Game Theory in Communication Systems

1. Game Theory in Communication Systems Budhaditya Pyne BEE-IV Roll No: 000910801081 Jadavpur University

2. Topics • 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 Systems

3. What is Game Theory? Game Theory in Communication Systems

4. Game Theory “…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 Systems

5. Game Theory: A Little History • 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 Game Theory in Communication Systems

6. Game Theory Basics • GAME = (P,A,U) • Players (P1; … ; PN): Finite number (N≥2) of decision makers. • Action sets (A1; … ;AN): player Pi has a nonempty set Ai of actions. • Payoff functions ui : A1x … xAN: 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 Systems

7. Types of Games • Cooperative and Non-Cooperative • Symmetric and Asymmetric • Zero-Sum and Non-Zero Sum • Simultaneous and Sequential • Static and Dynamic Game Theory in Communication Systems

8. A well-known example: The Prisoner’s Dilemma Game Theory in Communication Systems

9. Strategizing!!: The Min-Max Algorithm • What should Prisoner A do to minimize his maximum punishment when: • Prisoner B confesses? • Prisoner B stays quiet? • What should Prisoner B do to minimize his maximum punishment when: • Prisoner A confesses? • Prisoner A stays quiet? Game Theory in Communication Systems

10. The Prisoner’s Dilema Contd.. Game Theory in Communication Systems

11. Application of Game Theory in Communication Systems • Routing, Congestion Control and Channel Access • Network Security Game Theory in Communication Systems

12. An Inevitable Question!!! • How do we apply an abstract Mathematical Tool like Game Theory in something as realistic like Communication Systems? Game Theory in Communication Systems

13. An Interesting Analogy •  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 Systems

14. Non-Cooperative Game Theory in Wireless Networks Research Game Theory in Communication Systems

15. Medium Access Games for 802.11 WLAN • 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. Game Theory in Communication Systems

16. Power Control Games in CDMA systems • 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 Control may be: • Centralized • Distributed Game Theory in Communication Systems

17. Power Control Games in CDMA systems •  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 Systems

18. Cooperative/Coalitional Game Theory in Wireless Networks Research • 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 Systems

19. Routing in Max-Min Fair Networks: A Game Theoretic Approach • 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 Systems

20. Routing in Max-Min Fair Networks: A Game Theoretic ApproachContd… •  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 Systems

21. Routing Games vs Congestion Control Games • Routing games • users determine network routes • multi-path routing and traffic splitting is possible • users’ data rates are given and must be routed • Congestion games • users determine their data rate • network routes are given (single path) Game Theory in Communication Systems

22. Game Theory in Network Security Game Theory in Communication Systems

23. Who is attacking our communication Systems? Hacktivists Hackers Terrorists, Criminal Groups Foreign Governments Disgruntled Insiders ? Game Theory in Communication Systems

24. Why Game Theory for Security? Example: Remote Attack E.g.: Rate of Port Scanning IDS Tuning Traditional Security Solutions Defender: strategy 1 strategy 2 ….. Attacker strategy 1 strategy 2 ….. Attack Defense A mathematical problem!  Solution tool: Game Theory Predict players’ strategies, Build defense mechanisms, Compute cost of security, Understand attacker’s behavior, etc… Security Game Theory also helps: Trust Incentives Externalities Machine Intelligence Game Theory in Communication Systems

25. Key Concepts Example: Forwarder’s dilemma Forwarding has an energy cost of c (c<< 1) Successfully delivered packet: reward of 1 If Greendrops and Blueforwards: (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 Systems

26. Actions ofGreen Actions of Blue Reward ofGreen Reward of Blue Key Concepts Example: Forwarder’s dilemma Game: Players: Green, Blue Actions: Forward (F), Drop (D) Payoffs: (1-c,1-c), (0,0), (-c,1), (1,-c) Matrix representation: Game Theory in Communication Systems

27. Equilibrium Concept 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…” Game Theory in Communication Systems

28. 3 Communication Security Game Models Intruder Game Normal traffic a Xn Intelligent Virus Virus b Detection If Xn > l => Alarm Availability Attack Game Theory in Communication Systems

29. Intruder Game Scenario: Network M Source (Alice) User (Bob) M’ ¹ M M What if it is possible that: Intruder (Trudy) Encryption is not always practical …. Formulation: Game between Intruder and User Game Theory in Communication Systems

30. Intruder Game: Binary Trudy Bob Alice Z Intercept Y • Strategies (mixed i.e. randomized) • Trudy: (p0,p1), Bob: (q0,q1) • Payoffs: • One shot, simultaneous choice game • Nash Equilibrium? Game Theory in Communication Systems

31. What if the receiver (Bob) can verify the message?(by paying a cost and using a side secure channel) Pay: V Game Theory in Communication Systems

32. Intelligent Virus Game Scenario Normal traffic Xn a Virus b Detection If Xn > l => Alarm, …. Assume a known Virus: choose b to maximize infection cost Detection system: choose l to minimize cost of infection + clean up Game Theory in Communication Systems

33. Intelligent Virus Game (IDS) Scenario Normal traffic Xn a Virus b Detection If Xn > l => Alarm, …. Smart virus designer picks very large b, so that the cost is always high …. Regardless of l! Game Theory in Communication Systems b

34. Intelligent Virus Game (IPS) Modified Scenario Normal traffic Xn a Detection Virus b If Xn > l => Alarm • Detector: buffer traffic and test threshold • Xn < l  process • If Xn > l Flush & Alarm • Game between Virus (b) and Detector (l) Game Theory in Communication Systems

35. Availability Attack Models! Tree-Link Game: Game Theory in Communication Systems

36. Tree-Link Game • 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 TϵƬ of the network • The attacker simultaneously chooses a link eϵ€ to attack • The attacker wins if the attacked link belongs to the chosen spanning tree; the Defender wins elsewise Game Theory in Communication Systems

37. Model Example: • 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:-1eT • Attacker: 1eT - µe(µe cost of attacking e) Defender: 0 Attacker: - µ2 Defender: -1 Attacker: 1- µ1 • 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 Systems

38. Assume: zero attack cost µe=0 Let’s Play a Game! Graph Most vulnerable links a) 1/2 Chance 1/2 b) 1/2 1/7 1/7 1/7 Chance 4/7>1/2 c) 1/7 1/7 1/7 1/7 Game Theory in Communication Systems

39. Critical Subset of Links 1 2 4 3 7 6 5 (G)=1 (G)=1/2 (G)=4/7 • Definition 1&2: For any nonempty subset E Ε • 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 Εis said to be critical if • (C) = maxE Ε((E)) • (C has maximum vulnerability) • vulnerability of graph ((G)):= vulnerability of critical subset E={1,4,5} |T  E|=2 M(E) =1 (E) = 1/3 Defender: choose trees that minimally cross critical subset Game Theory in Communication Systems

40. Critical Subset Attack Theorem • 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 Systems

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

42. Conclusion Game Theory helps for a better understanding of the Security problem! 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 in Communication Systems

43. This is an “young” research field! • 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 checkpoint Allocate canine units Game Theory in Communication Systems

44. Further Scope of Research • 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 Systems

45. Thank you!Questions? Game Theory in Communication Systems