Network-based Learning for Understanding Collective Human ...xdong/talk/SICSS_NetworkLearning.pdf• Large-scale mobile phone data during Cirque de Soleil in Andorra • Study inﬂuence

Network-based Learning for Understanding Collective Human Behaviour

Summer Institute in Computational Social Science Oxford, June 2019

Xiaowen Dong Department of Engineering Science

University of Oxford

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Introduction

2

Auguste Comte defined “social physics” as the study of the laws of society or the science of civilisation

Early 1800s

Newtonian physics (society conceptualised as a machine)

http://www.eoht.info/page/Social+physics https://en.wikipedia.org/wiki/Royal_Statistical_Society

http://www.eoht.info/page/Social+physics

https://en.wikipedia.org/wiki/Royal_Statistical_Society

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Introduction

2

“...procuring, arranging and publishing facts to illustrate the condition and prospects of society”

1834

Auguste Comte defined “social physics” as the study of the laws of society or the science of civilisation

Early 1800s

Newtonian physics (society conceptualised as a machine)

http://www.eoht.info/page/Social+physics https://en.wikipedia.org/wiki/Royal_Statistical_Society

http://www.eoht.info/page/Social+physics

https://en.wikipedia.org/wiki/Royal_Statistical_Society

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Introduction

3

1940-50s

many social indicators have statistical regularities (Zipf distribution, gravity law)

Zipf, “Human behavior and the principle of least effort,” Addison-Wesley Press, 1949. Zipf, “The P1P2/D hypothesis: On the inter-city movement of persons,” American Sociological Review, 1946.

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Introduction

3

1940-50s

many social indicators have statistical regularities (Zipf distribution, gravity law)

Zipf, “Human behavior and the principle of least effort,” Addison-Wesley Press, 1949. Zipf, “The P1P2/D hypothesis: On the inter-city movement of persons,” American Sociological Review, 1946.

statistical regularities within human movement and communication

correlations with economic indicators

1990-2000s

Eagle et al., “Network diversity and economic development,” Science, 2010.

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Introduction

4

2010s

new data sources about human behaviour

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Introduction

4

advanced computational methods

2010s

new data sources about human behaviour

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Introduction

5

new perspectives from computational social science

t

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Introduction

5

new perspectives from computational social science current population

management

- demographics - individual records

- static information

the new way

- behavioural traits

- collective behaviour - dynamics

practical impact

t

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Introduction

5


management



the new way



practical impact

- need new models & tools to understand structure and dynamics - computational methods in the context of social sciences research

t

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Introduction

5


management



the new way



practical impact

- need new models & tools to understand structure and dynamics - computational methods in the context of social sciences research

t

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- how social network affects decision-making?

- how to infer unobserved social network structure from observed decisions?

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Motivation• From “six degrees of separation” to “three degrees of influence”

7

Milgram’s experiment

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7

Milgram’s experiment

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7Christakis and Fowler, “Connected,” Little, Brown and Company, 2009.

Milgram’s experimentspreading of obesity,

happiness, smoking behaviour

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7Christakis and Fowler, “Connected,” Little, Brown and Company, 2009.

• How influence propagates in social networks and affect decision-making?

Milgram’s experimentspreading of obesity,

happiness, smoking behaviour

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Setting• Large-scale mobile phone data during Cirque de Soleil in Andorra • Study influence on individual decision-making: whether or not to attend

the event after receiving phone calls from an attendee

8

Period 18 days

Attended and observed by mobile phone

16,043

Number of mobile phone users ‘influenced’

161,857

Number of mobile phone users not influenced 71,337

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Setting• Information cascade (phone calls) for an observation period

- initial adopters: attendees of event

- influenced/not influenced: connected/not connected to initial adopters in cascade

- hop index: shortest distance from an individual to any initial adopter in cascade

9

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Setting• Information cascade (phone calls) for an observation period

- initial adopters: attendees of event

- influenced/not influenced: connected/not connected to initial adopters in cascade

- hop index: shortest distance from an individual to any initial adopter in cascade

9

• Observe adoption decisions in “future”

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Homophily vs Influence• Decisions on adoption may be attributed to two factors

- homophily: similarity between friends

- influence: which drives contagion

10

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10

homophily

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10

homophily

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10

homophily influence

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10

homophily influence

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Matched sample estimation• Quantify effect of influence while controlling for bias due to homophily

11

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11

treatment control

- matched sample estimation via propensity score matching (PSM)

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11

treatment control

- matched sample estimation via propensity score matching (PSM)

- matching conditioned on preferences revealed by individual mobility history

Samuelson, “A note on the pure theory of consumer’s behaviour,” Economica, 1938.

explorative exploitative

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Matched sample estimation• Study effect of influence w.r.t. communication distance

- one treatment group for each hop index

- one corresponding control group from outside information cascade

12

treatment control explorative exploitative

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Matched sample estimation• Study effect of influence w.r.t. communication distance

- one treatment group for each hop index

- one corresponding control group from outside information cascade

12Aral et al., “Distinguishing influence-based contagion from homophily-driven diffusion in dynamic networks,” PNAS, 2009.

treatment control explorative exploitative

- difference in future adoption rate establishes upper bound of social influence effect

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Empirical results

13

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Empirical results

13

- social influence increases likelihood of future adoption

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Empirical results

13


- long range effect of social influence over communication network

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Empirical results




- over-estimation of effect based on random matching

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Empirical results




- over-estimation of effect based on random matching

- decaying pattern disappears after random shuffling of hop index

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Bayesian learning model

14

- an individual updates her estimation of “product” characteristics after dynamically aggregating local information

- she then makes adoption decision based on the perception and her own preference

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Bayesian learning model

15

- measure difference in estimation between individuals in information cascade and initial adopters

- difference increases w.r.t. hop index

- observed decaying influence may be related to bias in estimation which accumulates along cascade

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Discussion• Summary & Implication

- revealed preferences via behaviour patterns may provide more robust information than traditional socio-demographic factors

- long range effect of social influence highlights hidden connection among seemingly independent individuals

- implication in viral marketing, public health management, and social mobilisation

16

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Discussion• Summary & Implication

- revealed preferences via behaviour patterns may provide more robust information than traditional socio-demographic factors

- long range effect of social influence highlights hidden connection among seemingly independent individuals

- implication in viral marketing, public health management, and social mobilisation

16

• Open issues & future directions - identification of initial adopters

- multiple treatment effect via more than one communication path

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Motivation• Consider a group of students making choices on educational effort

- making effort is costly

- I will benefit from my own effort

- I will also benefit from my friends’ effort

18

more effort

less effort

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Motivation• Consider a group of students making choices on buying a book

- buying a book is costly

- if a friend of mine will buy, then I will not buy

- but if none of my friends will buy, then I will buy

19

buy a book

do not buy a book

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Motivation• Such strategic interactions can be modelled as games on networks

- players, actions, payoffs, interaction network

20

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20

- payoff of an individual depends on her action as well as her neighbours’ actions

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20

- strategic complements or strategic substitutes- payoff of an individual depends on her action as well as her neighbours’ actions

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20

- strategic complements or strategic substitutes- payoff of an individual depends on her action as well as her neighbours’ actions

buy a book

do not buy a book

more effort

less effort

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Motivation• Economics

- existence of equilibrium or how action/payoff depends on network structure

- on a given or predefined network

21

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21

• Computer Science (graphical games) - algorithms for computing equilibrium

- binary or finite discrete action space

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21

• This work - learning network given continuous actions



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21

• This work - learning network given continuous actions



• Many examples - observe individual decisions (e.g., adoptions), but not social relationship

- observe R&D activities of firms, but not collaboration networks

- observe international policies of countries, but not political alliance

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Network games with linear-quadratic payoffs• Consider a graph with edge weights

22

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22

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• Payoff of player i: ui

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22

Gij

• Games with linear-quadratic payoffs

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X

j2N (i)

Gijaj<latexit sha1_base64="tkq7e4J4le4vaLcszmh/BTFOcLY=">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</latexit><latexit sha1_base64="tkq7e4J4le4vaLcszmh/BTFOcLY=">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</latexit><latexit sha1_base64="tkq7e4J4le4vaLcszmh/BTFOcLY=">AAACO3icbVBNSwMxEM36bf2qevQSLIIilt0i6EUoetCTqFgtdOsym2Zt2mx2SbJCCfu/vPgnvHnx4kERr95Naw9aHZjw8t4MM/PClDOlXffJGRufmJyanpktzM0vLC4Vl1euVJJJQmsk4Ymsh6AoZ4LWNNOc1lNJIQ45vQ67R339+o5KxRJxqXspbcZwK1jECGhLBcWLLGD4AIf2BZs7fiSBGC83ldz+byp4G/sh1TBQfZXFgelgnwnsx6DbBLg5zTfZVo6PA8M6uS3rBMWSW3YHgf8CbwhKaBhnQfHRbyUki6nQhINSDc9NddOA1Ixwmhf8TNEUSBduacNCATFVTTO4PccblmnhKJE2hcYD9meHgVipXhzayv7GalTrk/9pjUxH+03DRJppKsj3oCjjWCe4byRuMUmJ5j0LgEhmd8WkDdY9be0uWBO80ZP/gqtK2XPL3vluqXo4tGMGraF1tIk8tIeq6ASdoRoi6B49o1f05jw4L8678/FdOuYMe1bRr3A+vwClYKwf</latexit><latexit sha1_base64="tkq7e4J4le4vaLcszmh/BTFOcLY=">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</latexit>





/35


22

Gij

individual action


ui = biai �1

2a2i + �ai

X

j2N (i)






/35


22

Gij

individual actionmarginal benefit


ui = biai �1

2a2i + �ai

X

j2N (i)






/35


22

Gij

individual actionmarginal benefit network factor


ui = biai �1

2a2i + �ai

X

j2N (i)






/35


22

Gij



individual effect network effect

ui = biai �1

2a2i + �ai

X

j2N (i)






/35

Network games with linear-quadratic payoffs

23Jackson and Zezou, “Games on networks,” Handbook of Game Theory with Economic Applications, 2015. Bramoullé and Kranton, “Games played on networks,” The Oxford Handbook of the Economics of Networks, 2016.

