1. Università degli Studi dell’Aquila
Academic Year 2018/2019
Course: Non-cooperative networks (3 CFU) (this course is integrated within the NEDAS curriculum with ‘’Social networks’’ (3 CFU), by Dott. Gianpiero Monaco, to form the ‘’Autonomous Networks’’ course)
Instructor: Prof. Guido Proietti
Schedule: Wednesday: – – Room A1.2
Thursday: – – Room A1.2
Questions?: Tuesday (or send an to
Slides plus other infos:

2. Autonomous versus non-autonomous (communication) networks
In a very general sense, an autonomus network is composed by many autonomous entities which interact by sharing some common infrastructure (e.g., a physical communication network), with no any central authority dictating how these entities should actually behave
Some examples of autonomous networks:
Mobile Ad hoc Networks
(Wireless) Sensor Networks
Social Networks …

3. The mother of all autonomous networks: the Internet

4. Lack of cooperativeness in large networks
Large autonomous networks (e.g., Internet) are often built/controlled/used by diverse and competitive entities:
Entities may for instance own different components of the network, and hold private information about the cost of using them, or they may use selfishly some physical component of an underlying network
 we call the resulting network non-cooperative, to emphasize this competitive behavior
 The classic network optimization field of research (where selfishness is not considered) does not fit properly!

5. Three main ingredients in the course: Networks + Algorithms + Game Theory
We will be concerned with the computational (i.e., algorithmic) and game-theoretic aspects of a Non-Cooperative Network (NCN). In other words, we will analyze some classic network optimization problems (e.g., multicommodity flow, network design, shortest paths, minimum spanning tree, etc.) by assuming that each selfish entity (say, agent or player) chooses strategically and non-cooperatively how to behave, by aiming to maximize his personal benefit.
Our topic is a subfield of the larger emerging Algorithmic Game-Theory (AGT) field.

6. Course structure and exams
FIRST PART: Strategic equilibria theory in NCN
Nash equilibria
Selfish routing
Network Design games
Network Creation games
SECOND PART: Implementation theory in NCN
Algorithmic mechanism design (AMD)
AMD for some basic graph optimization problems
Written Examination (week November 5-9): 10 multiple-choice tests, plus an open-answer question. IF a passing grade is earned, THEN this can be either maintained, or it can be (possibly) immediately improved through a quick-oral examination. In both cases, the final mark will be frozen until January, when it will be registered. OTHERWISE, you will directly access to the next described step.
Oral Examination: this will be concerned with the whole program. There will be fixed a total of 6 dates, namely:
3 in January-February
2 in June-July
1 in September
For those enrolled in the NEDAS curriculum, there will be a single final grade as a result of the grades obtained in this course and in the ‘Social Networks’’ course; the corresponding exams can be done separately, but they must be given within the same calendar year (e.g., 2019)

7. Suggested readings
Algorithmic Game Theory, Edited by Noam Nisan, Tim Roughgarden, Eva Tardos, and Vijay V. Vazirani, Cambridge University Press.
Blog by Noam Nisan

8. Algorithmic Game Theory:
an Introduction

9. Two Research Traditions
Theory of Algorithms: computational issues
What can be feasibly computed?
How long does it take to compute a solution?
Which is the quality of a computed solution?
Centralized or distributed computational models
Game Theory: interaction between self-interested individuals
What is the outcome of the interaction?
Which social goals are compatible with selfishness?

10. Different Assumptions
Theory of Algorithms (in distributed systems):
Processors are obedient, faulty (i.e., crash), adversarial (i.e., Byzantine), or they compete without being strategic (e.g., concurrent systems)
Large systems, limited computational resources
Game Theory:
Players are strategic (selfish)
Small systems, unlimited computational resources

11.  Both strategic and computational issues!
The Internet World
Users often selfish
Have their own individual goals
Own network components
Internet scale
Massive systems
Limited communication/computational resources
 Both strategic and computational issues!

