1. Workshop on Auction Theory and Practice Carnegie Mellon University 1 Strategic Information Acquisition in Auctions Kate Larson Carnegie Mellon University Pittsburgh, PA

2. Workshop on Auction Theory and Practice Carnegie Mellon University 2 Introduction Recently there has been a lot of interest in auctions and auction design –Fueled by interesting problems that appear in auction design when computational issues are considered Computational and communication complexity, approximation issues, preference elicitation, selling of digital goods…

3. Workshop on Auction Theory and Practice Carnegie Mellon University 3 Introduction Auctions are useful mechanisms for allocating items Tasks, resources, goods… Well studied by game theorists and economists There are tools and techniques that can be used to guarantee certain properties incentive compatibility, efficiency, revenue maximization…

4. Workshop on Auction Theory and Practice Carnegie Mellon University 4 Introduction Classic game theory makes many assumptions it often ignores computational and communication issues Agents are assumed to be fully rational! Cost Time constraints Hard problems

5. Workshop on Auction Theory and Practice Carnegie Mellon University 5 Classical Auction Agent 1 Agent 2 Value 1, v 1 Value 2, v 2 (x(b 1,b 2 ), p(b 1,b 2 )) Bid 1, b 1 Bid 2, b 2 allocation price

6. Workshop on Auction Theory and Practice Carnegie Mellon University 6 Package Delivery and Vehicle Routing Chicago to Pittsburgh Chicago to Toronto Pittsburgh to Chicago Chicago Toronto Pittsburgh Depot 2 3 4 5 1 The delivery route can be computed. Toronto to Pittsburgh

7. Workshop on Auction Theory and Practice Carnegie Mellon University 7 Package Delivery and Vehicle Routing Chicago to Pittsburgh Chicago to Toronto Pittsburgh to Chicago Chicago Toronto Pittsburgh Depot Toronto to Pittsburgh 1 2 3 4 5 The new package can be easily fit into the delivery route. The cost can be kept low, and thus the bid also.

8. Workshop on Auction Theory and Practice Carnegie Mellon University 8 Database Queries Product Review Database V? Cost per query How many reviewers liked the product? How many reviewers did not like it? Is there an equivalent product which has better reviews?

9. Workshop on Auction Theory and Practice Carnegie Mellon University 9 Valuation Determination and Game Theory Agents need some form of valuation information in order to participate in auctions Obtaining valuation information may involve complicated and expensive computation and information gathering actions Game Theory handles incentives for agents. Deliberation issues must be handled also! Interaction between incentives and deliberating

10. Workshop on Auction Theory and Practice Carnegie Mellon University 10 Our Approach Resource Bounded Reasoning from AI Game Theory and Mechanism Design Normative model of bounded rationality. Mechanism design for computationally bounded agents.

11. Workshop on Auction Theory and Practice Carnegie Mellon University 11 Three Questions How does one incorporate deliberative actions into a game theoretic setting? How do deliberation limitations affect agents’ equilibrium strategies in standard auctions? Is it possible to design mechanisms that have desirable deliberative properties?

12. Workshop on Auction Theory and Practice Carnegie Mellon University 12 Game Theory Background Game has a –Set of agents, I –Each agent i has a set of strategies, S i A strategy is a contingency plan that determines what actions the agent will take for every point in the game –Strategy profile,s, is a vector specifying one strategy for each agent –Outcome,o(s)  O, is determined by the strategy profile –Agents have utility functions u i :O  –Each agent tries to choose a strategy that maximizes its utility

13. Workshop on Auction Theory and Practice Carnegie Mellon University 13 Game Theory Background Equilibria are stable points in the space of strategy profiles –Dominant strategy equilibria: Every agent has a strategy that it is best off following, no matter what everyone else does –Nash Equilibria: No agent has incentive to deviate from its strategy as long as no other agent deviates –Bayes Nash Equilibrium….

14. Workshop on Auction Theory and Practice Carnegie Mellon University 14 Auction Design Agents have quasi-linear preferences Auction Mechanism It is possible to design auction mechanisms to obtain certain properties. –Efficiency, revenue maximising, … U i (o,  i )=v i (x,  I )+t i M=(S 1,…,S n,x(),t 1 (),…,t n ()) Allocation rule Transfers Strategy spaces

15. Workshop on Auction Theory and Practice Carnegie Mellon University 15 Three Questions How does one incorporate deliberative actions into a game theoretic setting? How do deliberation limitations affect agents’ equilibrium strategies in standard auctions? Is it possible to design mechanisms that have desirable deliberative properties?