� > 0<latexit sha1_base64="4FuzAc7bz3x7RjoD5RQgDT19KiE=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6EmKXjxWsB/QhrLZTtqlm03YnQil9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5YSqFIc/7dgpr6xubW8Xt0s7u3v5B+fCoaZJMc2zwRCa6HTKDUihskCCJ7VQji0OJrXB0N/NbT6iNSNQjjVMMYjZQIhKckZVa3RCJ3Xi9csWrenO4q8TPSQVy1Hvlr24/4VmMirhkxnR8L6VgwjQJLnFa6mYGU8ZHbIAdSxWL0QST+blT98wqfTdKtC1F7lz9PTFhsTHjOLSdMaOhWfZm4n9eJ6PoOpgIlWaEii8WRZl0KXFnv7t9oZGTHFvCuBb2VpcPmWacbEIlG4K//PIqaV5Ufa/qP1xWard5HEU4gVM4Bx+uoAb3UIcGcBjBM7zCm5M6L86787FoLTj5zDH8gfP5A7iljyY=</latexit><latexit sha1_base64="4FuzAc7bz3x7RjoD5RQgDT19KiE=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6EmKXjxWsB/QhrLZTtqlm03YnQil9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5YSqFIc/7dgpr6xubW8Xt0s7u3v5B+fCoaZJMc2zwRCa6HTKDUihskCCJ7VQji0OJrXB0N/NbT6iNSNQjjVMMYjZQIhKckZVa3RCJ3Xi9csWrenO4q8TPSQVy1Hvlr24/4VmMirhkxnR8L6VgwjQJLnFa6mYGU8ZHbIAdSxWL0QST+blT98wqfTdKtC1F7lz9PTFhsTHjOLSdMaOhWfZm4n9eJ6PoOpgIlWaEii8WRZl0KXFnv7t9oZGTHFvCuBb2VpcPmWacbEIlG4K//PIqaV5Ufa/qP1xWard5HEU4gVM4Bx+uoAb3UIcGcBjBM7zCm5M6L86787FoLTj5zDH8gfP5A7iljyY=</latexit><latexit sha1_base64="4FuzAc7bz3x7RjoD5RQgDT19KiE=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6EmKXjxWsB/QhrLZTtqlm03YnQil9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5YSqFIc/7dgpr6xubW8Xt0s7u3v5B+fCoaZJMc2zwRCa6HTKDUihskCCJ7VQji0OJrXB0N/NbT6iNSNQjjVMMYjZQIhKckZVa3RCJ3Xi9csWrenO4q8TPSQVy1Hvlr24/4VmMirhkxnR8L6VgwjQJLnFa6mYGU8ZHbIAdSxWL0QST+blT98wqfTdKtC1F7lz9PTFhsTHjOLSdMaOhWfZm4n9eJ6PoOpgIlWaEii8WRZl0KXFnv7t9oZGTHFvCuBb2VpcPmWacbEIlG4K//PIqaV5Ufa/qP1xWard5HEU4gVM4Bx+uoAb3UIcGcBjBM7zCm5M6L86787FoLTj5zDH8gfP5A7iljyY=</latexit><latexit sha1_base64="4FuzAc7bz3x7RjoD5RQgDT19KiE=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6EmKXjxWsB/QhrLZTtqlm03YnQil9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5YSqFIc/7dgpr6xubW8Xt0s7u3v5B+fCoaZJMc2zwRCa6HTKDUihskCCJ7VQji0OJrXB0N/NbT6iNSNQjjVMMYjZQIhKckZVa3RCJ3Xi9csWrenO4q8TPSQVy1Hvlr24/4VmMirhkxnR8L6VgwjQJLnFa6mYGU8ZHbIAdSxWL0QST+blT98wqfTdKtC1F7lz9PTFhsTHjOLSdMaOhWfZm4n9eJ6PoOpgIlWaEii8WRZl0KXFnv7t9oZGTHFvCuBb2VpcPmWacbEIlG4K//PIqaV5Ufa/qP1xWard5HEU4gVM4Bx+uoAb3UIcGcBjBM7zCm5M6L86787FoLTj5zDH8gfP5A7iljyY=</latexit>

� < 0<latexit sha1_base64="3ASQuhTVsnrPuyrinPf2HkCciQs=">AAAB7nicbVA9SwNBEJ2LXzF+RS1tDoNgFe5E0MIiaGMZwXxAcoS9zVyyZG/v2J0TQsiPsLFQxNbfY+e/cZNcoYkPBh7vzTAzL0ylMOR5305hbX1jc6u4XdrZ3ds/KB8eNU2SaY4NnshEt0NmUAqFDRIksZ1qZHEosRWO7mZ+6wm1EYl6pHGKQcwGSkSCM7JSqxsisRuvV654VW8Od5X4OalAjnqv/NXtJzyLURGXzJiO76UUTJgmwSVOS93MYMr4iA2wY6liMZpgMj936p5Zpe9GibalyJ2rvycmLDZmHIe2M2Y0NMveTPzP62QUXQcTodKMUPHFoiiTLiXu7He3LzRykmNLGNfC3uryIdOMk02oZEPwl19eJc2Lqu9V/YfLSu02j6MIJ3AK5+DDFdTgHurQAA4jeIZXeHNS58V5dz4WrQUnnzmGP3A+fwC1m48k</latexit><latexit sha1_base64="3ASQuhTVsnrPuyrinPf2HkCciQs=">AAAB7nicbVA9SwNBEJ2LXzF+RS1tDoNgFe5E0MIiaGMZwXxAcoS9zVyyZG/v2J0TQsiPsLFQxNbfY+e/cZNcoYkPBh7vzTAzL0ylMOR5305hbX1jc6u4XdrZ3ds/KB8eNU2SaY4NnshEt0NmUAqFDRIksZ1qZHEosRWO7mZ+6wm1EYl6pHGKQcwGSkSCM7JSqxsisRuvV654VW8Od5X4OalAjnqv/NXtJzyLURGXzJiO76UUTJgmwSVOS93MYMr4iA2wY6liMZpgMj936p5Zpe9GibalyJ2rvycmLDZmHIe2M2Y0NMveTPzP62QUXQcTodKMUPHFoiiTLiXu7He3LzRykmNLGNfC3uryIdOMk02oZEPwl19eJc2Lqu9V/YfLSu02j6MIJ3AK5+DDFdTgHurQAA4jeIZXeHNS58V5dz4WrQUnnzmGP3A+fwC1m48k</latexit><latexit sha1_base64="3ASQuhTVsnrPuyrinPf2HkCciQs=">AAAB7nicbVA9SwNBEJ2LXzF+RS1tDoNgFe5E0MIiaGMZwXxAcoS9zVyyZG/v2J0TQsiPsLFQxNbfY+e/cZNcoYkPBh7vzTAzL0ylMOR5305hbX1jc6u4XdrZ3ds/KB8eNU2SaY4NnshEt0NmUAqFDRIksZ1qZHEosRWO7mZ+6wm1EYl6pHGKQcwGSkSCM7JSqxsisRuvV654VW8Od5X4OalAjnqv/NXtJzyLURGXzJiO76UUTJgmwSVOS93MYMr4iA2wY6liMZpgMj936p5Zpe9GibalyJ2rvycmLDZmHIe2M2Y0NMveTPzP62QUXQcTodKMUPHFoiiTLiXu7He3LzRykmNLGNfC3uryIdOMk02oZEPwl19eJc2Lqu9V/YfLSu02j6MIJ3AK5+DDFdTgHurQAA4jeIZXeHNS58V5dz4WrQUnnzmGP3A+fwC1m48k</latexit><latexit sha1_base64="3ASQuhTVsnrPuyrinPf2HkCciQs=">AAAB7nicbVA9SwNBEJ2LXzF+RS1tDoNgFe5E0MIiaGMZwXxAcoS9zVyyZG/v2J0TQsiPsLFQxNbfY+e/cZNcoYkPBh7vzTAzL0ylMOR5305hbX1jc6u4XdrZ3ds/KB8eNU2SaY4NnshEt0NmUAqFDRIksZ1qZHEosRWO7mZ+6wm1EYl6pHGKQcwGSkSCM7JSqxsisRuvV654VW8Od5X4OalAjnqv/NXtJzyLURGXzJiO76UUTJgmwSVOS93MYMr4iA2wY6liMZpgMj936p5Zpe9GibalyJ2rvycmLDZmHIe2M2Y0NMveTPzP62QUXQcTodKMUPHFoiiTLiXu7He3LzRykmNLGNfC3uryIdOMk02oZEPwl19eJc2Lqu9V/YfLSu02j6MIJ3AK5+DDFdTgHurQAA4jeIZXeHNS58V5dz4WrQUnnzmGP3A+fwC1m48k</latexit>

remarks

- continuous actions

- for strategic complements ( ) and substitutes ( )

- can be used to approximate complex non-linear payoffs

- widely adopted in literature [Jackson15,Bramoullé16]



ui = biai �1

2a2i + �ai

X

j2N (i)


/35

Network games with linear-quadratic payoffs

23Jackson and Zezou, “Games on networks,” Handbook of Game Theory with Economic Applications, 2015. Bramoullé and Kranton, “Games played on networks,” The Oxford Handbook of the Economics of Networks, 2016.

� > 0<latexit sha1_base64="4FuzAc7bz3x7RjoD5RQgDT19KiE=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6EmKXjxWsB/QhrLZTtqlm03YnQil9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5YSqFIc/7dgpr6xubW8Xt0s7u3v5B+fCoaZJMc2zwRCa6HTKDUihskCCJ7VQji0OJrXB0N/NbT6iNSNQjjVMMYjZQIhKckZVa3RCJ3Xi9csWrenO4q8TPSQVy1Hvlr24/4VmMirhkxnR8L6VgwjQJLnFa6mYGU8ZHbIAdSxWL0QST+blT98wqfTdKtC1F7lz9PTFhsTHjOLSdMaOhWfZm4n9eJ6PoOpgIlWaEii8WRZl0KXFnv7t9oZGTHFvCuBb2VpcPmWacbEIlG4K//PIqaV5Ufa/qP1xWard5HEU4gVM4Bx+uoAb3UIcGcBjBM7zCm5M6L86787FoLTj5zDH8gfP5A7iljyY=</latexit><latexit sha1_base64="4FuzAc7bz3x7RjoD5RQgDT19KiE=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6EmKXjxWsB/QhrLZTtqlm03YnQil9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5YSqFIc/7dgpr6xubW8Xt0s7u3v5B+fCoaZJMc2zwRCa6HTKDUihskCCJ7VQji0OJrXB0N/NbT6iNSNQjjVMMYjZQIhKckZVa3RCJ3Xi9csWrenO4q8TPSQVy1Hvlr24/4VmMirhkxnR8L6VgwjQJLnFa6mYGU8ZHbIAdSxWL0QST+blT98wqfTdKtC1F7lz9PTFhsTHjOLSdMaOhWfZm4n9eJ6PoOpgIlWaEii8WRZl0KXFnv7t9oZGTHFvCuBb2VpcPmWacbEIlG4K//PIqaV5Ufa/qP1xWard5HEU4gVM4Bx+uoAb3UIcGcBjBM7zCm5M6L86787FoLTj5zDH8gfP5A7iljyY=</latexit><latexit sha1_base64="4FuzAc7bz3x7RjoD5RQgDT19KiE=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6EmKXjxWsB/QhrLZTtqlm03YnQil9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5YSqFIc/7dgpr6xubW8Xt0s7u3v5B+fCoaZJMc2zwRCa6HTKDUihskCCJ7VQji0OJrXB0N/NbT6iNSNQjjVMMYjZQIhKckZVa3RCJ3Xi9csWrenO4q8TPSQVy1Hvlr24/4VmMirhkxnR8L6VgwjQJLnFa6mYGU8ZHbIAdSxWL0QST+blT98wqfTdKtC1F7lz9PTFhsTHjOLSdMaOhWfZm4n9eJ6PoOpgIlWaEii8WRZl0KXFnv7t9oZGTHFvCuBb2VpcPmWacbEIlG4K//PIqaV5Ufa/qP1xWard5HEU4gVM4Bx+uoAb3UIcGcBjBM7zCm5M6L86787FoLTj5zDH8gfP5A7iljyY=</latexit><latexit sha1_base64="4FuzAc7bz3x7RjoD5RQgDT19KiE=">AAAB7nicbVBNS8NAEJ3Ur1q/qh69BIvgqSQi6EmKXjxWsB/QhrLZTtqlm03YnQil9Ed48aCIV3+PN/+N2zYHbX0w8Hhvhpl5YSqFIc/7dgpr6xubW8Xt0s7u3v5B+fCoaZJMc2zwRCa6HTKDUihskCCJ7VQji0OJrXB0N/NbT6iNSNQjjVMMYjZQIhKckZVa3RCJ3Xi9csWrenO4q8TPSQVy1Hvlr24/4VmMirhkxnR8L6VgwjQJLnFa6mYGU8ZHbIAdSxWL0QST+blT98wqfTdKtC1F7lz9PTFhsTHjOLSdMaOhWfZm4n9eJ6PoOpgIlWaEii8WRZl0KXFnv7t9oZGTHFvCuBb2VpcPmWacbEIlG4K//PIqaV5Ufa/qP1xWard5HEU4gVM4Bx+uoAb3UIcGcBjBM7zCm5M6L86787FoLTj5zDH8gfP5A7iljyY=</latexit>

� < 0<latexit sha1_base64="3ASQuhTVsnrPuyrinPf2HkCciQs=">AAAB7nicbVA9SwNBEJ2LXzF+RS1tDoNgFe5E0MIiaGMZwXxAcoS9zVyyZG/v2J0TQsiPsLFQxNbfY+e/cZNcoYkPBh7vzTAzL0ylMOR5305hbX1jc6u4XdrZ3ds/KB8eNU2SaY4NnshEt0NmUAqFDRIksZ1qZHEosRWO7mZ+6wm1EYl6pHGKQcwGSkSCM7JSqxsisRuvV654VW8Od5X4OalAjnqv/NXtJzyLURGXzJiO76UUTJgmwSVOS93MYMr4iA2wY6liMZpgMj936p5Zpe9GibalyJ2rvycmLDZmHIe2M2Y0NMveTPzP62QUXQcTodKMUPHFoiiTLiXu7He3LzRykmNLGNfC3uryIdOMk02oZEPwl19eJc2Lqu9V/YfLSu02j6MIJ3AK5+DDFdTgHurQAA4jeIZXeHNS58V5dz4WrQUnnzmGP3A+fwC1m48k</latexit><latexit sha1_base64="3ASQuhTVsnrPuyrinPf2HkCciQs=">AAAB7nicbVA9SwNBEJ2LXzF+RS1tDoNgFe5E0MIiaGMZwXxAcoS9zVyyZG/v2J0TQsiPsLFQxNbfY+e/cZNcoYkPBh7vzTAzL0ylMOR5305hbX1jc6u4XdrZ3ds/KB8eNU2SaY4NnshEt0NmUAqFDRIksZ1qZHEosRWO7mZ+6wm1EYl6pHGKQcwGSkSCM7JSqxsisRuvV654VW8Od5X4OalAjnqv/NXtJzyLURGXzJiO76UUTJgmwSVOS93MYMr4iA2wY6liMZpgMj936p5Zpe9GibalyJ2rvycmLDZmHIe2M2Y0NMveTPzP62QUXQcTodKMUPHFoiiTLiXu7He3LzRykmNLGNfC3uryIdOMk02oZEPwl19eJc2Lqu9V/YfLSu02j6MIJ3AK5+DDFdTgHurQAA4jeIZXeHNS58V5dz4WrQUnnzmGP3A+fwC1m48k</latexit><latexit sha1_base64="3ASQuhTVsnrPuyrinPf2HkCciQs=">AAAB7nicbVA9SwNBEJ2LXzF+RS1tDoNgFe5E0MIiaGMZwXxAcoS9zVyyZG/v2J0TQsiPsLFQxNbfY+e/cZNcoYkPBh7vzTAzL0ylMOR5305hbX1jc6u4XdrZ3ds/KB8eNU2SaY4NnshEt0NmUAqFDRIksZ1qZHEosRWO7mZ+6wm1EYl6pHGKQcwGSkSCM7JSqxsisRuvV654VW8Od5X4OalAjnqv/NXtJzyLURGXzJiO76UUTJgmwSVOS93MYMr4iA2wY6liMZpgMj936p5Zpe9GibalyJ2rvycmLDZmHIe2M2Y0NMveTPzP62QUXQcTodKMUPHFoiiTLiXu7He3LzRykmNLGNfC3uryIdOMk02oZEPwl19eJc2Lqu9V/YfLSu02j6MIJ3AK5+DDFdTgHurQAA4jeIZXeHNS58V5dz4WrQUnnzmGP3A+fwC1m48k</latexit><latexit sha1_base64="3ASQuhTVsnrPuyrinPf2HkCciQs=">AAAB7nicbVA9SwNBEJ2LXzF+RS1tDoNgFe5E0MIiaGMZwXxAcoS9zVyyZG/v2J0TQsiPsLFQxNbfY+e/cZNcoYkPBh7vzTAzL0ylMOR5305hbX1jc6u4XdrZ3ds/KB8eNU2SaY4NnshEt0NmUAqFDRIksZ1qZHEosRWO7mZ+6wm1EYl6pHGKQcwGSkSCM7JSqxsisRuvV654VW8Od5X4OalAjnqv/NXtJzyLURGXzJiO76UUTJgmwSVOS93MYMr4iA2wY6liMZpgMj936p5Zpe9GibalyJ2rvycmLDZmHIe2M2Y0NMveTPzP62QUXQcTodKMUPHFoiiTLiXu7He3LzRykmNLGNfC3uryIdOMk02oZEPwl19eJc2Lqu9V/YfLSu02j6MIJ3AK5+DDFdTgHurQAA4jeIZXeHNS58V5dz4WrQUnnzmGP3A+fwC1m48k</latexit>

remarks

- continuous actions

- for strategic complements ( ) and substitutes ( )

