CMU CS 15892 - Mechanism design for computationally limited agents (15 pages)

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Mechanism design for computationally limited agents



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Mechanism design for computationally limited agents

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15
School:
Carnegie Mellon University
Course:
Cs 15892 - Foundations of Electronic Marketplaces
Foundations of Electronic Marketplaces Documents
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Mechanism design for computationally limited agents previous slide deck discussed the case where valuation determination was complex Tuomas Sandholm Computer Science Department Carnegie Mellon University Part I Mechanisms that are computationally worst case hard to manipulate Voting mechanisms that are worst case hard to manipulate Bartholdi Tovey and Trick 1989 The computational difficulty of manipulating an election Social Choice and Welfare 1989 Bartholdi and Orlin Single Transferable Vote Resists Strategic Voting Social Choice and Welfare 1991 Conitzer V Sandholm T Lange J 2007 When are elections with few candidates hard to manipulate JACM Conitzer V and Sandholm T 2003 Universal Voting Protocol Tweaks to Make Manipulation H ard International Joint Conference on Artificial Intelligence IJCAI Elkin Lipmaa 2nd chance mechanism in paper Computationally Feasible VCG Mechanisms by Nisan Ronen EC 00 JAIR Interesting unrelated fact in the paper that has had lots of follow on research Any VCG mechanism that is maximal in range is IC Observation only way an agent can improve its utility in a VCG mechanism where an approximation algorithm is used is by helping the algorithm find a higher welfare allocation Second chance mechanism let each agent i submit a valuation fn vi and an appeal fn li V V Mechanism using alg k computes k v k li v k l2 v and picks the among those the allocation that maximizes welfare Pricing based on unappealed v Other mechanisms that are worst case hard to manipulate O Connell and Stearns 2000 Polynomial Time Mechanisms for Collective Decision Making SUNYA CS 00 1 Part II Usual case hardness of manipulation Impossibility of usual case hardness For voting Procaccia Rosenschein JAIR 97 Assumes constant number of candidates Impossibility of avg case hardness for Junta distributions that seem hard Conizer Sandholm AAAI 06 Any voting rule any number of candidates weighted voters coalitional manipulation Thm voting rule instance distribution cannot be usually hard to manipulate if It is weakly monotone either c2 does not win or if everyone ranks c2 first and c1 last then c1 does not win and If there exists a manipulation by the manipulators then with high probability the manipulators can only decide between two candidates Elections can be Manipulated Often by Friedgut Kalai Nisan FOCS 08 For 3 candidates Shows that randomly selected manipulations work with non vanishing probability Isaksson Kindler Mossel FOCS 10 For more than 3 candidates Still open directions available Multi stage voting protocols Combining randomization and manipulation hardness Open for other settings Problems with mechanisms that are worst case hard to manipulate Worst case hardness does not imply hardness in practice If agents cannot find a manipulation they might still not tell the truth One solution avenue Mechanisms like the one in Part III of this slide deck Part III Based on Computational Criticisms of the Revelation Principle by Conitzer Sandholm Criticizing truthful mechanisms Theorem There are settings where Executing the optimal truthful in terms of social welfare mechanism is NP complete There exists an insincere mechanism where The center only carries out polynomial computation Finding a beneficial insincere revelation is NP complete for the agents If the agents manage to find the beneficial insincere revelation the insincere mechanism is just as good as the optimal truthful one Otherwise the insincere mechanism is strictly better in terms of s w Holds both for dominant strategies and Bayes Nash implementation Proof in story form k of the n employees are needed for a project Head of organization must decide taking into account preferences of two additional parties Head of recruiting Job manager for the project Some employees are old friends Head of recruiting prefers at least one pair of old friends on team utility 2 Job manager prefers no old friends on team utility 1 Job manager sometimes not always has private information on exactly which k would make good team utility 3 n choose k 1 types for job manager uniform distribution Proof in story form Recruiting 2 utility for pair of friends Job manager 1 utility for no pair of friends 3 for the exactly right team if exists Claim if job manager reports specific team preference must give that team in optimal truthful mechanism Claim if job manager reports no team preference optimal truthful mechanism must give team without old friends to the job manager if possible Otherwise job manager would be better off reporting type corresponding to such a team Thus mechanism must find independent set of k employees which is NP complete Proof in story form Recruiting 2 utility for pair of friends Job manager 1 utility for no pair of friends 3 for the exactly right team if exists Alternative insincere mechanism If job manager reports specific team preference give that team Otherwise give team with at least one pair of friends Easy to execute To manipulate job manager needs to solve NP complete independent set problem If job manager succeeds or no manipulation exists get same outcome as best truthful mechanism Otherwise get strictly better outcome Criticizing truthful mechanisms Suppose utilities can only be computed by sometimes costly queries to oracle u t o u t o 3 oracle Then get similar theorem Using insincere mechanism can shift burden of exponential number of costly queries to agent If agent fails to make all those queries outcome can only get better Is there a systematic approach Previous result is for very specific setting How do we take such computational issues into account in general in mechanism design What is the correct tradeoff Cautious make sure that computationally unbounded agents would not make mechanism worse than best truthful mechanism like previous result Aggressive take a risk and assume agents are probably somewhat bounded Recent results on these manipulation optimal mechanisms in Othman Sandholm SAGT 09


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