16. Workshop on Auction Theory and Practice Carnegie Mellon University 16 Deliberative Agents We assume agents must compute or gather information to determine their values of the items in the auction. Agents have –Anytime algorithms which allow for a tradeoff between computing time and solution quality –Performance profiles which describe how deliberation changes the solution –Cost functions which limit their deliberative capabilities PP(v(t),t’)=  V(t+t’)|v(t)

17. Workshop on Auction Theory and Practice Carnegie Mellon University 17 Performance Profiles Performance profile deliberation control has been well studied in AI. Computing time Solution quality Optimum 0.40.7 0.50.3 0.50.30.0 Computing time Solution quality 0 4 2 4 5 10 7 15 20 A P(B|A) B 5 C P(C|A) Solution Quality Value Node Random Node P(1) P(2) P(3) [Dean and Boddy 91] [Hansen and Zilberstein 96] [Larson and Sandholm 01]

18. Workshop on Auction Theory and Practice Carnegie Mellon University 18 Auction for Computationally Bounded Agents Auctioneer agent result compute agent result compute bid (allocation, price) Deliberation controller (performance profile) Deliberation controller (performance profile) Domain problem solver (anytime algorithm) Domain problem solver (anytime algorithm)

19. Workshop on Auction Theory and Practice Carnegie Mellon University 19 Deliberation Equilibria An agent’s strategy consists of both deliberating and (bidding) actions D = set of deliberative actions A = set of non-deliberative (bidding) actions H(t) = set of histories are time t s i =(  i t ) where  i t :H(t)  DxA There are no restrictions on which problems an agent is allowed to deliberate on

20. Workshop on Auction Theory and Practice Carnegie Mellon University 20 Deliberation Equilibria A (Nash, dominant, perfect Bayesian..) deliberation equilibrium is a (Nash, dominant, perfect Bayesian..) equilibrium, where the strategies include agents’ deliberation.

21. Workshop on Auction Theory and Practice Carnegie Mellon University 21 Three Questions How does one incorporate deliberative actions into a game theoretic setting? How do deliberation limitations affect agents’ equilibrium strategies in standard auctions? Is it possible to design mechanisms that have desirable deliberative properties?

22. Workshop on Auction Theory and Practice Carnegie Mellon University 22 Impact of Deliberation on Agents’ Strategies Good estimates of other agents’ valuations can allow an agent to tailor its bidding strategy to achieve higher utility Strong Strategic Deliberating: An agent uses some of its computational resources to approximate another’s valuation Weak Strategic Deliberating: An agent uses information from another agent’s performance profile

23. Workshop on Auction Theory and Practice Carnegie Mellon University 23 Auctions and Strategic Deliberating yes no Generalized Vickrey On which  agent, bundle  pair to allocate next computation step ? Multiple items for sale no Ascending yes no Vickrey ( 2 nd price sealed bid ) yesDutch ( 1 st price descending) yes First price sealed-bidSingle item for sale Costly Deliberation Limited Deliberation Strong strategic Deliberating Counter- speculation by rational agents ? Auction mechanism [Larson and Sandholm 2001b, Larson and Sandholm 2001c]

24. Workshop on Auction Theory and Practice Carnegie Mellon University 24 Three Questions How does one incorporate deliberative actions into a game theoretic setting? How do deliberation limitations affect agents’ equilibrium strategies in standard auctions? Is it possible to design mechanisms that have desirable deliberative properties?

25. Workshop on Auction Theory and Practice Carnegie Mellon University 25 A Revelation Principle for Deliberative Agents Revelation Principle: Any mechanism can be transformed into a direct mechanism where in equilibrium agents truthfully reveal their types. (In classic auction setting, type=valuation) In a deliberative agent setting, define type to be an agents’ entire deliberation technology (algorithms, performance profiles, cost functions….)

26. Workshop on Auction Theory and Practice Carnegie Mellon University 26 Revelation Principle Revelation Principle still applies: Agents will truthfully reveal their types in equilibrium, (x,p) Algorithms, cost functions, performance profiles… Mechanism However, the mechanism is doing all the deliberation for the agents!

27. Workshop on Auction Theory and Practice Carnegie Mellon University 27 Proposed Desirable Properties A mechanism should be non-deliberative. –The mechanism should not deliberate for the agents. A mechanism should be deliberation-proof. –Strategic computing should not occur in equilibrium. A mechanism should be non-deceiving. –Let v be an agent’s (partial) value. In equilibrium the agent should not act in such a way so that all other agents place probability 0 on the event that v is the agent’s actual (partial) value.