- can be used to approximate complex non-linear payoffs

- widely adopted in literature [Jackson15,Bramoullé16]



ui = biai �1

2a2i + �ai

X

j2N (i)


examples - education: action is educational effort, utility is achievement

- collaboration: action is joint R&D activities, utility is firm profit

- urban dynamics: action is mobility behaviour, utility is convenience/satisfaction

/35

Network games with linear-quadratic payoffs• Pure-strategy Nash equilibrium (PSNE)

24

ui = biai �1

2a2i + �ai

X

j2VGijaj

/35


24

@ui

@ai= bi � ai + �(Ga)iui = biai �

1

2a2i + �ai

X

j2VGijaj

a = (I� �G)�1 b

/35


24

@ui


1

2a2i + �ai

X

j2VGijaj

a = (I� �G)�1 b

Ballester et al., “Who’s who in networks. Wanted: The key player,” Econometrica, 2006.

assumption: spectral radius is smaller than 1

- guarantees matrix inversion

- ensures uniqueness and stability of equilibrium action [Ballester06]

⇢(�G)<latexit sha1_base64="QwOy1LrktTiQ+Q4HlAxixf/fWkU=">AAACAHicbVBNS8NAEN3Ur1q/oh48eFksQr2URAQ9Fj3osYL9gKaUzXbTLt1kw+5EKCEX/4oXD4p49Wd489+4aXPQ1gcDj/dmmJnnx4JrcJxvq7Syura+Ud6sbG3v7O7Z+wdtLRNFWYtKIVXXJ5oJHrEWcBCsGytGQl+wjj+5yf3OI1Oay+gBpjHrh2QU8YBTAkYa2EeeGktc83wGBHshgbEfpLfZ2cCuOnVnBrxM3IJUUYHmwP7yhpImIYuACqJ1z3Vi6KdEAaeCZRUv0SwmdEJGrGdoREKm++nsgQyfGmWIA6lMRYBn6u+JlIRaT0PfdOYn6kUvF//zegkEV/2UR3ECLKLzRUEiMEicp4GHXDEKYmoIoYqbWzEdE0UomMwqJgR38eVl0j6vu07dvb+oNq6LOMroGJ2gGnLRJWqgO9RELURRhp7RK3qznqwX6936mLeWrGLmEP2B9fkDqjKVzA==</latexit><latexit sha1_base64="QwOy1LrktTiQ+Q4HlAxixf/fWkU=">AAACAHicbVBNS8NAEN3Ur1q/oh48eFksQr2URAQ9Fj3osYL9gKaUzXbTLt1kw+5EKCEX/4oXD4p49Wd489+4aXPQ1gcDj/dmmJnnx4JrcJxvq7Syura+Ud6sbG3v7O7Z+wdtLRNFWYtKIVXXJ5oJHrEWcBCsGytGQl+wjj+5yf3OI1Oay+gBpjHrh2QU8YBTAkYa2EeeGktc83wGBHshgbEfpLfZ2cCuOnVnBrxM3IJUUYHmwP7yhpImIYuACqJ1z3Vi6KdEAaeCZRUv0SwmdEJGrGdoREKm++nsgQyfGmWIA6lMRYBn6u+JlIRaT0PfdOYn6kUvF//zegkEV/2UR3ECLKLzRUEiMEicp4GHXDEKYmoIoYqbWzEdE0UomMwqJgR38eVl0j6vu07dvb+oNq6LOMroGJ2gGnLRJWqgO9RELURRhp7RK3qznqwX6936mLeWrGLmEP2B9fkDqjKVzA==</latexit><latexit sha1_base64="QwOy1LrktTiQ+Q4HlAxixf/fWkU=">AAACAHicbVBNS8NAEN3Ur1q/oh48eFksQr2URAQ9Fj3osYL9gKaUzXbTLt1kw+5EKCEX/4oXD4p49Wd489+4aXPQ1gcDj/dmmJnnx4JrcJxvq7Syura+Ud6sbG3v7O7Z+wdtLRNFWYtKIVXXJ5oJHrEWcBCsGytGQl+wjj+5yf3OI1Oay+gBpjHrh2QU8YBTAkYa2EeeGktc83wGBHshgbEfpLfZ2cCuOnVnBrxM3IJUUYHmwP7yhpImIYuACqJ1z3Vi6KdEAaeCZRUv0SwmdEJGrGdoREKm++nsgQyfGmWIA6lMRYBn6u+JlIRaT0PfdOYn6kUvF//zegkEV/2UR3ECLKLzRUEiMEicp4GHXDEKYmoIoYqbWzEdE0UomMwqJgR38eVl0j6vu07dvb+oNq6LOMroGJ2gGnLRJWqgO9RELURRhp7RK3qznqwX6936mLeWrGLmEP2B9fkDqjKVzA==</latexit><latexit sha1_base64="QwOy1LrktTiQ+Q4HlAxixf/fWkU=">AAACAHicbVBNS8NAEN3Ur1q/oh48eFksQr2URAQ9Fj3osYL9gKaUzXbTLt1kw+5EKCEX/4oXD4p49Wd489+4aXPQ1gcDj/dmmJnnx4JrcJxvq7Syura+Ud6sbG3v7O7Z+wdtLRNFWYtKIVXXJ5oJHrEWcBCsGytGQl+wjj+5yf3OI1Oay+gBpjHrh2QU8YBTAkYa2EeeGktc83wGBHshgbEfpLfZ2cCuOnVnBrxM3IJUUYHmwP7yhpImIYuACqJ1z3Vi6KdEAaeCZRUv0SwmdEJGrGdoREKm++nsgQyfGmWIA6lMRYBn6u+JlIRaT0PfdOYn6kUvF//zegkEV/2UR3ECLKLzRUEiMEicp4GHXDEKYmoIoYqbWzEdE0UomMwqJgR38eVl0j6vu07dvb+oNq6LOMroGJ2gGnLRJWqgO9RELURRhp7RK3qznqwX6936mLeWrGLmEP2B9fkDqjKVzA==</latexit>

