1. Budhaditya Pyne BEE-IV Roll No: 000910801081 Jadavpur University

2. / 34  What is Game Theory?  A Brief History of Game Theory  Game Theory Basics with a suitable example  An Interesting Analogy with Communication Systems  Non-Cooperative Game Theory in Wireless Communications Research  Coalitional Game Theory in Wireless Networks Research  Game Theory in Routing and Congestion Control  Game Theory in Network Security  Scope of Further Research Game Theory in Communication Systems1

3. / 34 Game Theory in Communication Systems2

4. / 34 “… Game Theory is designed to address situations in which the outcome of a person’s decision depends not just on how they choose among several options, but also on the choices made by the people they are interacting with …” “… Game theory is the study of the ways in which strategic interactions among economic (rational) agents produce outcomes with respect to the preferences (or utilities) of those agents ….” Game Theory in Communication Systems3

5. / 34 Cournot (1838), Bertrand (1883): Economics J. von Neumann, O. Morgenstern (1944) “Theory of Games and Economic Behavior” Existence of mixed strategy in 2-player game J. Nash (1950): Nash Equilibrium (Nobel Prize in Economic Sciences 1994) Selten (1965): Subgame Perfect Equilibrium Harsani (1967-68): Bayesian (Incomplete Information) Games The 80’s Nuclear disarmament negotiations Game Theory for Security (Burke) More recently: Auction modeling, mechanism design Routing, Congestion Control, Channel Access Network Economics Network Security Biology von Neumann 1903- 1957 John F. Nash (1928) O. Morgenstern 1902- 1977 Game Theory in Communication Systems4

6. / 34  GAME = (P,A,U) ◦ Players (P 1 ; … ; P N ): Finite number (N≥2) of decision makers. ◦ Action sets (A 1 ; … ;A N ): player P i has a nonempty set A i of actions. ◦ Payoff functions u i : A 1 x … xA N :  R ; i = 1;….;N - materialize players’ preference, - take a possible action profile and assign to it a real number (von Neumann-Morgenstern). Game Theory in Communication Systems5

7. / 34  Cooperative and Non-Cooperative  Symmetric and Asymmetric  Zero-Sum and Non-Zero Sum  Simultaneous and Sequential  Static and Dynamic Game Theory in Communication Systems6

8. / 34 Game Theory in Communication Systems7

9. / 34  What should Prisoner A do to minimize his maximum punishment when: 1. Prisoner B confesses? 2. Prisoner B stays quiet?  What should Prisoner B do to minimize his maximum punishment when: 1. Prisoner A confesses? 2. Prisoner A stays quiet? Game Theory in Communication Systems8

10. / 34 Game Theory in Communication Systems9

11. / 34  Routing, Congestion Control and Channel Access  Network Security Game Theory in Communication Systems10

12. / 34  How do we apply an abstract Mathematical Tool like Game Theory in something as realistic like Communication Systems? Game Theory in Communication Systems11

13. / 34  Communication Networks consists of several nodes which have to take decisions regarding several aspects like packet switching, packet forwarding, etc.  These nodes are considered as the players. Utility functions are often chosen to correspond to achieved connection rate or similar technical metrics. Game Theory in Communication Systems12

14. Game Theory in Communication Systems13

15. / 34  Various studies have analyzed radio resource management problems in 802.11 WLAN networks.  In such random access studies, researchers have considered selfish nodes, who try to maximize their own utility (throughput) only, and control their channel access probabilities to maximize their utilities.random access Game Theory in Communication Systems14

16. / 34  Power control refers to the process through which mobiles in CDMA cellular settings adjust their transmission powers so that they do not create unnecessary interference to other mobiles, trying, nevertheless, to achieve the required Quality of Service. Power controlQuality of Service  Power Control may be: 1. Centralized 2. Distributed Game Theory in Communication Systems15

17. / 34  In such distributed settings, the mobiles can be considered to be selfish agents (players) who try to maximize their utilities (often modeled as corresponding throughputs).  Game theory is considered to be a powerful tool to study such scenarios. Game Theory in Communication Systems16

