach based on competition

slide-21
SLIDE 21

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

slide-22
SLIDE 22

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

INBAL TALGAM-COHEN - AN MSC IN AGT 22

𝔽[2ndPrice revenue] 𝔽[OPT𝐺

1,…,𝐺 𝑛 revenue]

≥ with 𝑜 + linear(𝑛, 𝑜) agents with 𝑜 agents

slide-23
SLIDE 23

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)

INBAL TALGAM-COHEN - AN MSC IN AGT 23

𝐺

1

𝐺

𝑛

… … 𝑛

slide-24
SLIDE 24

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

slide-25
SLIDE 25

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

slide-26
SLIDE 26

1. Upper-bound expected revenue of OPT from item 𝑘 2. Lower-bound expected revenue of 2ndPrice from item 𝑘 3. Relate the bounds by coupling values for 𝑛 items with values of 𝑛 agents

  • Use “principal of deferred decision” for the coupling

Proof Steps

INBAL TALGAM-COHEN - AN MSC IN AGT 26

Result statement: 2ndPrice with 1 + 𝑛 agents ≥ OPT with 1 agent

… … … …

slide-27
SLIDE 27

Research Topic 2: A Surprising Connection Between Complexity and Markets

[Roughgarden-T.C.]

INBAL TALGAM-COHEN - AN MSC IN AGT 27

slide-28
SLIDE 28

Over-demand Demand = □

Resource Allocation, Decentralized

INBAL TALGAM-COHEN - AN MSC IN AGT 28

□ = $10 △ = $0 □ = $2 △ = $1 Agent Agent Price=$1 Price=$1 Marketplace Demand = □ Price=$2 Price=$0 Demand = Supply Demand = △

slide-29
SLIDE 29

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

slide-30
SLIDE 30

Market Equil. – A Fundamental Concept

ADAM SMITH’S INVISIBLE HAND ALAN TURING’S INVISIBLE HAND?

INBAL TALGAM-COHEN - AN MSC IN AGT 30

slide-31
SLIDE 31

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

  • f 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

slide-32
SLIDE 32

Equilibrium Complexity

Traditional complexity theory studies the trade-off between an algorithm’s complexity and the solution’s quality Need theory on the trade-off between an equilibrium’s complexity and its existence guarantees Our contribution: A connection between non-existence of a simple equilibrium, and computational complexity

INBAL TALGAM-COHEN - AN MSC IN AGT 32

Centralized algorithm Resource allocation problem Solution (an allocation) Decentralized market equilibrium

slide-33
SLIDE 33

Our Result

Theorem: A necessary condition for existence of market equilibrium with item prices for all markets with valuations from class 𝒲: DEMAND not computationally easier than MAX-WELFARE for 𝒲 DEMAND:

  • Input – a valuation in 𝒲 and item prices
  • Output – which item set to buy to maximize utility

Corollary: If assuming P ≠ NP, DEMAND is easier than MAX-WELFARE for 𝒲, then there exists a market with valuations from 𝒲 and no simple equilibrium

INBAL TALGAM-COHEN - AN MSC IN AGT 33

slide-34
SLIDE 34

𝑞5 𝑞4 𝑞3 𝑞2 𝑞1

Example: DEMAND

Let 𝒲 be the class of capped-additive valuations

INBAL TALGAM-COHEN - AN MSC IN AGT 34

DEMAND 𝑑 𝑤1 𝑤2 𝑤3 𝑤4 𝑤5

slide-35
SLIDE 35

Example: MAX-WELFARE

Let 𝒲 be the class of capped-additive valuations

INBAL TALGAM-COHEN - AN MSC IN AGT 35

𝑑1 𝑑2 𝑑3 𝑑4

slide-36
SLIDE 36

Example: Applying Our Theorem

Assuming P ≠ NP, for polynomially-bounded values: → There exists a market with capped-additive valuations and no equilibrium

INBAL TALGAM-COHEN - AN MSC IN AGT 36

NP (hard)

h

P (easy) MAX-WELFARE DEMAND

slide-37
SLIDE 37

Summary of Research Topic 2

➢Computational complexity applies directly to the fundamental economic question of equilibrium existence; ➢It offers a systematic approach for establishing equilibrium non-existence based on algorithmic aspects of the market.

INBAL TALGAM-COHEN - AN MSC IN AGT 37

slide-38
SLIDE 38

Research Topic 3: As-Fair-As-Possible Resource Allocation

[Babaioff-Nisan-T.C.]