/35


24

@ui


1

2a2i + �ai

X

j2VGijaj

a = (I� �G)�1 b


properties

- equilibrium related to Katz-Bonacich centrality

- payoff interdependency spreads indirectly through network

=+1X

p=0

�pGp b<latexit sha1_base64="HtPPVYSPBScOkKqgC6GVwhVIDdI=">AAACHnicbVBNSwMxEM3W7/pV9eglWARBKLui6KVQ9KBHBauF7rZk06yGZrMhmRXKsv4RL/4VLx4UETzpvzGtK2j1QeDlvRlm5oVKcAOu++GUJianpmdm58rzC4tLy5WV1QuTpJqyJk1EolshMUxwyZrAQbCW0ozEoWCXYf9o6F/eMG14Is9hoFgQkyvJI04JWKlb2av7Jo27maq7eSfb9rmMYJBjP2RAOgr7MYHrMMqO8466/f6EebdSdWvuCPgv8QpSRQVOu5U3v5fQNGYSqCDGtD1XQZARDZwKlpf91DBFaJ9csbalksTMBNnovBxvWqWHo0TbJwGP1J8dGYmNGcShrRxuaMa9ofif104hOggyLlUKTNKvQVEqMCR4mBXucc0oiIElhGpud8X0mmhCwSZatiF44yf/JRc7Nc+teWe71cZhEccsWkcbaAt5aB810Ak6RU1E0R16QE/o2bl3Hp0X5/WrtOQUPWvoF5z3T57Yo20=</latexit><latexit sha1_base64="HtPPVYSPBScOkKqgC6GVwhVIDdI=">AAACHnicbVBNSwMxEM3W7/pV9eglWARBKLui6KVQ9KBHBauF7rZk06yGZrMhmRXKsv4RL/4VLx4UETzpvzGtK2j1QeDlvRlm5oVKcAOu++GUJianpmdm58rzC4tLy5WV1QuTpJqyJk1EolshMUxwyZrAQbCW0ozEoWCXYf9o6F/eMG14Is9hoFgQkyvJI04JWKlb2av7Jo27maq7eSfb9rmMYJBjP2RAOgr7MYHrMMqO8466/f6EebdSdWvuCPgv8QpSRQVOu5U3v5fQNGYSqCDGtD1XQZARDZwKlpf91DBFaJ9csbalksTMBNnovBxvWqWHo0TbJwGP1J8dGYmNGcShrRxuaMa9ofif104hOggyLlUKTNKvQVEqMCR4mBXucc0oiIElhGpud8X0mmhCwSZatiF44yf/JRc7Nc+teWe71cZhEccsWkcbaAt5aB810Ak6RU1E0R16QE/o2bl3Hp0X5/WrtOQUPWvoF5z3T57Yo20=</latexit><latexit sha1_base64="HtPPVYSPBScOkKqgC6GVwhVIDdI=">AAACHnicbVBNSwMxEM3W7/pV9eglWARBKLui6KVQ9KBHBauF7rZk06yGZrMhmRXKsv4RL/4VLx4UETzpvzGtK2j1QeDlvRlm5oVKcAOu++GUJianpmdm58rzC4tLy5WV1QuTpJqyJk1EolshMUxwyZrAQbCW0ozEoWCXYf9o6F/eMG14Is9hoFgQkyvJI04JWKlb2av7Jo27maq7eSfb9rmMYJBjP2RAOgr7MYHrMMqO8466/f6EebdSdWvuCPgv8QpSRQVOu5U3v5fQNGYSqCDGtD1XQZARDZwKlpf91DBFaJ9csbalksTMBNnovBxvWqWHo0TbJwGP1J8dGYmNGcShrRxuaMa9ofif104hOggyLlUKTNKvQVEqMCR4mBXucc0oiIElhGpud8X0mmhCwSZatiF44yf/JRc7Nc+teWe71cZhEccsWkcbaAt5aB810Ak6RU1E0R16QE/o2bl3Hp0X5/WrtOQUPWvoF5z3T57Yo20=</latexit><latexit sha1_base64="HtPPVYSPBScOkKqgC6GVwhVIDdI=">AAACHnicbVBNSwMxEM3W7/pV9eglWARBKLui6KVQ9KBHBauF7rZk06yGZrMhmRXKsv4RL/4VLx4UETzpvzGtK2j1QeDlvRlm5oVKcAOu++GUJianpmdm58rzC4tLy5WV1QuTpJqyJk1EolshMUxwyZrAQbCW0ozEoWCXYf9o6F/eMG14Is9hoFgQkyvJI04JWKlb2av7Jo27maq7eSfb9rmMYJBjP2RAOgr7MYHrMMqO8466/f6EebdSdWvuCPgv8QpSRQVOu5U3v5fQNGYSqCDGtD1XQZARDZwKlpf91DBFaJ9csbalksTMBNnovBxvWqWHo0TbJwGP1J8dGYmNGcShrRxuaMa9ofif104hOggyLlUKTNKvQVEqMCR4mBXucc0oiIElhGpud8X0mmhCwSZatiF44yf/JRc7Nc+teWe71cZhEccsWkcbaAt5aB810Ak6RU1E0R16QE/o2bl3Hp0X5/WrtOQUPWvoF5z3T57Yo20=</latexit>





/35


24

@ui


1

2a2i + �ai

X

j2VGijaj

a = (I� �G)�1 b


properties

- equilibrium related to Katz-Bonacich centrality

- payoff interdependency spreads indirectly through network

- action is filtered version of marginal benefit on graph

G=�⇤�T

======== �(I� �⇤)�1�Tb<latexit sha1_base64="5jV2fNUQHD+3WJd+cVijRq43Q58=">AAACsnicbVHBbtNAEF2bFtpSIMCp6mVFhFQOjWxUCS6ICg60EodWatqKOI3G63Gy6nrX7I6hkeWv4mv4Az6DdZpKTZORVvv0Zt7M6E1aKukoiv4G4aO19cdPNja3nm4/e/6i8/LVuTOVFdgXRhl7mYJDJTX2SZLCy9IiFKnCi/T6a5u/+IXWSaPPaFrisICxlrkUQJ4adf4kN8roMf6sQPE6KYAmaV5/a/gnnqRGZW5a+K9OxEQ2i8x3PySDZrns6mwFyffueh83+0mKBCu7vbuq9+OVPfmdPm1GnW7Ui2bBl0E8B102j5NR51+SGVEVqEkocG4QRyUNa7AkhcJmK6kcliCuYYwDDzUU6Ib1zNyGv/VMxnNj/dPEZ+x9RQ2Fa1f1le2G7mGuJVflBhXlH4e11GVFqMXtoLxSnAxvL8UzaVGQmnoAwkq/KxcTsCDI33NhCt4QWGt+u9aa+KERy+D8fS+OevHpQffwy9ykDbbL3rA9FrMP7JAdsRPWZyLYCT4HR8FxeBD+CCEUt6VhMNe8ZgsRqv9Omtox</latexit><latexit sha1_base64="5jV2fNUQHD+3WJd+cVijRq43Q58=">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</latexit><latexit sha1_base64="5jV2fNUQHD+3WJd+cVijRq43Q58=">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</latexit><latexit sha1_base64="5jV2fNUQHD+3WJd+cVijRq43Q58=">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</latexit>





/35

Learning quadratic games on networks

25

a = (I� �G)�1 b (I� �G)a = bNash equilibrium

/35


25


consider K games B = [b(1),b(2), · · · ,b(k)] 2 RN⇥K

A = [a(1),a(2), · · · ,a(K)] 2 RN⇥K

marginal

action

/35


25



A = [a(1),a(2), · · · ,a(K)] 2 RN⇥K

marginal

action

joint learning of graph and marginal

✓2R(B)<latexit sha1_base64="lRd//gsi6Jz0y+ytuY+hW4qyYaU=">AAAB/3icbVDLSsNAFJ34rPUVFdy4GSxC3ZSkCLosdeOyin1AE8JkOmmHTh7M3AglduGvuHGhiFt/w51/46TNQlsPDBzOuZd75viJ4Aos69tYWV1b39gsbZW3d3b39s2Dw46KU0lZm8Yilj2fKCZ4xNrAQbBeIhkJfcG6/vg697sPTCoeR/cwSZgbkmHEA04JaMkzjx0YMSBeHd9VnZDAyA+y5vTcMytWzZoBLxO7IBVUoOWZX84gpmnIIqCCKNW3rQTcjEjgVLBp2UkVSwgdkyHraxqRkCk3m+Wf4jOtDHAQS/0iwDP190ZGQqUmoa8n84hq0cvF/7x+CsGVm/EoSYFFdH4oSAWGGOdl4AGXjIKYaEKo5DorpiMiCQVdWVmXYC9+eZl06jXbqtm3F5VGs6ijhE7QKaoiG12iBrpBLdRGFD2iZ/SK3own48V4Nz7moytGsXOE/sD4/AHZDJVV</latexit><latexit sha1_base64="lRd//gsi6Jz0y+ytuY+hW4qyYaU=">AAAB/3icbVDLSsNAFJ34rPUVFdy4GSxC3ZSkCLosdeOyin1AE8JkOmmHTh7M3AglduGvuHGhiFt/w51/46TNQlsPDBzOuZd75viJ4Aos69tYWV1b39gsbZW3d3b39s2Dw46KU0lZm8Yilj2fKCZ4xNrAQbBeIhkJfcG6/vg697sPTCoeR/cwSZgbkmHEA04JaMkzjx0YMSBeHd9VnZDAyA+y5vTcMytWzZoBLxO7IBVUoOWZX84gpmnIIqCCKNW3rQTcjEjgVLBp2UkVSwgdkyHraxqRkCk3m+Wf4jOtDHAQS/0iwDP190ZGQqUmoa8n84hq0cvF/7x+CsGVm/EoSYFFdH4oSAWGGOdl4AGXjIKYaEKo5DorpiMiCQVdWVmXYC9+eZl06jXbqtm3F5VGs6ijhE7QKaoiG12iBrpBLdRGFD2iZ/SK3own48V4Nz7moytGsXOE/sD4/AHZDJVV</latexit><latexit sha1_base64="lRd//gsi6Jz0y+ytuY+hW4qyYaU=">AAAB/3icbVDLSsNAFJ34rPUVFdy4GSxC3ZSkCLosdeOyin1AE8JkOmmHTh7M3AglduGvuHGhiFt/w51/46TNQlsPDBzOuZd75viJ4Aos69tYWV1b39gsbZW3d3b39s2Dw46KU0lZm8Yilj2fKCZ4xNrAQbBeIhkJfcG6/vg697sPTCoeR/cwSZgbkmHEA04JaMkzjx0YMSBeHd9VnZDAyA+y5vTcMytWzZoBLxO7IBVUoOWZX84gpmnIIqCCKNW3rQTcjEjgVLBp2UkVSwgdkyHraxqRkCk3m+Wf4jOtDHAQS/0iwDP190ZGQqUmoa8n84hq0cvF/7x+CsGVm/EoSYFFdH4oSAWGGOdl4AGXjIKYaEKo5DorpiMiCQVdWVmXYC9+eZl06jXbqtm3F5VGs6ijhE7QKaoiG12iBrpBLdRGFD2iZ/SK3own48V4Nz7moytGsXOE/sD4/AHZDJVV</latexit><latexit sha1_base64="lRd//gsi6Jz0y+ytuY+hW4qyYaU=">AAAB/3icbVDLSsNAFJ34rPUVFdy4GSxC3ZSkCLosdeOyin1AE8JkOmmHTh7M3AglduGvuHGhiFt/w51/46TNQlsPDBzOuZd75viJ4Aos69tYWV1b39gsbZW3d3b39s2Dw46KU0lZm8Yilj2fKCZ4xNrAQbBeIhkJfcG6/vg697sPTCoeR/cwSZgbkmHEA04JaMkzjx0YMSBeHd9VnZDAyA+y5vTcMytWzZoBLxO7IBVUoOWZX84gpmnIIqCCKNW3rQTcjEjgVLBp2UkVSwgdkyHraxqRkCk3m+Wf4jOtDHAQS/0iwDP190ZGQqUmoa8n84hq0cvF/7x+CsGVm/EoSYFFdH4oSAWGGOdl4AGXjIKYaEKo5DorpiMiCQVdWVmXYC9+eZl06jXbqtm3F5VGs6ijhE7QKaoiG12iBrpBLdRGFD2iZ/SK3own48V4Nz7moytGsXOE/sD4/AHZDJVV</latexit>

