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Cooperation, Power and Conspiracies

Cooperation, Power and Conspiracies. Yoram Bachrach. High Level Vision. Artificial Intelligence. John McCarthy: “making a machine behave in ways that would be called intelligent if a human we so behaving” (1955). Coordinating. Strategizing. Negotiating. Agenda. UK Elections 2010.

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Cooperation, Power and Conspiracies

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  1. Cooperation, Power and Conspiracies Yoram Bachrach

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

  3. Agenda

  4. UK Elections 2010 Required: 326

  5. Alternate Universe Elections Required: 326

  6. Treasure Island $200 $1000

  7. Cooperative Games

  8. Sharing Rewards $1000 • Stable or Shaky? • Is it Fair? • requires • very valuable p1 p2 p3 Imputation: A payoff vector such that $50 $50 $900 Dummy agents Equivalent agents Game composition

  9. The Shapley Value • Average contribution across all permutations

  10. Weighted Voting Games • Agent has weight • Quota • A coalition C wins if • Shorthand: • A simplegame Power Weight [

  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 Split Merge

  12. False-Name Power Manipulations q = 4 Power Increase q = 3 Power Decrease

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

  14. Manipulation Heuristics (Bachrach et al., JAIR 2011) Heuristic algorithm: try integer splits and approximate power. Tested on random weighted voting games. 95% Manipulability

  15. Control in Firms

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

  17. Auctions Speculations Long (increasing) bidding Truthful bidding Truthful Efficient allocation VCG

  18. Collusion Collusion: an agreement between several agents to limit competition by manipulating or defrauding to obtain an unfair advantage

  19. Sponsored Search Auctions

  20. What Blocks Agreements? < $1000 The Core [Gillies 55’]: Unblocked agreements p1 p2 p3 Potential Blockers: $50 $50 $900 $200 $1000 Make sure get at least $200 (1,1,998)

  21. Collusion in Auctions (Bachrach, AAMAS, 2010; Bachrach, Key, Zadimoghaddam, WINE 2010)

  22. Multi-Unit Auctions T=5

  23. Multi-Unit Auctions T=5

  24. Collusion in Auctions T=3

  25. Collusion in Auctions T=4

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

  27. The Collusion Game T=3 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). • Proof sketch: • Marginal contribution vectors • Centroid is the Shapley value • Convex hull is the Weber set • Contains the core • Weber set identifies with the core for convex games • Adding an agent helps more for large coalitions • The game is convex • Smaller coalitions incur higher payments for the additional player’s items • Denote j’s contribution to is • Show -) • Convexity: • Manipulations of marginal valuation vectors C C’

  29. Non-Diminishing Marginals 2a+2 Items 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

  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. • Proof sketch: • Coalition value: dynamic programs based on optimal collusion scheme for specific amounts of allocated items • Core defined by an exponential LP over : • Can maintain a single variable for each agent type (core and equivalent agents) • Constant number of variables • Coalition profile: number agents of each type • Less than profiles • Constraint for coalition of profile

  31. 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

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

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

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