Algorithms, Games and the Internet Christos H. Papadimitriou UC Berkeley

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

SODA: January 8, Goal of CS Theory ( ): 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, 20014

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, 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, )

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

SODA: January 8, ,-1-1,1 1,-1 0,00,00,10,1 1,01,0-1,-1 3,33,30,40,4 4,04,01,11,1 matching penniesprisoner’s dilemma chicken auction 1 … n 1..n1..n u – x, 0 0, v – y

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

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

SODA: January 8, 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,  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 u  i i i i ii def ii i 1 i n1i n i budget balance  v = c ( T [x]) Shapley mechanism i i

SODA: January 8, 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,  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 u  i i i i ii def ii i 1 i n1i n i budget balance  v = c ( T [x]) Shapley mechanism i i

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

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

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

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

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

SODA: January 8, 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 some thoughts on privacy

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