/35


25



A = [a(1),a(2), · · · ,a(K)] 2 RN⇥K

marginal

action



/35


25



A = [a(1),a(2), · · · ,a(K)] 2 RN⇥K

marginal

action



Dong et al., “Learning Laplacian matrix in smooth graph signal representations,” IEEE Transactions on Signal Processing, 2016.

/35


25



A = [a(1),a(2), · · · ,a(K)] 2 RN⇥K

marginal

action



Dong et al., “Learning Laplacian matrix in smooth graph signal representations,” IEEE Transactions on Signal Processing, 2016.

/35

Learning with homophilous marginal benefits• Phenomenon of homophily in social networks [McPherson01]

26McPherson et al., “Birds of a feather: Homophily in social networks,” Annual Review of Sociology, 2001.

/35


26

v1

v2v3 v4

v5v6v7v8

v9

b : V ! RN<latexit sha1_base64="kDxq3U7fchYNzkYE3pSvFx0b9Gc=">AAACGXicbZDLSsNAFIYn9VbrLerSzWARXJVEBMVV0Y0rqWIv0MQyM520QyeZMDNRSshruPFV3LhQxKWufBsnaRfa+sPAx3/OYc75ccyZ0o7zbZUWFpeWV8qrlbX1jc0te3unpUQiCW0SwYXsYKQoZxFtaqY57cSSohBz2saji7zevqdSMRHd6nFM/RANIhYwgrSxerbjhUgPcZDi7AwWTBBPWxn0JBsMNZJSPEx8jNOb7O6qZ1edmlMIzoM7hSqYqtGzP72+IElII004UqrrOrH2UyQ1I5xmFS9RNEZkhAa0azBCIVV+WlyWwQPj9GEgpHmRhoX7eyJFoVLjEJvOfEc1W8vN/2rdRAenfsqiONE0IpOPgoRDLWAeE+wzSYnmYwOISGZ2hWSIJCLahFkxIbizJ89D66jmOjX3+rhaP5/GUQZ7YB8cAhecgDq4BA3QBAQ8gmfwCt6sJ+vFerc+Jq0lazqzC/7I+voBfZWhNg==</latexit><latexit sha1_base64="kDxq3U7fchYNzkYE3pSvFx0b9Gc=">AAACGXicbZDLSsNAFIYn9VbrLerSzWARXJVEBMVV0Y0rqWIv0MQyM520QyeZMDNRSshruPFV3LhQxKWufBsnaRfa+sPAx3/OYc75ccyZ0o7zbZUWFpeWV8qrlbX1jc0te3unpUQiCW0SwYXsYKQoZxFtaqY57cSSohBz2saji7zevqdSMRHd6nFM/RANIhYwgrSxerbjhUgPcZDi7AwWTBBPWxn0JBsMNZJSPEx8jNOb7O6qZ1edmlMIzoM7hSqYqtGzP72+IElII004UqrrOrH2UyQ1I5xmFS9RNEZkhAa0azBCIVV+WlyWwQPj9GEgpHmRhoX7eyJFoVLjEJvOfEc1W8vN/2rdRAenfsqiONE0IpOPgoRDLWAeE+wzSYnmYwOISGZ2hWSIJCLahFkxIbizJ89D66jmOjX3+rhaP5/GUQZ7YB8cAhecgDq4BA3QBAQ8gmfwCt6sJ+vFerc+Jq0lazqzC/7I+voBfZWhNg==</latexit><latexit sha1_base64="kDxq3U7fchYNzkYE3pSvFx0b9Gc=">AAACGXicbZDLSsNAFIYn9VbrLerSzWARXJVEBMVV0Y0rqWIv0MQyM520QyeZMDNRSshruPFV3LhQxKWufBsnaRfa+sPAx3/OYc75ccyZ0o7zbZUWFpeWV8qrlbX1jc0te3unpUQiCW0SwYXsYKQoZxFtaqY57cSSohBz2saji7zevqdSMRHd6nFM/RANIhYwgrSxerbjhUgPcZDi7AwWTBBPWxn0JBsMNZJSPEx8jNOb7O6qZ1edmlMIzoM7hSqYqtGzP72+IElII004UqrrOrH2UyQ1I5xmFS9RNEZkhAa0azBCIVV+WlyWwQPj9GEgpHmRhoX7eyJFoVLjEJvOfEc1W8vN/2rdRAenfsqiONE0IpOPgoRDLWAeE+wzSYnmYwOISGZ2hWSIJCLahFkxIbizJ89D66jmOjX3+rhaP5/GUQZ7YB8cAhecgDq4BA3QBAQ8gmfwCt6sJ+vFerc+Jq0lazqzC/7I+voBfZWhNg==</latexit><latexit sha1_base64="kDxq3U7fchYNzkYE3pSvFx0b9Gc=">AAACGXicbZDLSsNAFIYn9VbrLerSzWARXJVEBMVV0Y0rqWIv0MQyM520QyeZMDNRSshruPFV3LhQxKWufBsnaRfa+sPAx3/OYc75ccyZ0o7zbZUWFpeWV8qrlbX1jc0te3unpUQiCW0SwYXsYKQoZxFtaqY57cSSohBz2saji7zevqdSMRHd6nFM/RANIhYwgrSxerbjhUgPcZDi7AwWTBBPWxn0JBsMNZJSPEx8jNOb7O6qZ1edmlMIzoM7hSqYqtGzP72+IElII004UqrrOrH2UyQ1I5xmFS9RNEZkhAa0azBCIVV+WlyWwQPj9GEgpHmRhoX7eyJFoVLjEJvOfEc1W8vN/2rdRAenfsqiONE0IpOPgoRDLWAeE+wzSYnmYwOISGZ2hWSIJCLahFkxIbizJ89D66jmOjX3+rhaP5/GUQZ7YB8cAhecgDq4BA3QBAQ8gmfwCt6sJ+vFerc+Jq0lazqzC/7I+voBfZWhNg==</latexit>

• Given homophily marginal benefits are smooth functions on graph

McPherson et al., “Birds of a feather: Homophily in social networks,” Annual Review of Sociology, 2001.

