Algorithmic Game Theory, Slides of Game Theory

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IA168 Algorithmic Game Theory

Tomáš Brázdil

Organization of This Course

Sources:

I Lectures (slides, notes)

I (^) based on several sources I (^) slides are prepared for lectures, some stuff on greenboard (⇒ attend the lectures)

Evaluation

I Oral exam

I Homework

I 3 times homework

I A computer implementation of a strategy

Notable features of the course

I No computer games course!

I Very demanding!

I Mathematical!

Notable features of the course

I No computer games course!

I Very demanding!

I Mathematical!

An unusual exam system!

You can repeat the oral exam as many times as needed (only

the best grade goes into IS).

An example of an instruction email (from another course with

the same system):

It is typically not sufficient to devote a single

afternoon to the preparation for the exam.

You have to know everything (which means every

single thing) starting with the slide 42

and ending with the slide 245 with notable exceptions

of slides: 121 - 123, 137 - 140, 165, 167.

Proofs presented on the whiteboard are also mandatory.

Most importantly,

The previous slide is not

a joke!

What is Algorithmic Game Theory?

First, what is the game theory?

According to the Oxford dictionary it is "the branch of mathematics concerned with the analysis of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants"

What is Algorithmic Game Theory?

First, what is the game theory?

According to the Oxford dictionary it is "the branch of mathematics concerned with the analysis of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants"

According to Myerson it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers"

What is Algorithmic Game Theory?

First, what is the game theory?

According to the Oxford dictionary it is "the branch of mathematics concerned with the analysis of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants"

According to Myerson it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers"

What does the "algorithmic" mean? I (^) It means that we are "concerned with the computational questions that arise in game theory, and that enlighten game theory. In particular, questions about finding efficient algorithms to ‘solve’ games.”

Let’s have a look at some examples ....

Prisoner’s Dilemma

I (^) Two suspects of a serious crime are arrested and imprisoned.

Prisoner’s Dilemma

I (^) Two suspects of a serious crime are arrested and imprisoned. I (^) Police has enough evidence of only petty theft, and to nail the suspects for the serious crime they need testimony from at least one of them. I (^) The suspects are interrogated separately without any possibility of communication.

Prisoner’s Dilemma

I (^) Two suspects of a serious crime are arrested and imprisoned. I (^) Police has enough evidence of only petty theft, and to nail the suspects for the serious crime they need testimony from at least one of them. I (^) The suspects are interrogated separately without any possibility of communication. I (^) Each of the suspects is offered a deal: If he confesses (C) to the crime, he is free to go. The alternative is not to confess, that is remain silent (S).

Prisoner’s Dilemma

I (^) Two suspects of a serious crime are arrested and imprisoned. I (^) Police has enough evidence of only petty theft, and to nail the suspects for the serious crime they need testimony from at least one of them. I (^) The suspects are interrogated separately without any possibility of communication. I (^) Each of the suspects is offered a deal: If he confesses (C) to the crime, he is free to go. The alternative is not to confess, that is remain silent (S).

Sentence depends on the behavior of both suspects. The problem: What would the suspects do?

Prisoner’s Dilemma – Solution(?)

C S

C − 5 , − 5 0 , − 20

S − 20 , 0 − 1 , − 1

Rational "row" suspect (or his adviser) may reason as follows: