Novel Techniques for theUnderstanding of Complex Games

Guido SchaferCWI / VU University Amsterdam

g.schaefer@cwi.nl

NWO EW TOP Grant Module 2 InterviewHotel Park Plaza, Utrecht

October 6, 2014

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Motivation

Many real-world problems are complex and distributed:• involve several strategic decision makers• each decision maker wants to maximize his own utility• individual utility depends on the choices made by others

Examples: network routing, auctions, Internet applications

Fact: strategic choices lead to outcomes that are inefficient

Need: precise understanding of the inefficiency caused bystrategic decision making

Guido Schafer Novel Techniques for the Understanding of Complex Games 1

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Motivation

Many real-world problems are complex and distributed:• involve several strategic decision makers• each decision maker wants to maximize his own utility• individual utility depends on the choices made by others

Examples: network routing, auctions, Internet applications

Fact: strategic choices lead to outcomes that are inefficient

Need: precise understanding of the inefficiency caused bystrategic decision making

Guido Schafer Novel Techniques for the Understanding of Complex Games 1

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Motivation

Guido Schafer Novel Techniques for the Understanding of Complex Games 1

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Motivation

Guido Schafer Novel Techniques for the Understanding of Complex Games 1

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Motivation

Guido Schafer Novel Techniques for the Understanding of Complex Games 1

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Motivation

Guido Schafer Novel Techniques for the Understanding of Complex Games 1

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Motivation

Guido Schafer Novel Techniques for the Understanding of Complex Games 1

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Motivation

Guido Schafer Novel Techniques for the Understanding of Complex Games 1

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Motivation

Many real-world problems are complex and distributed:• involve several strategic decision makers• each decision maker wants to maximize his own utility• individual utility depends on the choices made by others

Examples: network routing, auctions, Internet applications

Fact: strategic choices lead to outcomes that are inefficient

Need: precise understanding of the inefficiency caused bystrategic decision making

Guido Schafer Novel Techniques for the Understanding of Complex Games 1

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Motivation

Many real-world problems are complex and distributed:• involve several strategic decision makers• each decision maker wants to maximize his own utility• individual utility depends on the choices made by others

Examples: network routing, auctions, Internet applications

Fact: strategic choices lead to outcomes that are inefficient

Need: precise understanding of the inefficiency caused bystrategic decision making

Guido Schafer Novel Techniques for the Understanding of Complex Games 1

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Game-theoretical model

A strategic game is given by:• set of players N = {1, . . . , n}• for every player i ∈ N: a set of strategies Si and a

cost function Ci : S1 × · · · × Sn → R

→ every player i chooses si ∈ Si to minimize Ci(s1, . . . , sn)

A joint strategy s = (s1, . . . , sn) is a Nash equilibrium if no playerhas an incentive to deviate unilaterally

The social cost of a joint strategy s = (s1, . . . , sn) is

SC(s) =∑

i

Ci(s)

Guido Schafer Novel Techniques for the Understanding of Complex Games 2

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Game-theoretical model

A strategic game is given by:• set of players N = {1, . . . , n}• for every player i ∈ N: a set of strategies Si and a

cost function Ci : S1 × · · · × Sn → R

→ every player i chooses si ∈ Si to minimize Ci(s1, . . . , sn)

A joint strategy s = (s1, . . . , sn) is a Nash equilibrium if no playerhas an incentive to deviate unilaterally

The social cost of a joint strategy s = (s1, . . . , sn) is

SC(s) =∑

i

Ci(s)

Guido Schafer Novel Techniques for the Understanding of Complex Games 2

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Game-theoretical model

A strategic game is given by:• set of players N = {1, . . . , n}• for every player i ∈ N: a set of strategies Si and a

cost function Ci : S1 × · · · × Sn → R

→ every player i chooses si ∈ Si to minimize Ci(s1, . . . , sn)

A joint strategy s = (s1, . . . , sn) is a Nash equilibrium if no playerhas an incentive to deviate unilaterally

The social cost of a joint strategy s = (s1, . . . , sn) is

SC(s) =∑

i

Ci(s)

Guido Schafer Novel Techniques for the Understanding of Complex Games 2

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Game-theoretical model

A strategic game is given by:• set of players N = {1, . . . , n}• for every player i ∈ N: a set of strategies Si and a

cost function Ci : S1 × · · · × Sn → R

→ every player i chooses si ∈ Si to minimize Ci(s1, . . . , sn)

A joint strategy s = (s1, . . . , sn) is a Nash equilibrium if no playerhas an incentive to deviate unilaterally

The social cost of a joint strategy s = (s1, . . . , sn) is

SC(s) =∑

i

Ci(s)

Guido Schafer Novel Techniques for the Understanding of Complex Games 2

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Quantifying the inefficiency

Inefficiency of equilibria:• predominant yardstick: price of anarchy

POA =social cost of worst Nash equilibrium

minimum social cost

[Koutsoupias and Papadimitriou (1999)]

• Godel Prize awarded in 2012 by the Association ofComputing Machinery

→ price of anarchy of fundamental games is well-understood

Guido Schafer Novel Techniques for the Understanding of Complex Games 3

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Quantifying the inefficiency

