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Lecture 12: Introduction to Game Theory

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Quizzes

Anonymous Questions (during or after the lecture)

The Lecture will be recorded

vevox.app�106-040-333

Feedback for the course (at the end)

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The process of designing “Decision-making” frameworks

Define

Design

Validate

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The process of designing “Decision-making” frameworks

Define

Design

Validate

Simpler policies first

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MDPs in plain English

How often do you need/get to make a decision?

What do you get to decide/control?

What is your metric of success/ key performance indicator?

What can you measure/observe?

How is your metric affected by your decisions?

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Game Theory

Georgios Tsaousoglou

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Let’s play a game!

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Let’s play a game!

Take-away: Strategic players make decisions by considering what are the effects of their own, and of the others’, actions on their payoff

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Let’s play again!

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Let’s play again!

Reflections:

Did your choice change?

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The Nash Equilibrium

In this game, the point (0, 0, 0, …, 0) is the game’s Nash Equilibrium

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The Nash Equilibrium

In this game, the point (0, 0, 0, …, 0) is the game’s Nash Equilibrium

So, what is a Nash Equilibrium in general?

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Formally…

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Formally…

Why do we care about equilibria of Games?

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Why is this relevant?

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Why is this relevant?

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Why is this relevant?

What is the Nash Equilibrium of this game?

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Equilibria and Efficiency

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Split or Steal?

Let’s watch a TV show…

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Split or Steal?

Let’s watch a TV show…

First, they talk to each other. �What do you think they will declare?

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Split or Steal?

Let’s watch a TV show…

First, they talk to each other. �

What do you think they will actually pick?

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Let’s analyze

		Woman
		Split	Steal
Man	Split
	Steal

They just lost like 100 thousand Euros over a single decision. And yet their decision was… not stupid??

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Let’s analyze

		Woman
		Split	Steal
Man	Split
	Steal

They just lost like 100 thousand Euros over a single decision. And yet their decision was… not stupid??

Rational behavior does not always lead to socially optimal outcomes.�Can you think of examples where such phenomena might be at play?

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Public goods game

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Split or Steal?

Now, let’s watch another pair…

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Split or Steal?

Now, let’s watch another pair…

What do you think Ibrahim will pick? �

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Let’s be rational again

		Nick
		Split	Steal
Ibrahim	Split
	Steal

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Let’s be rational again

		Nick
		Split	Steal
Ibrahim	Split
	Steal

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Let’s be rational again

		Nick
		Split	Steal
Ibrahim	Split
	Steal

This is something you can observe out there:

Armies burning their own ships

People declaring “I am crazy” in various ways

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Let’s be rational again

		Nick
		Split	Steal
Ibrahim	Split
	Steal

		Nick
		Split	Steal
Ibrahim	Split
	Steal

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Multi-agent systems are the (near) future

Designing agents for decision-making under uncertainty
Studying the (in)efficiency of equilibria in multi-agent systems
Designing the rules to steer equilibria into desirable regions

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Thesis / Special Course Topics

Game-theoretic analysis of electricity markets (Linus)

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How inefficient can an electricity market be?

And what does it have to do with game theory and decision making under uncertainty?

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Anonymous Feedback for the course

Scan me:

vevox.app�106-040-333

Feedback for the course

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How is the power system operated?

Imag from: https://www.britannica.com/

Demand

Quantity (MWh)

Price (€/MWh)

Market clearing price

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How is the power system operated?

Imag from: https://www.britannica.com/

Quantity (MWh)

Price (€/MWh)

Market clearing price

Generating power

Off

Generator	Producing cost	Generation
G1	10	100%
G2	15	100%
G3	20	80%
G4	0	0%
Total	45	-

Demand

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Strategic behaviour

Imag from: https://www.britannica.com/

Demand

Quantity (MWh)

Price (€/MWh)

Everyone reports their true cost

G1 and G2 earn some money, the rest does not

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Strategic behaviour

Imag from: https://www.britannica.com/

Quantity (MWh)

Price (€/MWh)

G3 bids higher than their true cost, to maximize its profit

Demand

True cost

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Strategic behaviour

Imag from: https://www.britannica.com/

Quantity (MWh)