/35


26

v1

v2v3 v4

v5v6v7v8

v9

b : V ! RN<latexit sha1_base64="kDxq3U7fchYNzkYE3pSvFx0b9Gc=">AAACGXicbZDLSsNAFIYn9VbrLerSzWARXJVEBMVV0Y0rqWIv0MQyM520QyeZMDNRSshruPFV3LhQxKWufBsnaRfa+sPAx3/OYc75ccyZ0o7zbZUWFpeWV8qrlbX1jc0te3unpUQiCW0SwYXsYKQoZxFtaqY57cSSohBz2saji7zevqdSMRHd6nFM/RANIhYwgrSxerbjhUgPcZDi7AwWTBBPWxn0JBsMNZJSPEx8jNOb7O6qZ1edmlMIzoM7hSqYqtGzP72+IElII004UqrrOrH2UyQ1I5xmFS9RNEZkhAa0azBCIVV+WlyWwQPj9GEgpHmRhoX7eyJFoVLjEJvOfEc1W8vN/2rdRAenfsqiONE0IpOPgoRDLWAeE+wzSYnmYwOISGZ2hWSIJCLahFkxIbizJ89D66jmOjX3+rhaP5/GUQZ7YB8cAhecgDq4BA3QBAQ8gmfwCt6sJ+vFerc+Jq0lazqzC/7I+voBfZWhNg==</latexit><latexit sha1_base64="kDxq3U7fchYNzkYE3pSvFx0b9Gc=">AAACGXicbZDLSsNAFIYn9VbrLerSzWARXJVEBMVV0Y0rqWIv0MQyM520QyeZMDNRSshruPFV3LhQxKWufBsnaRfa+sPAx3/OYc75ccyZ0o7zbZUWFpeWV8qrlbX1jc0te3unpUQiCW0SwYXsYKQoZxFtaqY57cSSohBz2saji7zevqdSMRHd6nFM/RANIhYwgrSxerbjhUgPcZDi7AwWTBBPWxn0JBsMNZJSPEx8jNOb7O6qZ1edmlMIzoM7hSqYqtGzP72+IElII004UqrrOrH2UyQ1I5xmFS9RNEZkhAa0azBCIVV+WlyWwQPj9GEgpHmRhoX7eyJFoVLjEJvOfEc1W8vN/2rdRAenfsqiONE0IpOPgoRDLWAeE+wzSYnmYwOISGZ2hWSIJCLahFkxIbizJ89D66jmOjX3+rhaP5/GUQZ7YB8cAhecgDq4BA3QBAQ8gmfwCt6sJ+vFerc+Jq0lazqzC/7I+voBfZWhNg==</latexit><latexit sha1_base64="kDxq3U7fchYNzkYE3pSvFx0b9Gc=">AAACGXicbZDLSsNAFIYn9VbrLerSzWARXJVEBMVV0Y0rqWIv0MQyM520QyeZMDNRSshruPFV3LhQxKWufBsnaRfa+sPAx3/OYc75ccyZ0o7zbZUWFpeWV8qrlbX1jc0te3unpUQiCW0SwYXsYKQoZxFtaqY57cSSohBz2saji7zevqdSMRHd6nFM/RANIhYwgrSxerbjhUgPcZDi7AwWTBBPWxn0JBsMNZJSPEx8jNOb7O6qZ1edmlMIzoM7hSqYqtGzP72+IElII004UqrrOrH2UyQ1I5xmFS9RNEZkhAa0azBCIVV+WlyWwQPj9GEgpHmRhoX7eyJFoVLjEJvOfEc1W8vN/2rdRAenfsqiONE0IpOPgoRDLWAeE+wzSYnmYwOISGZ2hWSIJCLahFkxIbizJ89D66jmOjX3+rhaP5/GUQZ7YB8cAhecgDq4BA3QBAQ8gmfwCt6sJ+vFerc+Jq0lazqzC/7I+voBfZWhNg==</latexit><latexit sha1_base64="kDxq3U7fchYNzkYE3pSvFx0b9Gc=">AAACGXicbZDLSsNAFIYn9VbrLerSzWARXJVEBMVV0Y0rqWIv0MQyM520QyeZMDNRSshruPFV3LhQxKWufBsnaRfa+sPAx3/OYc75ccyZ0o7zbZUWFpeWV8qrlbX1jc0te3unpUQiCW0SwYXsYKQoZxFtaqY57cSSohBz2saji7zevqdSMRHd6nFM/RANIhYwgrSxerbjhUgPcZDi7AwWTBBPWxn0JBsMNZJSPEx8jNOb7O6qZ1edmlMIzoM7hSqYqtGzP72+IElII004UqrrOrH2UyQ1I5xmFS9RNEZkhAa0azBCIVV+WlyWwQPj9GEgpHmRhoX7eyJFoVLjEJvOfEc1W8vN/2rdRAenfsqiONE0IpOPgoRDLWAeE+wzSYnmYwOISGZ2hWSIJCLahFkxIbizJ89D66jmOjX3+rhaP5/GUQZ7YB8cAhecgDq4BA3QBAQ8gmfwCt6sJ+vFerc+Jq0lazqzC/7I+voBfZWhNg==</latexit>

• Given homophily marginal benefits are smooth functions on graph

bTLb =1

2

NX

i,j=1

Gij(bi � bj)2

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measure of “smoothness” [Zhou04]

McPherson et al., “Birds of a feather: Homophily in social networks,” Annual Review of Sociology, 2001.Zhou and Schölkopf, “A regularization framework for learning from graph data,” ICML Workshop, 2004.

/35

Learning with homophilous marginal benefits

27


/35


27


/35


27


remarks

- not jointly convex in G and B, but convex in subproblems of solving one fixing other

/35


27


remarks



- spectral radius impact learning performance

• approaching 0: action independent from graph structure

• approaching 1: action related to eigenvector centrality

/35


27


remarks



- spectral radius impact learning performance

• approaching 0: action independent from graph structure

• approaching 1: action related to eigenvector centrality

- other factors: number of games, noise level, network density

/35

Experiments on synthetic data• Random graphs with 20 nodes

- Erdős-Rényi (ER): edges created independently with certain probability

- Watts-Strogatz (WS): regular graph followed by random rewiring

- Barabási-Albert (BA): graph generated using preferential attachment

28

/35

Experiments on synthetic data• Random graphs with 20 nodes

- Erdős-Rényi (ER): edges created independently with certain probability

- Watts-Strogatz (WS): regular graph followed by random rewiring

- Barabási-Albert (BA): graph generated using preferential attachment

28

b ⇠ N (0,L† +1

10I)

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⇢(�G) 2 (0, 1)<latexit sha1_base64="0akU5DMsA1f39NZP/4WF0cwO6rI=">AAACCXicbVBNS8NAEJ3Ur1q/oh69LBahBSmJCHosetBjBfsBTSib7aZdutmE3Y1QQq9e/CtePCji1X/gzX/jpu1BWx8MPN6bYWZekHCmtON8W4WV1bX1jeJmaWt7Z3fP3j9oqTiVhDZJzGPZCbCinAna1Exz2kkkxVHAaTsYXed++4FKxWJxr8cJ9SM8ECxkBGsj9WzkyWFc8QKqMfIirIdBmN1MqshjAlWcU7fas8tOzZkCLRN3TsowR6Nnf3n9mKQRFZpwrFTXdRLtZ1hqRjidlLxU0QSTER7QrqECR1T52fSTCToxSh+FsTQlNJqqvycyHCk1jgLTmR+rFr1c/M/rpjq89DMmklRTQWaLwpQjHaM8FtRnkhLNx4ZgIpm5FZEhlphoE17JhOAuvrxMWmc116m5d+fl+tU8jiIcwTFUwIULqMMtNKAJBB7hGV7hzXqyXqx362PWWrDmM4fwB9bnD6SlmFc=</latexit><latexit sha1_base64="0akU5DMsA1f39NZP/4WF0cwO6rI=">AAACCXicbVBNS8NAEJ3Ur1q/oh69LBahBSmJCHosetBjBfsBTSib7aZdutmE3Y1QQq9e/CtePCji1X/gzX/jpu1BWx8MPN6bYWZekHCmtON8W4WV1bX1jeJmaWt7Z3fP3j9oqTiVhDZJzGPZCbCinAna1Exz2kkkxVHAaTsYXed++4FKxWJxr8cJ9SM8ECxkBGsj9WzkyWFc8QKqMfIirIdBmN1MqshjAlWcU7fas8tOzZkCLRN3TsowR6Nnf3n9mKQRFZpwrFTXdRLtZ1hqRjidlLxU0QSTER7QrqECR1T52fSTCToxSh+FsTQlNJqqvycyHCk1jgLTmR+rFr1c/M/rpjq89DMmklRTQWaLwpQjHaM8FtRnkhLNx4ZgIpm5FZEhlphoE17JhOAuvrxMWmc116m5d+fl+tU8jiIcwTFUwIULqMMtNKAJBB7hGV7hzXqyXqx362PWWrDmM4fwB9bnD6SlmFc=</latexit><latexit sha1_base64="0akU5DMsA1f39NZP/4WF0cwO6rI=">AAACCXicbVBNS8NAEJ3Ur1q/oh69LBahBSmJCHosetBjBfsBTSib7aZdutmE3Y1QQq9e/CtePCji1X/gzX/jpu1BWx8MPN6bYWZekHCmtON8W4WV1bX1jeJmaWt7Z3fP3j9oqTiVhDZJzGPZCbCinAna1Exz2kkkxVHAaTsYXed++4FKxWJxr8cJ9SM8ECxkBGsj9WzkyWFc8QKqMfIirIdBmN1MqshjAlWcU7fas8tOzZkCLRN3TsowR6Nnf3n9mKQRFZpwrFTXdRLtZ1hqRjidlLxU0QSTER7QrqECR1T52fSTCToxSh+FsTQlNJqqvycyHCk1jgLTmR+rFr1c/M/rpjq89DMmklRTQWaLwpQjHaM8FtRnkhLNx4ZgIpm5FZEhlphoE17JhOAuvrxMWmc116m5d+fl+tU8jiIcwTFUwIULqMMtNKAJBB7hGV7hzXqyXqx362PWWrDmM4fwB9bnD6SlmFc=</latexit><latexit sha1_base64="0akU5DMsA1f39NZP/4WF0cwO6rI=">AAACCXicbVBNS8NAEJ3Ur1q/oh69LBahBSmJCHosetBjBfsBTSib7aZdutmE3Y1QQq9e/CtePCji1X/gzX/jpu1BWx8MPN6bYWZekHCmtON8W4WV1bX1jeJmaWt7Z3fP3j9oqTiVhDZJzGPZCbCinAna1Exz2kkkxVHAaTsYXed++4FKxWJxr8cJ9SM8ECxkBGsj9WzkyWFc8QKqMfIirIdBmN1MqshjAlWcU7fas8tOzZkCLRN3TsowR6Nnf3n9mKQRFZpwrFTXdRLtZ1hqRjidlLxU0QSTER7QrqECR1T52fSTCToxSh+FsTQlNJqqvycyHCk1jgLTmR+rFr1c/M/rpjq89DMmklRTQWaLwpQjHaM8FtRnkhLNx4ZgIpm5FZEhlphoE17JhOAuvrxMWmc116m5d+fl+tU8jiIcwTFUwIULqMMtNKAJBB7hGV7hzXqyXqx362PWWrDmM4fwB9bnD6SlmFc=</latexit>

a = (I� �G)�1 b

• Compute so that

• Initialise marginal benefits for 50 games - homophilous:

• Generate equilibrium actions:

/35

Learning interaction network• Evaluate on area under the curve (AUC)

• Baselines: sample correlation and regularised graphical Lasso [Lake10]

29Lake and Tenenbaum, “Discovering structure by learning sparse graph,” Annual Cognitive Science Conference, 2010.