Inefficiency of equilibria:• predominant yardstick: price of anarchy

POA =social cost of worst Nash equilibrium

minimum social cost

[Koutsoupias and Papadimitriou (1999)]

• Godel Prize awarded in 2012 by the Association ofComputing Machinery

→ price of anarchy of fundamental games is well-understood

Guido Schafer Novel Techniques for the Understanding of Complex Games 3

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More complex games: example

Social context games: player i ’s perceived cost is

Cαi (s) =

∑j∈N

αijCj(s),

where αij ∈ R specifies how much player i cares about player j .

animosity

αij < 0

friendship

αij > 0

indifferent

αij = 0

[Anagnostopoulos, Becchetti, de Keijzer, Schafer (2013)]

Guido Schafer Novel Techniques for the Understanding of Complex Games 4

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State of the art

Inefficiency of complex games:• price of anarchy of complex games is not well-understood• partial results for altruistic games (αij ≥ 0)

– [Chen, Kempe, de Keijzer, Schafer (2011)]– [Anagnostopoulos, Becchetti, de Keijzer, Schafer (2013)]– [Rahn and Schafer (2013)]

• existing techniques fail in general• main difficulty: complex interdependencies

Guido Schafer Novel Techniques for the Understanding of Complex Games 5

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Main goals

1 Invent new techniques to study theinefficiency of complex games

2 Derive coordination mechanisms toreduce the inefficiency

Guido Schafer Novel Techniques for the Understanding of Complex Games 6

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Main goals

1 Invent new techniques to study theinefficiency of complex games

2 Derive coordination mechanisms toreduce the inefficiency

Guido Schafer Novel Techniques for the Understanding of Complex Games 6

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Approach

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base game

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G = (N, (Si), (Ci))

.modifier Mα .

Gα = Mα(G)

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complex game

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Gα = (N, (Si), (Cαi ))

.Example: social context game

Cαi =

∑j∈N

αijCj

Guido Schafer Novel Techniques for the Understanding of Complex Games 7

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Approach

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base game

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G = (N, (Si), (Ci))

.modifier Mα .

Gα = Mα(G)

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complex game

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Gα = (N, (Si), (Cαi ))

.Example: social context game

Cαi =

∑j∈N

αijCj

Guido Schafer Novel Techniques for the Understanding of Complex Games 7

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Approach

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base game

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G = (N, (Si), (Ci))

.modifier Mα .

Gα = Mα(G)

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complex game

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Gα = (N, (Si), (Cαi ))

.Example: social context game

Cαi =

∑j∈N

αijCj

Guido Schafer Novel Techniques for the Understanding of Complex Games 7

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Approach

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base game

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G = (N, (Si), (Ci))

.modifier Mα .

Gα = Mα(G)

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complex game

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Gα = (N, (Si), (Cαi ))

.Example: social context game

Cαi =

∑j∈N

αijCj

Guido Schafer Novel Techniques for the Understanding of Complex Games 7

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Key objectives

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Foundations:1 sensitivity analysis2 reduction techniques3 decomposition techniques

.Applications (examples):1 social context games2 congestion games with perturbed delays

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Key objectives

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Foundations:1 sensitivity analysis2 reduction techniques3 decomposition techniques

.Applications (examples):1 social context games2 congestion games with perturbed delays

Guido Schafer Novel Techniques for the Understanding of Complex Games 8

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Implications

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optimal taxes forcongestion games

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congestion games withrisk-averse players

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smoothed analysis ofcongestion games

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games withother-regarding

preferences

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Foundations:1 sensitivity analysis2 reduction techniques3 decomposition techniques

.Applications (examples):1 social context games2 congestion games with perturbed delays

Guido Schafer Novel Techniques for the Understanding of Complex Games 9

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Significance

We envision that our research• brings game-theoretical analyses closer to reality• enriches the methodologies and techniques of the field• leads to a general theory for inefficiency studies• contributes to a better understanding of complex games• provides coordination mechanisms to reduce the inefficiency

Guido Schafer Novel Techniques for the Understanding of Complex Games 10

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Quality of applicant

• publications 2014: STACS, SAGT, WINE, JAIR, MP, TEAC• experienced in all key aspects of proposal• program committees 2014: EC, WINE• supervision: MSs (10+), PhDs (3), (Postdocs)• international research network• invited talks 2014:

– German Day on Algorithmic Game Theory– TI Conference 70 Years Theory of Games and Economic

Behavior– Dagstuhl Seminar Equilibrium Computation

• lecturer national Mastermath & LNMB PhD program• organizer of WINE 2015

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Quality, innovativeness & impact of research

• research is timely, bears large potential• objectives are ambitious but manageable• methodology is novel and promising• research agenda defined in key steps and adaptable• high impact in AGT community and beyond

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Knowledge utilization

• fundamental research• impact mainly scientific (AGT community and beyond)

• key aspects are motivated through real-life• ambition to better reflect reality is present on all levels

– modeling: complex games are closer to reality– analysis: novel techniques for exact inefficiency studies– algorithms: coordination mechanisms to reduce inefficiency

• recent interest in our findings on altruistic games (ERCIMNews, ESB Economisch Statistische Berichten)

Guido Schafer Novel Techniques for the Understanding of Complex Games 13