1. Cooperation, Power and Conspiracies Yoram Bachrach

2. High Level Vision John McCarthy: “making a machine behave in ways that would be called intelligent if a human we so behaving” (1955) Coordinating Negotiating Strategizing

3. Agenda

4. UK Elections 2010 ConservativesLabourLib-Dems 30625857 Required: 326

5. Alternate Universe Elections ConservativesLabourLiberalsDemocrats 3062582829 Required: 326

6. Treasure Island $200 $1000 Coalition: CValue: v(C)

7. Cooperative Games CooperationCompetition Cannot achieve goal alone Coordination Maximize rewards Increase influence

8. Sharing Rewards – Stable or Shaky? – Is it Fair? requires very valuable $1000 p1p2p3 $50 $900 Dummy agents Equivalent agents Game composition

9. The Shapley Value Average contribution across all permutations Contribution $0$1000 $0$200 266.66366.66

10. Weighted Voting Games

11. Power in the UK Elections Game 1: [306, 258, 57; 326] Game 2: [306, 258, 28, 29; 326] Split makes the Labour less powerful – But the power goes to the Conservatives… – … not the Lib-Dems ConservativesLabourLib-Dems 30625857 66.66%16.66% ConservativesLabourLiberalsDemocrats 3062582829 75%8.33% Split Merge

12. False-Name Power Manipulations AB 22 1/2 ABB’ 211 1/3 q = 4 AB 22 1/2 ABB’ 211 4/61/6 q = 3 Power Increase Power Decrease

13. Effects of False-Name Manipulation Manipulator loss bound Hardness of manipulability It is a hard computational problem to test if a beneficial manipulation exists. Manipulation Gain Bound Quota manipulations: Bounds on quota perturbations influence on power. Hardness of testing which quota is better for a player’s power. (Bachrach & Elkind, AAMAS 2008; Bachrach et al., AAAI 2008)

14. Manipulation Heuristics Heuristic algorithm: try integer splits and approximate power. Tested on random weighted voting games. (Bachrach et al., JAIR 2011)

15. Control in Firms

16. The “Rip-off” Game (Bachrach, Kohli, Graepel, AAMAS 2011)

17. Auctions Valuation / Auction $900$500$400$300 Sealed bid (1 st price) English (ascending) Vickrey (2 nd Price) Speculations Long (increasing) bidding Truthful bidding Truthful Efficient allocation

18. Collusion Collusion: an agreement between several agents to limit competition by manipulating or defrauding to obtain an unfair advantage $900$500$400$300 Truthful$900$500$400$300 Collusion$900$400 $300

19. Sponsored Search Auctions Selling advertisements on search engines. Tailored to users and search queries. Model: Key part of the online business model.Uses: Google, Yahoo, MicrosoftKey players: Microsoft – $2 Billion/year (Bing ads) Google - $25 Billion/year (AdWords, AdSense) Revenue: (Extrapolation, Q1 2010)

20. What Blocks Agreements? $50 $900 Value v(C)Payment p(C)Coalition 200 p1p2p3 $1000 $200 $1000 Potential Blockers: Make sure get at least $200 (1,1,998)

21. Collusion in Auctions 3810 579 246 38 579 246 38 579 246 38 579 246 38 579 246 38 579 246 DefinitionVCG ruleProperty Optimal according to reportsAllocation Impact on othersPayments (Bachrach, AAMAS, 2010; Bachrach, Key, Zadimoghaddam, WINE 2010)

22. Multi-Unit Auctions 3810 579 246 T=5

23. Multi-Unit Auctions 3810 579 246 T=5

24. Collusion in Auctions 18810 8119 8119 0111 T=3

25. Collusion in Auctions 31119 31119 223410 T=4

26. Collusion in Auctions 50099 00000 023410 T=4 Optimal scheme for diminishing marginals: Proxy agent bids for all colluders

27. The Collusion Game 18810 8119 8119 0111 T=3 Coalition: C v(C) = welfare under optimal collusion

28. Games with Diminishing Marginals Fairness and Stability with diminishing marginals Always have non-empty cores (stable imputations). The Shapley value is in the core (fair and stable imputation). C’ C

29. Non-Diminishing Marginals Core PaymentMarginalsNumberType (H,H,0,…,0)a=b+1A (0,…,0)bB 1C Optimal AttackMembers Marginal merging attack (H,H,H,…,H,0), with 2a Hs.All A’s Same as all A’s.A’s and B’s False-name marginal splitting: both declare (H,0,0,…,0).(A,B) pair Type B agents serve as a false-identity Helpful for single A agent, but not for a large set of A’s Empty core – no stable agreement 2a+2 Items

30. Non-Diminishing Marginals Collusion games with arbitrary marginal utility functions – polynomial algorithms: Computing the value (welfare) of a coalition. When all but few agents have identical valuations: compute Shapley value. When there are few valuation functions: test core emptiness.

31. Non-Diminishing Marginals Collusion games with arbitrary marginal utility functions – polynomial algorithms: Computing the value (welfare) of a coalition. When there are few valuation functions: test core emptiness.

32. Collusion in Sponsored Search Auctions Collusion by advertisers Specific keyword market Top 3 advertiser bids for that keyword Appearances in “mainline” Jointly set bids once for the duration Simulate auction FeatureChange Appearances (mainline)-3% Clicks estimate-2% Revenue-30%

33. High Level Vision John McCarthy: “making a machine behave in ways that would be called intelligent if a human we so behaving” (1955) Coordinating Negotiating Strategizing Game Theory Heuristics & Data Analysis Algorithms

34. Conclusion CooperationCompetition Big Challenges Incorporating negotiation and agreement models Understanding human bounded-rational behaviour Designing efficient and attack-resistant mechanisms Scaling up to real-world systems