Workshop on Auction Theory and Practice Carnegie Mellon University 1 Strategic Information...

Workshop on Auction Theory and Practice Carnegie Mellon University

1

Strategic Information Acquisition in Auctions

Kate Larson Carnegie Mellon University

Pittsburgh, PA


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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!

CostTime

constraintsHard

problems


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Classical Auction

Agent 1 Agent 2

Value 1, v1

Value 2, v2

(x(b1,b2), p(b1,b2))

Bid 1, b1 Bid 2, b2allocation

price


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Package Delivery and Vehicle Routing

Chicago to Pittsburgh

Chicago to Toronto

Pittsburgh to Chicago

Chicago

Toronto

Pittsburgh

Depot

23 4

5

1

The delivery route can be computed.

Toronto to Pittsburgh


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Package Delivery and Vehicle Routing

Chicago to Pittsburgh

Chicago to Toronto

Pittsburgh to Chicago

Chicago

Toronto

Pittsburgh

Depot

Toronto to Pittsburgh

12

3

4

5The new package can be easily fit into the delivery route. The cost can be kept low, and thus the bid also.


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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?


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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.


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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?


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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


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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….


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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())

Allocation rule TransfersStrategy spaces


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Three Questions



auctions?



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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)


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Performance Profiles

• Performance profile deliberation control has been well studied in AI.

Computing time

Solution quality

Optimum 0.4 0.7

0.5 0.3 0.3

0.5 0.3 0.0

Computing time

Solution quality

0

4

2

45

10

7

15

20

A

P(B|A)B

5

CP(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]


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Auction for Computationally Bounded Agents

Auctioneer

agent

resultcompute

agent

resultcompute

bid bid

(allocation, price)

Deliberation controller

(performance profile)

Deliberation controller

(performance profile)

Domain problem solver

(anytime algorithm)

Domain problem solver

(anytime algorithm)


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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

si=(it)

where

it:H(t)DxA

There are no restrictions on which problems an agent is allowed to deliberate on


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Deliberation Equilibria

A (Nash, dominant, perfect Bayesian..) deliberation equilibrium is

a (Nash, dominant, perfect Bayesian..) equilibrium,

where the strategies include agents’ deliberation.


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Three Questions



auctions?



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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


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Auctions and Strategic Deliberating

yesyesno

Generalized VickreyOn which agent, bundle pair to allocate next computation step ?

Multiple items for

sale

noAscending yes

yes

no

nonoVickrey (2nd price sealed bid)

yesDutch (1st price descending) yesyes

yesyesyesFirst price sealed-bidSingle item for

sale

Costly Deliberation

Limited Deliberation

Strong strategic DeliberatingCounter-speculation by

rational agents ?

Auctionmechanism

[Larson and Sandholm 2001b, Larson and Sandholm 2001c]


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Three Questions



auctions?



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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….)


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Revelation Principle

Revelation Principle still applies:

Agents will truthfully reveal their types in equilibrium,

(x,p)

Algorithms, cost functions, performance profiles…

Algorithms, cost functions, performance profiles…

Mechanism

However, the mechanism is doing all the deliberation for the agents!


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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.


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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.


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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…


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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.


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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.


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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


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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.


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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.


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Conclusions


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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 WelfareSW(o(s))=I ui(o(s))


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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


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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


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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.


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Conclusions

• Simply placing restrictions on agents’ capabilities may not be enough

Restriction Strategic Behavior

Social Welfare

Free computing with deadlinesCostly Computing


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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.


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• Papers can be found at

http://www.cs.cmu.edu/~klarson

Workshop on Auction Theory and Practice Carnegie Mellon University 1 Strategic Information...

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