Algorithms, Games and the Internet

1. Algorithms, Gamesand the Internet Christos H. Papadimitriou UC Berkeley www.cs.berkeley.edu/~christos

2. Outline • “new” vs. “old theory” • Game Theory • pricing multicast content • the price of anarchy • the economics of clustering • the economics of privacy SODA: January 8, 2001

3. Goal of CS Theory (1950-2000): Develop a mathematical understanding of the capabilities and limitations of the von Neumann computer and its software –the dominant and most novel computational artifacts of that time (Mathematical tools: combinatorics, logic) • What should Theory’s goals be today? SODA: January 8, 2001

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5. The Internet • huge, growing, open, anarchic • built, operated and used by a multitude of diverse economic interests • as information repository: huge, available, unstructured • theoretical understanding urgently needed SODA: January 8, 2001

6. new math for the new Theory? cf: George Boole The Laws of Thought, 1854 Part I: propositional logic, Part II:probability cf: John von Neumann The Report on EDVAC, 1945 Theory of Games and Economic Behavior, 1944 (cf: Alan Turing On Computable Numbers, 1936 Studies in Quantum Mechanics, 1932-35) SODA: January 8, 2001

7. Game Theory Studies the behavior of rational agents in competitive and collaborative situations Osborne and Rubinstein, A Course in GT Kreps, A Course in Microeconomic Theory Hart and Aumann, The Handbook of GT, volumes I and II(III, 2001 to appear) SODA: January 8, 2001

8. Games, games… strategies strategies 3,-2 payoffs random information set SODA: January 8, 2001

9. matching pennies prisoner’s dilemma auction chicken 0, v – y u – x, 0 SODA: January 8, 2001

10. concepts of rationality • undominated strategy • Nash equilibrium • randomized Nash equilibrium (  P?) • perfect equilibrium • subgame perfect equilibrium • focal point    SODA: January 8, 2001

11. Some current areas of algorithmic interest • repeated games (played by automata) and the emergence of cooperation • evolutionary game theory • mechanism design: given an “economic situation,” a concept of rational behavior, and a set of desiderata, design a game that achieves them (e.g, Vickrey auction) SODA: January 8, 2001

12. e.g., pricing multicasts [Feigenbaum, P., Shenker, STOC2000] 52 30 costs {} 21 21 40 70 {11, 10, 9, 9} {14, 8} {9, 5, 5, 3} 32 {23, 17, 14, 9} {17, 10} utilities of agents in the node (u = the intrinsic value of the information agent i, known only to agent i) i SODA: January 8, 2001

13. We wish to design a protocol that will result • in the computation of: • x (= 0 or 1, will i get it?) • v (how much will i pay? (0 if x = 0) ) • protocol must obey a set of desiderata: i i SODA: January 8, 2001

14. 0  v  u, • lim x = 1 • strategy proofness: (w = u  x  v ) • w (u …u …u )  w (u … u'…u ) • welfare maximization • w = max • marginal cost mechanism i i i u  i def i i i i i i i 1 n 1 i n • budget balance •  v = c ( T [x]) • Shapley mechanism i i SODA: January 8, 2001

15. our contribution: In the context of the Internet, there is another desideratum: Tractability: the protocol should require few (constant? logarithmic?) messages per link. This new requirement changes drastically the space of available solutions. SODA: January 8, 2001

16. 0  v  u • lim x = 1 • strategy proofness: (w = u  x  v ) • w (u …u …u )  w (u … u'…u ) • welfare maximization • w = max • marginal cost mechanism i i i u  i def i i i i i i i 1 n 1 i n • budget balance •  v = c ( T [x]) • Shapley mechanism i i SODA: January 8, 2001

17. Bounding Nash equilibria: the price of anarchy cost of worst Nash equilibrium “socially optimum” cost s t 3/2 [Koutsoupias and P, 1998] general multicommodity network 2 [Roughgarden and Tardos, 2000] SODA: January 8, 2001

18. Some interesting directions: • What is the price of the Internet architecture? • Of which game is TCP/IP a Nash equilibrium? [Karp, Koutsoupias, P., Shenker, FOCS 2000] SODA: January 8, 2001

19. The economics of clustering • The practice of clustering: Confusion, too many criteria and heuristics, no guidelines • The theory of clustering: ditto! • “It’s the economy, stupid!” • [Kleinberg, P., Raghavan STOC 98, JDKD 99] SODA: January 8, 2001

20. Example: market segmentation quantity Segment monopolistic market to maximize revenue q = a – b  p price SODA: January 8, 2001

21. or, in the a – b plane: b Theorem: Optimum clustering is by lines though the origin (hence: O(n ) DP) ? 2 a SODA: January 8, 2001

22. on privacy • arguably the most crucial and • far-reaching current challenge and mission • of Computer Science • least understood (e.g., is it rational?) • www.sims.berkeley.edu/~hal, ~/pam, • [Stanford Law Review, June 2000] SODA: January 8, 2001

23. some thoughts on privacy • also an economic problem • surrendering private information is either good or bad for you • personal information is intellectual property controlled by others, often bearing negative royalty • selling mailing lists vs. selling aggregate information: false dilemma • Proposal: Take into account the individual’s utility when using personal data for decision-making SODA: January 8, 2001

24. e.g., marketing survey [with Kleinberg and Raghavan] “likes” • company’s utility is proportional to the majority • customer’s utility is 1 if in the majority • how should all participants be compensated? customers possible products SODA: January 8, 2001