Auctions +? Al Roth Dept of Economics, Harvard and Harvard Business School 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 s1: Values: v1(s1) = 2s1 - 1; v2(s1) = 3s1 – 2 Efficiency: bidder 1 gets the object if 1/2 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…

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?

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

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)

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 first- best solutions…