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Department of InformaticsNon-Cooperative Game Theory

Heinrich H. Nax

www.nax.science

September 30, 2019

Department of InformaticsTwo parts:

1. An introduction to the game-theoretic view on decision-making in interactive environments

2. Some course admin on peer review (and an illustration of game theory in practice)

Department of InformaticsTwo parts:

1. An introduction to the game-theoretic view on decision-making in interactive environments

2. Some course admin on peer review (and an illustration of game theory in practcve)

Department of Informatics…what exactly is Game Theory? andhow is it useful for “ABM and SSS”?

Department of InformaticsLet’s start with a game

Department of InformaticsLet’s start with a game

Department of InformaticsKeynesian Beauty Contest

Department of InformaticsKeynesian Beauty Contest

Keynesian Beauty Contest (1/2 version)

Department of InformaticsKeynesian Beauty Contest (2/3 version)

Department of InformaticsKeynesian Beauty Contest (2/3 version)

Department of InformaticsKeynesian Beauty Contest (2/3 version)

Department of InformaticsKeynesian Beauty Contest (2/3 version)

Department of InformaticsKeynesian Beauty Contest (2/3 version)

Department of InformaticsKeynesian Beauty Contest (2/3 version)

Department of InformaticsKeynesian Beauty Contest (2/3 version)

Department of Informatics

What is game theory?

Department of Informatics

What is game theory?

Department of Informatics«2 Johns»

Department of Informatics

Recipe

Department of InformaticsEveryday games

Department of InformaticsEveryday games

Department of InformaticsThe theory’s impact

Department of Informatics

Page 8

GT’s many agendas

Macro

Micro

Macro

Microstructuring

Department of InformaticsSolution concepts

Department of InformaticsNash’s solution

Department of InformaticsPrisoner’s dilemma

Department of InformaticsHarmony

Department of InformaticsPure coordination games

Department of InformaticsMatching pennis

Department of Informatics

Department of Informatics…How is GT useful for “ABM and SSS”?

cognitive hierarchy

imitation,

herd behavior,learning,hypothesis testing,trial and error,…

…How is GT useful for “ABM and SSS”?

To formulate behavior!

Department of InformaticsEvolutionary Game Theory

Heinrich H. Nax

www.nax.science

December 2, 2019

Department of InformaticsTwo parts:

1. An introduction to the game-theoretic view on decision-making in interactive environments

2. Some course admin on peer review (and an illustration of game theory in practice)

Department of InformaticsAnother game

Department of InformaticsVoluntary Contributions Game

Department of Informatics«Voluntary Contributions Game»

Department of InformaticsWhat happens in experiments?

Department of InformaticsThe «freerider» problem

Department of InformaticsThe «freerider» problem

mpcr<<1

Department of InformaticsA mechanism design approach…

www.DVSN.app

Department of Informatics…= how you will

receive your grades!

Working in groups @school/uni =

Pros• Synergies• Learning transfer• Social skills• Larger scope

Cons• Freeriding• Collusion• Coordination

• A group collaborated and generated some “value”• Who deserves what/ how much?

Our desiderata

The general use case

• A group collaborated and generated some “value”• Who deserves what/ how much?

Our desiderata

• A mechanismPreventing free-ridingFostering synergetic collaboration Enabling fair division: instead of one size fits all

Without dissecting or micro-managing as a supervisor (i.e. without “looking into the process”)

The general use case

My use case: “Controversies in Game Theory”

A group collaborated and earned a project gradeWho deserves which individual grade?

Prologue on a mechanism1. First theory for basic case by de Clippel et al (JET 2008)2. Adapted for a collective action framework 3. Implemented as a grading tool at ETH through a Critical Thinking Award

(thanks!)

3. 1. 2. 3. 2. 1.

Solution The mechanism desiderata:Adequate

• Sum of individual shares= total

Consensual • shares implement consensus when

everyone agreesAnonymous

• equal treatment of everyoneImpartial

• own verdicts of one’s own contribution cannot improve one’s share

Solution The mechanism desiderata:Adequate

• Sum of individual shares= total

Consensual • shares implement consensus when

everyone agreesAnonymous

• equal treatment of everyoneImpartial

• own verdicts of one’s own contribution cannot improve one’s share

• Contributors review each other• A formula aggregates the reviews

to yield individual shares

Solution The mechanism desiderata:Adequate

• Sum of individual shares= total

Consensual • shares implement consensus when

everyone agreesAnonymous

• equal treatment of everyoneImpartial

• own verdicts of one’s own contribution cannot improve one’s share

• Contributors review each other• A formula aggregates the reviews

to yield individual shares

Unique “formula”fulfilling these!

The formula

Average relative contribution jk

Average RC jk without i’s opinion

Auxiliary function assigning share to i when j excluded

Final payment

share in the other slicesi’s residual in his slice

Complicated?

Yes, kind of.But…

Illustration of the formula

5.75

Illustration of the formula

5.75 5.755.75

5.75

Illustration of the formula

Illustration of the formula

5.75

Illustration of the formula

Illustration of the formula

residual

Illustration of the formula

residual

Illustration of the formula

residuali

j

k

l

Complicated? AND it is the unique formula achieving:• Adequateness• Consensus• Anonymity• Impartiality

Aim: Aligning individual and collective incentives through, projects suffer less from free-riding, get better, and individual marks are fairer.

Yes, kind of.But the properties are intuitive and the rating is very simple

Complicated? AND it is the unique formula achieving:• Adequateness• Consensus• Anonymity• Impartiality

Aim: Aligning individual and collective incentives through, projects suffer less from free-riding, get better, and individual marks are fairer.

Yes, kind of.But the properties are intuitive and the rating is very simplePlus the burden is on the computer software, not on the student…

An example

The group gets a 5.25.Who gets which grade?

Caroline, Heiko, Sarah, Tobias

Caroline, Heiko, Sarah, Tobias

Heiko

Sarah

Tobias

Caroline’s evaluation

Caroline, Heiko, Sarah, Tobias

Caroline

Sarah

Tobias

Heiko’s evaluation

Caroline, Heiko, Sarah, Tobias

Caroline

Heiko

Tobias

Sarah’s evaluation

Caroline, Heiko, Sarah, Tobias

Caroline

Heiko

Sarah

Tobias’ evaluation

Caroline

Heiko

Sarah

Tobias

5.5

5.25

5

5.25

The key effect

low effort = low reward+high effort = high reward

The key effect

= mpcr>1

low effort = low reward+high effort = high reward

The key effect

= mpcr>1

low effort = low reward+high effort = high reward

• Given the situation where a group collaborated to generate a “value”

We use

• A mechanismPreventing free-ridingFostering synergetic collaboration Enabling fair division: instead of one size fits all Where indeed all equal contributors will again get the same

Without dissecting or micro-managing as a supervisor (i.e. without “looking into the process”)

As a result

Department of Informatics

Non-CooperativeGame Theory

• Game theoryA useful language for ABMs,

SSSs, behavioral scientistsA toolbox that requires clear

premises regarding use and context of its solution conceptsA rich domain for behavioral

experimentsUseful for mechanism design