INBAL TALGAM-COHEN - AN MSC IN AGT 38

slide-39
SLIDE 39

Motivation

Indivisible items need to be allocated among 2 additive agents without the use

  • f money

Objective: Fairness Example: Food banks

INBAL TALGAM-COHEN - AN MSC IN AGT 39

slide-40
SLIDE 40

Classic Solution

Give agents equal budgets of artificial money Find a market equilibrium [Notice DEMAND changes a bit: agents maximize value subject to budget rather than value minus payment] Intuitively fair – agents face the same prices Formally fair – fair-share and envy-freeness guarantees

INBAL TALGAM-COHEN - AN MSC IN AGT 40

slide-41
SLIDE 41

Problems with Classic Solution

Complication 1: Indivisible items

  • An equilibrium doesn’t exist already in the simplest imaginable market

Complication 2: Agents can be a priori unequal

  • Intuitive fairness – give agents unequal budgets of artificial money
  • Formal fairness – ?

INBAL TALGAM-COHEN - AN MSC IN AGT 41

Budget = ½ Budget = ½ Price ≤ ½ → over-demand Price > ½ → under-demand

slide-42
SLIDE 42

Our Solution

INBAL TALGAM-COHEN - AN MSC IN AGT 42

Give agents budgets of artificial money proportional to their entitlements Add tiny random perturbations to the budgets Find a market equilibrium We call this “equilibrium with generic budgets” Budget = ½+𝜗 Budget = ½-𝜗 Price = ½ → demand=supply

slide-43
SLIDE 43

In What Sense is Our Solution Fair?

INBAL TALGAM-COHEN - AN MSC IN AGT 43

Definition: An agent’s maximin share is any set of items she values at least as much as the set she can guarantee for herself via the cut-and-choose protocol The cutter maximizes her minimum, hence “maximin share” 𝑤1,1 = 5 𝑤1,2 = 3 𝑤1,3 = 2

slide-44
SLIDE 44

Generalization of Fairness Notion

Maximin share and cut-and-choose generalize by allowing:

  • the cutter to cut into more than 2 parts
  • the chooser to choose more than 1 part

Example: Consider agent 1 with budget 1/3; cuts into 3 parts; agent 2 chooses 2

INBAL TALGAM-COHEN - AN MSC IN AGT 44

𝑤1,1 = 5 𝑤1,2 = 3 𝑤1,3 = 2

slide-45
SLIDE 45

Our Fairness Guarantee

Proposition: Consider a market equilibrium for agents with budgets 𝑐1, … , 𝑐𝑜. For every agent 𝑗 with budget 𝑐𝑗 and any rational number

ℓ 𝑒 ≤ 𝑐𝑗,

the equilibrium allocation gives agent 𝑗 his ℓ-out-of-𝑒 maximin share.

INBAL TALGAM-COHEN - AN MSC IN AGT 45

slide-46
SLIDE 46

Our Existence Result

Theorem: Consider 2 additive agents. An equilibrium with generic budgets exists in several cases of interest:

  • When both agents can get their entitlements despite indivisibilities
  • With equal entitlements
  • When the agents’ valuations are identical

INBAL TALGAM-COHEN - AN MSC IN AGT 46

slide-47
SLIDE 47

Immediate Open Questions

Does an equilibrium with generic budgets always exist? Does a non-equilibrium allocation satisfying our fairness guarantee always exist?

INBAL TALGAM-COHEN - AN MSC IN AGT 47

slide-48
SLIDE 48

Summary: Common Theme

INBAL TALGAM-COHEN - AN MSC IN AGT 48

slide-49
SLIDE 49

Theory vs. Reality

Auctions for maximizing revenue

  • Theory (revenue-optimal auction) holds for single item
  • In reality, simplicity and participation (competition) are crucial
  • With enough competition a simple auction matches the optimal benchmark

Market equilibrium

  • Theory (equilibrium existence guarantee) holds for substitutes
  • In reality, markets “work” despite complements but we have no explanation
  • A computational complexity barrier to existence beyond substitutes

INBAL TALGAM-COHEN - AN MSC IN AGT 49

slide-50
SLIDE 50

Theory vs. Reality

Fair resource allocation

  • Theory (fairness via market equilibrium) holds for divisible items
  • In reality, as-fair-as-possible solutions suffice
  • Generic budgets may guarantee existence of such solutions

INBAL TALGAM-COHEN - AN MSC IN AGT 50

slide-51
SLIDE 51

Keywords

Market design Online markets Socio-economic implications Interdisciplinary approach Thank you for listening! Questions?

INBAL TALGAM-COHEN - AN MSC IN AGT 51