Strategic Information Acquisition in Auctions

1. Strategic Information Acquisition in Auctions Kate Larson Carnegie Mellon University Pittsburgh, PA

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. 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. Introduction • Classic game theory makes many assumptions it often ignores computational and communication issues Agents are assumed to be fully rational! Hard problems Time constraints Cost

5. Classical Auction (x(b1,b2), p(b1,b2)) price Bid 1, b1 Bid 2, b2 allocation Value 2, v2 Value 1, v1 Agent 2 Agent 1

6. Package Delivery and Vehicle Routing Chicago to Pittsburgh Toronto to Pittsburgh Chicago Chicago to Toronto The delivery route can be computed. Pittsburgh 2 4 1 3 Pittsburgh to Chicago Depot 5 Toronto

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

8. Database Queries How many reviewers liked the product? How many reviewers did not like it? Is there an equivalent product which has better reviews? Product Review Database Cost per query V?

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. Our Approach Resource Bounded Reasoning from AI Game Theory and Mechanism Design Normative model of bounded rationality. Mechanism design for computationally bounded agents.

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. Game Theory Background • Game has a • Set of agents, I • Each agent i has a set of strategies, Si • 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 ui:O • Each agent tries to choose a strategy that maximizes its utility

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. Auction Design • Agents have quasi-linear preferences • Auction Mechanism • It is possible to design auction mechanisms to obtain certain properties. • Efficiency, revenue maximising, … Ui(o,i)=vi(x, I)+ti M=(S1,…,Sn,x(),t1(),…,tn()) Transfers Strategy spaces Allocation rule

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. Deliberative Agents • We assume agents must computeorgather informationto 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. Solution quality Optimum Computing time Performance Profiles • Performance profile deliberation control has been well studied in AI. [Hansen and Zilberstein 96] Solution quality [Dean and Boddy 91] Computing time P(B|A) 5 B 4 4 P(1) 10 A P(2) 0 7 Solution Quality C P(3) P(C|A) 15 2 5 20 Value Node [Larson and Sandholm 01] Random Node

18. Auction for Computationally Bounded Agents Auctioneer (allocation, price) bid bid agent agent Deliberation controller (performance profile) Deliberation controller (performance profile) compute result compute result Domain problem solver (anytime algorithm) Domain problem solver (anytime algorithm)

19. Deliberation Equilibria • An agent’s strategyconsists of both deliberating and (bidding) actions si=(it) where it:H(t)DxA D = set of deliberative actions A = set of non-deliberative (bidding) actions H(t) = set of histories are time t There are no restrictions on which problems an agent is allowed to deliberate on

20. Deliberation Equilibria A (Nash, dominant, perfect Bayesian..) deliberation equilibrium is a (Nash, dominant, perfect Bayesian..) equilibrium, where the strategies include agents’ deliberation.

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

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. 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. Revelation Principle Revelation Principle still applies: Agents will truthfully reveal their types in equilibrium, Algorithms, cost functions, performance profiles… (x,p) Mechanism Algorithms, cost functions, performance profiles… However, the mechanism is doing all the deliberation for the agents!

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. 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. 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. 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… If 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. 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. 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. 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. 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. Conclusions

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 ui(o(s))

37. Miscomputing Ratio 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. 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. 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. Conclusions • Simply placing restrictions on agents’ capabilities may not be enough

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. Papers can be found at http://www.cs.cmu.edu/~klarson