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Auction Mechanisms for Robot Coordination Boston July 17, 2006

Auctions +? Al Roth Dept of Economics, Harvard and Harvard Business School http://www.economics.harvard.edu/~aroth/alroth.html. Auction Mechanisms for Robot Coordination Boston July 17, 2006. Can robot teams.

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Auction Mechanisms for Robot Coordination Boston July 17, 2006

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  1. Auctions +?Al RothDept of Economics, Harvard and Harvard Business Schoolhttp://www.economics.harvard.edu/~aroth/alroth.html Auction Mechanisms for Robot CoordinationBoston July 17, 2006

  2. Can robot teams • Use auctions and related allocation tools more effectively than is possible for competitors? • Use more general kinds of auctions (e.g. auctions with scoring rules) to solve simple matching problems involving forming workgroups? • Use matching technology to solve more complex tasks that require collaboration? • Use auctions to select among tasks?

  3. When can team members with different information coordinate better than competing individuals? • E.g. when one person has information that determines the value of an object to be allocated • For example, my wife and I have no trouble allocating the car, even if she is the only one who knows in the morning whether I will need it. • In such a case we can do better than in a simple auction in which each agent only bids for himself. • E.g. each agent could submit values for the agents whose value he knows.

  4. Why doesn’t this work for competitors? • Example: (Maskin) 2 bidders, one object. Only bidder 1 observes signal s1: • Values: v1(s1) = 2s1 - 1; v2(s1) = 3s1 – 2 • Efficiency: bidder 1 gets the object if 1/2 < s1 < 1; bidder 2 if s1 > 1 • Incentive constraints (for human/non-team) bidders: Let ½<s’<1<s”. The constraints for truthful revelation are • t1(s’’)>2s”-1 + t1(s’); 2s’-1 + t1(s’) >t1(s”) • But these are inconsistent (s’-s”)>0…

  5. More general auctions:Matching for robot soccer? • To whom to pass? • Each potential pass receiver can calculate a probability of scoring a goal • The passer can calculate the probability of a successful pass to each receiver • Whom to guard?

  6. .5! .6 .5 .3 .9! To whom to pass? (a simplified view:) Auctions with scoring rules .4!

  7. Matching • Matching problems generalize auctions to cases in which forming groups of agents may be important, and there are agents with information on both sides of the transaction, and/or big externalities e.g. • Labor market matching • Doctors: NRMP and fellowship matches • Matching children to schools • NYC high schools and Boston Public Schools • Kidney Exchange • New England Program for Kidney Exchange • Ohio • National? • Often, the solution is constrained by the incentives of the agents (who aren’t teams with one objective)

  8. Auctions for general (intra-robot?) decision making in AI? • Modeling the allocation of attention; i.e. using auctions to select a task. • E.g. how do you decide what to do when • you are hungry, • but your foot is on fire?

  9. Much of market design is shaped by incentive constraints • The difficult problems in team coordination markets will be (just:) those concerning • Asymmetric information (e.g. I have information relevant to determining your values) • Externalities (e.g. congestion) • Markets for team decisions will have more chance of being able to implement first-best solutions…

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