18. / 34  Coalitional game theory is a branch of game theory that deals with cooperative behavior.  By cooperating, the players can strengthen their position in a given game as well as improve their utilities.  Coalitional game theory proves to be a powerful tool for modeling cooperative behavior in many wireless networking applications such as cognitive radio networks, wireless system, physical layer security, virtual MIMO. Game Theory in Communication Systems17

19. / 34  It’s a non-cooperative game where the goal of each user is to maximize it’s own bandwidth by selecting its path.  First, the existence of the Nash Equilibrium(NE) is determined because at NE no user has the incentive to change its routing strategy. Game Theory in Communication Systems18

20. / 34  It is investigated how the selfish behavior of the users may affect the performance of the network as a whole.  A concept of observed available bandwidth is introduced on each link which allows a user to find a path with maximum bandwidth under max-min fair congestion control.  A game-based algorithm is formulated to compute the Nash Equilibrium (NE).  It is seen that by following the natural game course the network converges to an NE. Game Theory in Communication Systems19

21. / 34  Routing games ◦ users determine network routes ◦ multi-path routing and traffic splitting is possible ◦ users’ data rates are given and must be routed r Congestion games m users determine their data rate m network routes are given (single path) Game Theory in Communication Systems20

22. / 34 Game Theory in Communication Systems21

23. / 34 HackersTerrorists, Criminal Groups Hacktivists Disgruntled Insiders Foreign Governments Game Theory in Communication Systems22

24. / 34 Example: Remote Attack Security Traditional Security Solutions AttackDefense Game Theory also helps: TrustIncentivesExternalitiesMachine Intelligence Attacker strategy 1 strategy 2 ….. Defender: strategy 1 strategy 2 ….. A mathematical problem!  Solution tool: Game Theory Predict players’ strategies, Build defense mechanisms, Compute cost of security, Understand attacker’s behavior, etc… E.g.: Rate of Port ScanningIDS Tuning Game Theory in Communication Systems23

25. / 34 Key Concepts Forwarding has an energy cost of c (c<< 1) Successfully delivered packet: reward of 1 If Green drops and Blue forwards: (1,-c) If Green forwards and Blue drops: (-c,1) If both forward: (1-c,1-c) If both drop: (0,0) Each player is trying to selfishly maximize it’s net gain. What can we predict? Game Theory in Communication Systems24

26. / 34 Key Concepts Game: Players: Green, Blue Actions: Forward (F), Drop (D) Payoffs: (1-c,1-c), (0,0), (-c,1), (1,-c) Matrix representation: Actions of Green Actions of Blue Reward of Blue Reward of Green Game Theory in Communication Systems25

27. / 34 Nash equilibrium: “… a solution concept of a game involving two or more players, in which no player has anything to gain by changing his own strategy unilaterally …” John F. Nash (1928) Game Theory in Communication Systems26

28. / 34 Intruder Game Availability Attack Intelligent Virus  Normal traffic Virus  XnXn Detection If X n > => Alarm Game Theory in Communication Systems27

29. / 34 M’  M Intruder (Trudy) What if it is possible that: M Scenario: Network Source (Alice) User (Bob) M Encryption is not always practical …. Formulation: Game between Intruder and User Game Theory in Communication Systems28

30. / 34 Y Payoffs: Strategies (mixed i.e. randomized) Trudy: (p 0,p 1 ), Bob: (q 0,q 1 ) Alice Trudy Bob Intercept One shot, simultaneous choice game Nash Equilibrium? Z Game Theory in Communication Systems29

31. / 34 Pay: V Game Theory in Communication Systems30

32. / 34 Scenario  Normal traffic Virus  XnXn Detection If X n > => Alarm, …. Assume  known Detection system: choose to minimize cost of infection + clean up Virus: choose  to maximize infection cost Game Theory in Communication Systems31

33. / 34 Smart virus designer picks very large , so that the cost is always high …. Regardless of   Scenario  Normal traffic Virus  XnXn Detection If X n > => Alarm, …. Game Theory in Communication Systems32

34. / 34 Modified Scenario  Normal traffic Virus  XnXn Detection If X n > => Alarm Detector: buffer traffic and test threshold X n <    process If X n >  Flush & Alarm Game between Virus (  ) and Detector ( ) Game Theory in Communication Systems33