Price (€/MWh)

Re-arrangement according to the reported cost

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Strategic behaviour

Quantity (MWh)

Price (€/MWh)

Demand

Market clearing price

Market is cleared with this information

Suddenly G3 makes a (small) profit

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Strategic behaviour

Quantity (MWh)

Price (€/MWh)

Demand

Market clearing price

Generator	Producing cost	Generation
G1	10	100%
G2	15	100%
G3	5	20%
G4	35	100%
Total	65	-

Generating power

Off

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Original system

Quantity (MWh)

Price (€/MWh)

Market clearing price

Generating power

Off

Generator	Producing cost	Generation
G1	10	100%
G2	15	100%
G3	20	80%
G4	0	0%
Total	45	-

Demand

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Strategic behaviour

Quantity (MWh)

Price (€/MWh)

Demand

Market clearing price

Generator	Producing cost	Generation
G1	10	100%
G2	15	100%
G3	5	20%
G4	35	100%
Total (old)	45	-
Total (new)	65	-

Generating power

Off

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Which scenario do you think is more realistic?

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How to measure inefficiency

𝑷𝒓𝒊𝒄𝒆 𝒐𝒇 𝑨𝒏𝒂𝒓𝒄𝒉𝒚 = 1, society pays as little as possible to satisfy demand

𝑷𝒓𝒊𝒄𝒆 𝒐𝒇 𝑨𝒏𝒂𝒓𝒄𝒉𝒚 = 2, we might pay twice as much to satisfy (same) demand

We know that they like money, so they might want to use some advanced algorithms…

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Learning goals for the special course

Get to know different ways to run and model electricity markets
Understand the concept of the price of anarchy
Understand how different assumptions on the behavior of the players influence what market outcomes are realistic and how that influences the price of anarchy
Familiarize with different methods and approaches to calculate or estimate the price of anarchy in such models (that is the hard part)
Be able to discuss the pros and cons of the different models
Use some of the models and methods to discuss the inefficiency of electricity markets in Denmark (or any other country)

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Thesis / Special Course Topics

Game-theoretic analysis of electricity markets: Special Course (Autumn 2026)

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Thesis / Special Course Topics

Game-theoretic analysis of electricity markets: Special Course (Autumn 2026)

Decision-making under uncertainty, advanced project-based Special Course (Autumn 2026) or Thesis

Model electricity market participation strategies
Energy management of distributed energy resources (modelling and optimization)

DTU Compute

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Thesis / Special Course Topics

Game-theoretic analysis of electricity markets: Special Course (Autumn 2026)

Decision-making under uncertainty, advanced project-based Special Course (Autumn 2026) or Thesis

Model electricity market participation strategies
Energy management of distributed energy resources (modelling and optimization)

Thesis: Your own idea or a company’s problem. �But there has to be a research component (not just “I will build a 2-stage stochastic program”)

DTU Compute

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Thesis / Special Course Topics

Game-theoretic analysis of electricity markets: Special Course (Autumn 2026)

Decision-making under uncertainty, advanced project-based Special Course (Autumn 2026) or Thesis

Model electricity market participation strategies
Energy management of distributed energy resources (modelling and optimization)

Thesis: Your own idea or a company’s problem. �But there has to be a research component (not just “I will build a 2-stage stochastic program”)

4. Thesis or self-study Special Course: Validation/Stress-testing of given policies operating critical infrastructure e.g. a power system

DTU Compute

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Thesis / Special Course Topics

Game-theoretic analysis of electricity markets: Special Course (Autumn 2026)

Decision-making under uncertainty, advanced project-based Special Course (Autumn 2026) or Thesis

Model electricity market participation strategies
Energy management of distributed energy resources (modelling and optimization)

Thesis: Your own idea or a company’s problem. �But there has to be a research component (not just “I will build a 2-stage stochastic program”)

4. Thesis or self-study Special Course: Validation/Stress-testing of given policies operating critical infrastructure e.g. a power system

Email me geots@dtu.dk if you are interested. Include:

Which topics (1-4) you are interested in
Your timeline, if for a thesis
Your CV and transcripts

And spread the word ☺

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