Cooperation, Power and Conspiracies Yoram Bachrach

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

Agenda

UK Elections 2010 ConservativesLabourLib-Dems Required: 326

Alternate Universe Elections ConservativesLabourLiberalsDemocrats Required: 326

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

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

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

The Shapley Value Average contribution across all permutations Contribution $0$1000 $0$

Weighted Voting Games

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 %16.66% ConservativesLabourLiberalsDemocrats %8.33% Split Merge

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

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)

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

Control in Firms

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

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

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

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)

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)

Collusion in Auctions DefinitionVCG ruleProperty Optimal according to reportsAllocation Impact on othersPayments (Bachrach, AAMAS, 2010; Bachrach, Key, Zadimoghaddam, WINE 2010)

Multi-Unit Auctions T=5

Multi-Unit Auctions T=5

Collusion in Auctions T=3

Collusion in Auctions T=4

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

The Collusion Game T=3 Coalition: C v(C) = welfare under optimal collusion

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

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

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.

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.

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%

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

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