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Outline Privacy Collaborative Game Theory Clustering. Christos H. Papadimitriou with Jon Kleinberg and P. Raghavan www.cs.berkeley.edu/~christos. What is privacy?. one of society’s most vital concerns central for e-commerce arguably the most crucial and far-reaching - PowerPoint PPT Presentation

Christos H. Papadimitriouwith Jon Kleinberg and P. Raghavanwww.cs.berkeley.edu/~christosOutlinePrivacyCollaborative Game TheoryClustering

CS206: May 9, 2002

What is privacy?one of societys most vital concernscentral for e-commercearguably the most crucial and far-reaching current challenge and mission of CSleast understood scientifically (e.g., is it rational?) see, e.g., www.sims.berkeley.edu/~hal, ~/pam, [Stanford Law Review, June 2000]

CS206: May 9, 2002

also an economic problemsurrendering private information is either good or bad for youexample: privacy vs. search costs in computer purchasingsome thoughts on privacy

CS206: May 9, 2002

personal information is intellectual property controlled by others, often bearing negative royaltyselling mailing lists vs. selling aggregate information: false dilemmaProposal: Take into account the individuals utility when using personal data for decision-makingthoughts on privacy (cont.)

CS206: May 9, 2002

e.g., marketing surveycustomerspossibleversions of productlikes companys utility is proportional to the majority customers utility is 1 if in the majority

how should all participants be compensated?e.g. total revenue: 2m = 10

CS206: May 9, 2002

Collaborative Game TheoryHow should A, B, C split the loot (=20)?We are given what each subset can achieve by itself as a function v from the powerset of {A,B,C} to the reals v({}) = 0Values of vA:10B:0C:6AB:14BC:9AC:16ABC:20

CS206: May 9, 2002

first idea (notion of fairness): the coreA vector (x1, x2,, xn) with i x i = v([n]) (= 20)is in the core if for all S we have x[S] v(S)In our example:A gets 11, B gets 3, C gets 6

Problem: Core is often empty (e.g., AB 15)

CS206: May 9, 2002

second idea: the Shapley valuexi = E(v[{j: (j) (i)}] - v[{j: (j) < (i)}])Theorem [Shapley]: The Shapley value is theonly allocation that satisfies Shapleys axioms.(Meaning: Assume that the agents arrive at random. Pay each one his/her contribution.Average over all possible orders of arrival.)

CS206: May 9, 2002

In our exampleA gets:10/3 + 14/6 + 10/6 + 11/3 = 11B gets:0/3 + 4/6+ 3/6 +4/3 = 2.5C gets the rest = 6.5NB: Split the cost of a trip among hostsValues of vA:10B:0C:6AB:14BC:9AC:16ABC:20

CS206: May 9, 2002

e.g., the UN security council5 permanent, 10 non-permanentA resolution passes if voted by a majority of the 15, including all 5 Pv[S] = 1 if |S| > 7 and S contains 1,2,3,4,5;otherwise 0 What is the Shapley value (~power) of each P member? Of each NP member?

CS206: May 9, 2002

e.g., the UN security councilWhat is the probability, when you are the 8th arrival, that all of 1,,5 have arrived?Ans: Choose(10,2)/Choose(15,7) ~ .7%Permanent members: ~ 18%

Therefore, P NP

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third idea: bargaining setfourth idea: nucleolus ...seventeenth idea: the von Neumann-Morgenstern solution[Deng and P. 1990] complexity-theoreticcritique of solution concepts

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Applying to the market survey problemSuppose largest minority is rAn allocation is in the core as long as losers get 0, vendor gets > 2r, winners split an amount up to twice their victory margin(plus another technical condition saying that split must not be too skewed)

CS206: May 9, 2002

market survey problem: Shapley valueSuppose margin of victory is at least > 0%(realistic, close elections never happen in real life)Vendor gets m(1+ )Winners get 1+ Losers get (and so, no compensation is necessary)

CS206: May 9, 2002

e.g., recommendation systemEach participant i knows a set of items BiEach benefits 1 from every new itemCore: empty, unless the sets are disjoint!Shapley value: For each item you know, you are owed an amount equal to 1 / (#people who know about it)--i.e., novelty pays

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e.g., collaborative filteringEach participant likes/dislikes a set of items(participant is a vector of 0, 1)The similarity of two agents is the inner product of their vectorsThere are k well separated types (vectors of 1), and each agent is a random perturbation and random masking of a type

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collaborative filtering (cont.)An agent gets advice on a 0 by asking the most similar other agent who has a 1 in that positionValue of this advice is the product of the agents true value and the advice.How should agents be compensated (or charged) for their participation?

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collaborative filtering (result)Theorem: An agents compensation (= value to the community) is an increasing function of how typical (close to his/her type) the agent is.

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The economics of clusteringThe practice of clustering: Confusion, too many criteria and heuristics, no guidelines

Its the economy, stupid! [Kleinberg, P., Raghavan STOC 98, JDKD 99] The theory of clustering: ditto!

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pricequantityq = a b pExample: market segmentationSegment monopolistic market to maximize revenue

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or, in the a b plane:ab?Theorem: Optimumclustering is by linesthough the origin(hence: O(n ) DP)2

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SoPrivacy has an interesting (and,I think, central) economic aspectWhich gives rise to neat math/algorithmic problemsArchitectural problems wide openAnd clustering is a meaningful problem only in a well-defined economic context

CS206: May 9, 2002