11 Economics and Computation Econ 425/563 and CPSC 455/555, Fall 2008 Time: Tu & Th, 2:30-3:45 pm Room: BCT 102

22 Topic Outline Review of basic microeconomic theory and basic computational theory Routing in data networks Combinatorial auctions Sponsored search Privacy and security Reputation management

33 Schedule Oct. 2: First HW Assignment Due Oct. 14: Second HW Assignment Due Oct. 16: First Exam (in class) Oct. 24: Fall Semester Drop Date Oct. 30: Third HW Assignment Due Nov. 13: Fourth HW Assignment Due Nov. 20: Fifth HW Assignment Due Dec. 4: Second Exam (in class)

44 Requirements Reading assignments 5 Written HW Assignments, each worth 10% of the course grade 2 In-Class Exams, each worth 25% of the course grade No final exam during exam week

55 Rules and Guidelines Deadlines are firm. Late penalty: 5% per day. Announcements and assignments will be posted on the class webpage (as well as conveyed in class). No “collaboration” on homeworks unless you are told otherwise. Pick up your graded homeworks and exams promptly, and tell the TA promptly if one is missing.

66 Instructor: Dirk Bergemann Office: 30 Hillhouse Avenue, Room 24 Office Hours: Tuesdays, 1:00 - 2:30 pm Phone: Assistant: Megan Carney , 30 Hillhouse Avenue, Room 31)

77 Instructor: Joan Feigenbaum Office: AKW 512 Office Hours: Thursdays 11:30 am - 12:30 pm and by appointment Phone: Assistant: Judi Paige , AKW 507a, 8:30 am – 4:30 pm M-F) Note: Do not send to Professor Feigenbaum, who suffers from RSI. Contact her through Ms. Paige or the TA.

88 TA: Aaron Johnson Office: AKW 406 Office Hours: Weds, 2:30 – 3:30 pm and by appointment

99 If you’re undecided, check out: J. Feigenbaum, D. Parkes, and D. Pennock, “Computational Challenges in Electronic Commerce,” to appear in Communications of the ACM. ( for a preprint) H. Varian, “Designing the Perfect Auction,” Communications of the ACM, 51 (2008), pp (Brief overview of auctions in e-commerce, by the Chief Economist of Google. Search for it on from a machine on the Yale network.) (incentive issues in distributed computation, particularly interdomain routing in the Internet)

10 Questions?

11 Two Views of Multi-agent Systems CSECON Focus is on Computational & Communication Efficiency Agents are Correct, Faulty, or Adversarial Focus is on Incentives Agents are Strategic

12 Internet Computation Both incentives and computational and communication efficiency matter. “Ownership, operation, and use by numerous independent self-interested parties give the Internet the characteristics of an economy as well as those of a computer.”  Decade-long explosion of research in “Econ-CS”

13 Computational Complexity Themes “Easy” vs. “Hard” Reductions (Equivalence) Approximation Randomness, average case Communication, distrib. comp.

14 Poly-Time Solvable Nontrivial Example : Matching

15 Poly-Time Solvable Nontrivial Example : Matching

16 Poly-Time Verifiable Trivial Example : Hamiltonian Cycle

17 Poly-Time Verifiable Trivial Example : Hamiltonian Cycle

18 Is it Easier to Verify a Proof than to Find one? Fundamental Conjecture of Computational Complexity: P  NP

19 Matching: HC: Fundamentally Different Distinctions

20 Reduction of B to A If A is “Easy”, then B is, too. B Algorithm A “oracle” “black box”

21 NP-completeness P-time reduction Cook’s theorem If B ε NP, then B ≤ P-time SAT HC is NP-complete

22 Equivalence NP-complete problems are an equivalence Class under polynomial-time reductions. 10k’s problems Diverse fields Math, CS, Engineering, Economics, Physical Sci., Geography, Politics…

23 Definitions and Notation t 1t 1 t nt n Agent 1 Agent n Mechanism... p 1p 1 a 1a 1 p np n a na n O (Private) types: t 1, …, t n Strategies: a 1, …, a n Payments: p i = p i (a 1, …, a n ) Output: O = O (a 1, … a n ) Valuations: v i = v i (t i, O ) Utilities: u i = v i + p i Agent i chooses a i to maximize u i.

24 “Strategyproof” Mechanism For all i, t i, a i, and a –i = (a 1, …, a i-1, a i+i, … a n ) v i (t i, O (a –i, t i )) + p i (a –i, t i )  v i (t i, O (a –i, a i )) + p i (a –i, a i ) “Dominant-Strategy Solution Concept” Appropriate for analysis of incentives in Internet- based commerce, according to [NR’01]. “Truthfulness”

25 Algorithmic Mechanism Design Polynomial-time computable functions O( ) and p i ( )  Introduced computational efficiency into mechanism-design framework. Centralized model of computation N. Nisan and A. Ronen Games and Economic Behavior 35 (2001), pp

26 Example: Task Allocation Input: Tasks z 1, …, z k Agent i ’s type: t = (t 1, …, t k ) (t j is the minimum time in which i can complete z j.) Feasible outputs: Z = Z 1 Z 2 … Z n (Z i is the set of tasks assigned to agent i.) Valuations: v i (t, Z) = −  t j Goal: Minimize max  t j i i i i i i zj  Z izj  Z i zj  Z izj  Z i iZ i

27 Min-Work Mechanism [NR ’01] O (a 1, …, a n ): Assign z j to agent with smallest a j p i (a 1, …, a n ) =  min a j Theorem: This mechanism is strategyproof and polynomial-time, and the outcome is n-approximately optimal. Notes: In general, approximation destroys str’pfness. Open problems: average cases, distrib. comp. i i’ i  i’ zj  Z izj  Z i