Università degli Studi dell’Aquila Academic Year 20 19 /20 20

1. Università degli Studi dell’Aquila Academic Year 2019/2020 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: 9.30 – 11.15 – Room A1.2 Thursday: 11.30 – 13.15 – Room A1.1 Questions?: Tuesday 16.30 - 18.30 (or send an email to guido.proietti@univaq.it) Slides plus other infos: http://people.disim.univaq.it/guido.proietti/2019.html

2. Autonomous versus non-autonomous (communication) networks • In a very general sense, an autonomus networkiscomposed by manyindependententitieswhichinteract by means of some common infrastructure (e.g., a physicalcommunication network), with no anycentral authority dictatinghowtheseentitiesshouldactuallybehave • 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 properlyhere to study computational and design problems!

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 orplayer) chooses strategicallyand 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 November4-8): 10 multiple-choicetests, plus an open-answerquestion. IF a passing grade isearned, THEN this can be EITHERmaintained, ORit can be immediatelyquestionedthrough a quick-oralexamination. In bothcases, the finalmarkwill be frozenuntilJanuary, whenitwill be registered (possiblyafter an integration with the ‘Social Networks’’ course). OTHERWISE, youwilldirectlyaccess to the nextdescribedstep. • Oral Examination: this will be concerned with the whole program. Therewill be fixed a total of 6 dates, namely: • 3 in January-February • 2 in June-July • 1 in September • For thoseenrolled in the NEDAS curriculum, therewill be a single final grade as a result of the gradesobtained in thiscourse and in the ‘Social Networks’’ course (Dott. Gianpiero Monaco); the correspondingexams can be doneseparately, butthey must be givenwithin the samecalendaryear (e.g., 2020)

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 http://agtb.wordpress.com/

8. Algorithmic Game Theory: an Introduction

9. Two Research Traditions • Theory of Algorithms: computational issues • What can be feasibly computed? • How much it is intrinsically difficult a problem? • 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. 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 • 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 in DSE • 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 • A set of Nrational players • For each player i, a strategy set Si • Apayoff matrix: for each strategy combination (s1, s2, …, sN), where siSi, a corresponding payoff vector (p1, p2, …, pN), where piis the payoff of player i  |S1||S2|… |SN| payoff matrix 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:

19. A famous game: the Prisoner’s Dilemma Non-cooperative, symmetric, non-zero sum, simultaneous, perfect information, one-shot, 2-player game Strategy Set 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

21. Prisoner II’s decision • Prisoner II’s decision: • If I chooses Don’t Implicatethen it is best to Implicate • If I chooses Implicatethen it is best to Implicate • It is best to Implicate for II, regardless of what I does: Dominant Strategy

22. Hence… • 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 • Remark: If they might collaborate, then it would be beneficial for both to Not Implicate, but in the provided setting the players would reciprocally betray each other, as both have incentive to deviate