- Slides: 9
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 • 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?
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.
Why doesn’t this work for competitors? • Example: (Maskin) 2 bidders, one object. Only bidder 1 observes signal s 1: • Values: v 1(s 1) = 2 s 1 - 1; v 2(s 1) = 3 s 1 – 2 • Efficiency: bidder 1 gets the object if 1/2 < s 1 < 1; bidder 2 if s 1 > 1 • Incentive constraints (for human/non-team) bidders: Let ½<s’<1<s”. The constraints for truthful revelation are • t 1(s’’)>2 s”-1 + t 1(s’); 2 s’-1 + t 1(s’) >t 1(s”) • But these are inconsistent (s’-s”)>0…
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?
To whom to pass? (a simplified view: ) Auctions with scoring rules . 5!. 6. 4! . 5. 3 . 9!
Matching • Matching problems generalize auctions to cases in which forming groups of agents may be important, and there 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)
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?
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 firstbest solutions…