12. Fundamental question Algorithmic Game Theory Theory of Algorithms
How the computational aspects of a strategic distributed system should be addressed?
Algorithmic
Game Theory
Theory of Algorithms
Game Theory = +

13. Basics of Game Theory A game consists of:
A set of players (or agents)
A specification of the information available to each player
A set of rules of encounter: Who should act when, and what are the possible actions (strategies)
A specification of payoffs for each possible outcome (combination of strategies) of the game
Game Theory attempts to predict the final outcomes (or solutions) of the game by taking into account the individual behavior of the players

14. Solution concept
How do we establish that an outcome is a solution? Among the possible outcomes of a game, those enjoying the following property play a fundamental role:
Equilibrium solution: strategy combination in which players are not willing to change their state. But this is quite informal: what does it rationally mean that a player does not want to change his state? In the Homo Economicus model, this makes sense when he has selected a strategy that maximizes his individual wealth, knowing that other players are also doing the same.

15. Roadmap
We will focus on two prominent types of equilibria: Nash Equilibria (NE) and Dominant Strategy Equilibria (DSE)
Computational Aspects of Nash Equilibria
Can a NE be feasibly computed, once it exists?
What about the “quality” of a NE?
Cases study: Network Flow Games (i.e., selfish routing in Internet), Network Design Games, Network Creation Games
(Algorithmic) Mechanism Design
Which social goals can be (efficiently) implemented in a strategic distributed system?
Strategy-proof mechanisms in DSE: Vickrey-Clarke-Groves (VCG)-mechanisms and one-parameter mechanisms
Cases study: Shortest Path, Minimum Spanning Tree, Single-source Shortest-path Tree

16. FIRST PART:
Dominant
strategy and
Nash Equilibria

17. (Some) Types of games Cooperative/Non-cooperative
Symmetric/Asymmetric (for 2-player games)
Zero sum/Non-zero sum
Simultaneous/Sequential
Perfect information/Imperfect information
One-shot/Repeated

18. Games in Normal-Form
We start by considering simultaneous, perfect-information and non-cooperative games. These games are usually represented explicitly by listing all possible strategies and corresponding payoffs of all players (this is the so-called normal–form); more formally, we have:
A set of N rational players
For each player i, a strategy set Si
A payoff matrix: for each strategy combination (s1, s2, …, sN), where siSi, a corresponding payoff vector (p1, p2, …, pN), where pi is the payoff of player i
 |S1||S2| … |SN| payoff matrix

19. A famous game: the Prisoner’s Dilemma
Non-cooperative, symmetric, non-zero sum, simultaneous, perfect information, one-shot, 2-player game
Strategy
Set
Prisoner I
Prisoner II
Don’t Implicate
Implicate
1, 1
6, 0
0, 6
5, 5
Strategy Set
Payoffs (for this game, these are years in jail, so they should be seen as a cost that a player wants to minimize)

20. Prisoner I’s decision Prisoner I’s decision:
If II chooses Don’t Implicate then it is best to Implicate
If II chooses Implicate then it is best to Implicate
It is best to Implicate for I, regardless of what II does: Dominant Strategy
Prisoner I
Prisoner II
Don’t Implicate
Implicate
1, 1
6, 0
0, 6
5, 5

21. Prisoner II’s decision
Don’t Implicate
Implicate
1, 1
6, 0
0, 6
5, 5
Prisoner II’s decision:
If I chooses Don’t Implicate then it is best to Implicate
If I chooses Implicate then it is best to Implicate
It is best to Implicate for II, regardless of what I does: Dominant Strategy

22. Hence… Prisoner I Prisoner II Don’t Implicate Implicate 1, 1 6, 0 0, 6
5, 5
It is best for both to implicate regardless of what the other one does
Implicate is a Dominant Strategy for both
(Implicate, Implicate) becomes the Dominant Strategy Equilibrium
Note: If they might collude, then it’s beneficial for both to Not Implicate, but it’s not an equilibrium as both have incentive to deviate