35. / 34 Tree-Link Game : Game Theory in Communication Systems34

36. / 34  Consider a tree with € links and n nodes. Let Ƭ be the set of spanning trees.  To get all the nodes connected in a cycle-free way, the Network Manager/Defender chooses a spanning tree TƬ of the network  The attacker simultaneously chooses a link e€ to attack  The attacker wins if the attacked link belongs to the chosen spanning tree; the Defender wins elsewise Game Theory in Communication Systems35

37. / 34  Game( modeled as a one-shot 2 player game) ◦ Graph = (nodes V, links E, spanning trees T )  Defender: chooses T  T  Attacker: chooses e  E (+ “No Attack”) ◦ Rewards  Defender: -1 e  T  Attacker: 1 e  T - µ e (µ e cost of attacking e) Example: Defender: 0 Attacker: - µ 2 Defender: -1 Attacker: 1- µ 1 – Defender : choose a distribution  on T, to minimize the expected attack loss --Attacker: Choose a distribution  on E, to maximize the attack gain Game Theory in Communication Systems36

38. / 34 Graph Most vulnerable links Chance 1/2 Chance 4/7>1/2 a) b) c) Assume: zero attack cost µ e =0 1/2 1/7 Game Theory in Communication Systems37

39. / 34 Definition 1&2: For any nonempty subset E  Ε 1. M (E) = min{| T  E|, T  Т } (minimum number of links E has in common with any spanning tree) 2. Vulnerability of E (E) = M (E)/|E| (minimum fraction of links E has in common with any spanning tree) Definition 3: A nonempty subset C  Ε is said to be critical if (C) = max E  Ε ( (E)) (C has maximum vulnerability) vulnerability of graph ( (G)) := vulnerability of critical subset 1 2 3 4 5 67 E={1,4,5} |T  E|=2 M (E) =1 Defender: choose trees that minimally cross critical subset (E) = 1/3 (G)=1 (G)=1/2 (G)=4/7 Game Theory in Communication Systems38

40. / 34 Theorem 1: There exists a Nash Equilibrium where Attacker attacks only the links of a critical set C, with equal probabilities Defender chooses only spanning trees that have a minimal intersection with C, and have equal likelihood of using each link of C, no larger than that of using any link not in C. [Such a choice is possible.] There exists a polynomial algorithm to find C [Cunningham 1982 ] Theorem generalizes to a large class of games. Game Theory in Communication Systems39

41. / 34 If ν ≤ 0: Attacker: “No Attack” Defender can invest to make µ high  Deter attacker from attacking Need to randomize choice of tree Edge-Connectivity is not always the right metric! ν= 3/4ν= 2/3ν= 3/5 2/3 > 3/5 Network in b) is more vulnerable than network in c) Additional link Network Design a)b)c) Game Theory in Communication Systems40

42. / 34 Availability Games ◦ Critical set  Vulnerability ( (G)): a metric more refined than edge- connectivity  Analyzing NE helps determine most vulnerable subset of links  Importance in topology design  Polynomial-time algorithm to compute critical set ◦ Generalization  Set of resources for mission critical task  Most vulnerable subset of resources. Intruder and Intelligent Virus Games : Most aggressive attackers are not the most dangerous ones Mechanisms to deter attackers from attacking Game Theory helps for a better understanding of the Security problem ! Game Theory in Communication Systems41

43. / 34  A certain number of issues ◦ Costs model  Not based on solid ground ◦ Mixed strategy equilibrium  How to interpret it? ◦ Nash equilibrium computation  In general difficult to compute Game Theory for Airport Security ARMOR (LAX) Airports create security systems and terrorists seek out breaches. Placing checkpointAllocate canine units Game Theory in Communication Systems42

44. / 34 Repeated versions of the games – More realistic models – Applications: Attack Graphs Collaborative Security – Team of Attackers vs Team of Defenders – Trust and Security – Role of Information Security of Cloud Computing – Are you willing to give away your information? Policing the Internet – Who is responsible for security flaws? Game Theory in Communication Systems43

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