28. Workshop on Auction Theory and Practice Carnegie Mellon University 28 Value-Based Mechanisms We restrict analysis to Value-Based mechanisms. The mechanism restricts the strategy space of the agents so that they can only submit messages about their deliberation results (valuations). Agents can not submit algorithms, performance profiles, cost functions etc. to the mechanism. Value based mechanisms are non-deliberative.

29. Workshop on Auction Theory and Practice Carnegie Mellon University 29 A First Result There exist value-based mechanisms which are –Non-deliberative, –Deliberation-proof and –Non-deceiving Any non-sensitive mechanism is deliberation-proof and non-deceiving in a weakly dominant manner. A non-sensitive mechanism is one where the outcome does not depend on any agent’s actions. Dictatorial auctions, auctions that randomly allocate items…

30. Workshop on Auction Theory and Practice Carnegie Mellon University 30 Sensitive Mechanisms There exists no sensitive, value-based direct mechanism that is deliberation- proof across all instances. An instance is defined by agents performance profiles, algorithms, cost functions… I f it is very costly to determine ones own valuations, it may be better to determine the likelihood of being in the final allocation first.

31. Workshop on Auction Theory and Practice Carnegie Mellon University 31 Sensitive Mechanisms Moving to indirect auctions There exists no sensitive value-based mechanism that is non-deliberative, deliberation-proof, and non-deceiving across all problem instances.

32. Workshop on Auction Theory and Practice Carnegie Mellon University 32 Conclusions There are many auction settings where agents do not simply know their valuations Instead, agents may have to use resources to compute/gather information on their values. By not modeling agents’ deliberation actions, designers overlook important issues: –Classical mechanisms may no longer be strategy proof

33. Workshop on Auction Theory and Practice Carnegie Mellon University 33 Conclusions We propose a set of properties which are desirable in auctions for deliberative agents –Non-deliberative –Deliberation-proof –Non-deceiving We can not achieve all three properties in “interesting” auctions.

34. Workshop on Auction Theory and Practice Carnegie Mellon University 34 The Future It may be possible to weaken one of the properties slightly, while still achieving the others –It may be possible to design multi-stage mechanisms that are not non-deliberative. –The mechanism may be able to use some deliberation information to help guide agents in their deliberation decisions.

35. Workshop on Auction Theory and Practice Carnegie Mellon University 35 Conclusions

36. Workshop on Auction Theory and Practice Carnegie Mellon University 36 Impact of Computing on Social Welfare How does valuation computation affect the overall system? I is the set of agents and o(s) is the outcome under strategy profile s Will there be “wasted computation”? Is it better if agents have –Free but limited computation? –Costly computation? Social Welfare SW(o(s))=  I u i (o(s))

37. Workshop on Auction Theory and Practice Carnegie Mellon University 37 Miscomputing Ratio R=SW(o*)/SW(o(NE)) o* is the outcome which occurs if a global controller dictates computing policies so to maximize social welfare o(NE) is the outcome which has the lowest social welfare, among all outcomes that occur in Nash Equilibrium Larson and Sandholm, 2003

38. Workshop on Auction Theory and Practice Carnegie Mellon University 38 Miscomputing Ratio… So, the Miscomputing Ratio compares the social welfare obtained in different situations: 1. Computation is controlled to maximize social welfare 2. Agents compute in their own self interest Isolates selfish computing from traditional strategic behavior: Even in the setting with a centralized controller, the agents are allowed to bid in their own self interest

39. Workshop on Auction Theory and Practice Carnegie Mellon University 39 Miscomputing Ratio Results Free computing but with deadlines: (Allowing agents to freely choose their computing actions can lead to outcomes arbitrarily far from optimal) Costly computing: Miscomputing Ratio can be infinite. Depending on the performance profiles, cost functions can be designed so that the Miscomputing Ratio = 1.

40. Workshop on Auction Theory and Practice Carnegie Mellon University 40 Conclusions Simply placing restrictions on agents’ capabilities may not be enough RestrictionStrategic Behavior Social Welfare Free computing with deadlines Costly Computing

41. Workshop on Auction Theory and Practice Carnegie Mellon University 41 The Future Important research directions –Creating new market mechanisms (auctions, exchanges,…) that are game theoretically engineered to work well with computational agents. –Developing design principles for auction mechanisms for computationally bounded agents.

42. Workshop on Auction Theory and Practice Carnegie Mellon University 42 Papers can be found at http://www.cs.cmu.edu/~klarson