/35

Learning interaction network• Evaluate on area under the curve (AUC)

• Baselines: sample correlation and regularised graphical Lasso [Lake10]

29Lake and Tenenbaum, “Discovering structure by learning sparse graph,” Annual Cognitive Science Conference, 2010.

/35

Performance vs. network structure• Set

• Parameters in random graph models - ER: each node pair connected with probability p

- WS: k-regular graph with rewiring probability p

- BA: m nodes added at each graph generation step

30

⇢(�G) = 0.6<latexit sha1_base64="AL5VxfJ0JwGuS/3hkLJDcb2RSxA=">AAACA3icbVDLSsNAFJ34rPUVdaebwSLUTUhE1I1QdKHLCvYBTSiT6aQdOpkJMxOhhIIbf8WNC0Xc+hPu/BsnbRbaeuDC4Zx7ufeeMGFUadf9thYWl5ZXVktr5fWNza1te2e3qUQqMWlgwYRsh0gRRjlpaKoZaSeSoDhkpBUOr3O/9UCkooLf61FCghj1OY0oRtpIXXvflwNR9UOiEfRjpAdhlN2Mjy9d56xrV1zHnQDOE68gFVCg3rW//J7AaUy4xgwp1fHcRAcZkppiRsZlP1UkQXiI+qRjKEcxUUE2+WEMj4zSg5GQpriGE/X3RIZipUZxaDrzM9Wsl4v/eZ1URxdBRnmSasLxdFGUMqgFzAOBPSoJ1mxkCMKSmlshHiCJsDaxlU0I3uzL86R54niu492dVmpXRRwlcAAOQRV44BzUwC2ogwbA4BE8g1fwZj1ZL9a79TFtXbCKmT3wB9bnD0Pzlps=</latexit><latexit sha1_base64="AL5VxfJ0JwGuS/3hkLJDcb2RSxA=">AAACA3icbVDLSsNAFJ34rPUVdaebwSLUTUhE1I1QdKHLCvYBTSiT6aQdOpkJMxOhhIIbf8WNC0Xc+hPu/BsnbRbaeuDC4Zx7ufeeMGFUadf9thYWl5ZXVktr5fWNza1te2e3qUQqMWlgwYRsh0gRRjlpaKoZaSeSoDhkpBUOr3O/9UCkooLf61FCghj1OY0oRtpIXXvflwNR9UOiEfRjpAdhlN2Mjy9d56xrV1zHnQDOE68gFVCg3rW//J7AaUy4xgwp1fHcRAcZkppiRsZlP1UkQXiI+qRjKEcxUUE2+WEMj4zSg5GQpriGE/X3RIZipUZxaDrzM9Wsl4v/eZ1URxdBRnmSasLxdFGUMqgFzAOBPSoJ1mxkCMKSmlshHiCJsDaxlU0I3uzL86R54niu492dVmpXRRwlcAAOQRV44BzUwC2ogwbA4BE8g1fwZj1ZL9a79TFtXbCKmT3wB9bnD0Pzlps=</latexit><latexit sha1_base64="AL5VxfJ0JwGuS/3hkLJDcb2RSxA=">AAACA3icbVDLSsNAFJ34rPUVdaebwSLUTUhE1I1QdKHLCvYBTSiT6aQdOpkJMxOhhIIbf8WNC0Xc+hPu/BsnbRbaeuDC4Zx7ufeeMGFUadf9thYWl5ZXVktr5fWNza1te2e3qUQqMWlgwYRsh0gRRjlpaKoZaSeSoDhkpBUOr3O/9UCkooLf61FCghj1OY0oRtpIXXvflwNR9UOiEfRjpAdhlN2Mjy9d56xrV1zHnQDOE68gFVCg3rW//J7AaUy4xgwp1fHcRAcZkppiRsZlP1UkQXiI+qRjKEcxUUE2+WEMj4zSg5GQpriGE/X3RIZipUZxaDrzM9Wsl4v/eZ1URxdBRnmSasLxdFGUMqgFzAOBPSoJ1mxkCMKSmlshHiCJsDaxlU0I3uzL86R54niu492dVmpXRRwlcAAOQRV44BzUwC2ogwbA4BE8g1fwZj1ZL9a79TFtXbCKmT3wB9bnD0Pzlps=</latexit><latexit sha1_base64="AL5VxfJ0JwGuS/3hkLJDcb2RSxA=">AAACA3icbVDLSsNAFJ34rPUVdaebwSLUTUhE1I1QdKHLCvYBTSiT6aQdOpkJMxOhhIIbf8WNC0Xc+hPu/BsnbRbaeuDC4Zx7ufeeMGFUadf9thYWl5ZXVktr5fWNza1te2e3qUQqMWlgwYRsh0gRRjlpaKoZaSeSoDhkpBUOr3O/9UCkooLf61FCghj1OY0oRtpIXXvflwNR9UOiEfRjpAdhlN2Mjy9d56xrV1zHnQDOE68gFVCg3rW//J7AaUy4xgwp1fHcRAcZkppiRsZlP1UkQXiI+qRjKEcxUUE2+WEMj4zSg5GQpriGE/X3RIZipUZxaDrzM9Wsl4v/eZ1URxdBRnmSasLxdFGUMqgFzAOBPSoJ1mxkCMKSmlshHiCJsDaxlU0I3uzL86R54niu492dVmpXRRwlcAAOQRV44BzUwC2ogwbA4BE8g1fwZj1ZL9a79TFtXbCKmT3wB9bnD0Pzlps=</latexit>

/35

Experiments on real world data• Learning social network

- players: 182 households in a village in rural India [Banerjee13]

- actions in 31 games: number of facilities adopted by each household

- strategic complements: conformity to social norms (decisions made by neighbours)

- compare with groundtruth: self-reported friendship

31Banerjee et al., “The diffusion of microfinance,” Science, 2013.

/35

Experiments on real world data• Learning trade network

- players: 235 countries

- actions in 192 games: import/export of 96 products of countries in 2008

- strategic substitutes: complementary demand/supply leads to nonsmooth signals on trade network

- compare with groundtruth: trade network of countries in 2002

32

/35

Discussion• Applications in practical scenarios

- detect communities of players (for stratification)

- compute centrality measures (for efficient targeting strategies)

- design intervention mechanisms to achieve planning objective

maximise total utilities of players (via adjusting marginal benefits) [Galeotti17]

reduce inequality between players (via adjusting interaction network)

33Galeotti et al., “Targeting interventions in networks,”, arXiv, 2017.

/35

Discussion• Applications in practical scenarios

- detect communities of players (for stratification)

- compute centrality measures (for efficient targeting strategies)

- design intervention mechanisms to achieve planning objective

maximise total utilities of players (via adjusting marginal benefits) [Galeotti17]

reduce inequality between players (via adjusting interaction network)

33Galeotti et al., “Targeting interventions in networks,”, arXiv, 2017.

• Open issues & future directions - determination of (strength of strategic interaction)

- probabilistic interpretation of learning framework

- theoretical understanding, e.g., recovery guarantee

- more general payoff functions

- real-world intervention

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Summary

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- collective decision-making is key to understanding of human behaviour

- network-based learning provides natural models and tools

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Summary

34

- collective decision-making is key to understanding of human behaviour

- network-based learning provides natural models and tools

- learning and inference need to be combined with social theories for better interpretability

- ethical implications and consequences

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Papers & Acknowledgement• Y. Leng, X. Dong, E. Moro and A. Pentland, “The ripple effect: You are more

influential than you think,” NetSci, 2017.

• Y. Leng, X. Dong, E. Moro and A. Pentland, “A Bayesian learning model for decision-making in social networks,” NetSci, 2018.

• Y. Leng, X. Dong and A. Pentland, “Learning network structure in linear quadratic games,” IC2S2, 2019.

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Yan Leng Alex ‘Sandy’ PentlandEsteban Moro

Documents

Network-based Learning for Understanding Collective Human ...xdong/talk/SICSS_NetworkLearning.pdf• Large-scale mobile phone data during Cirque de Soleil in Andorra • Study inﬂuence