A Principled Study of Design Tradeoffs for Autonomous Trading

AgentsIoannis A. Vetsikas Bart Selman

Cornell University

Agents’ Preferences

• Bidders have preferences for bundles of items– Complementarities

• Combination of goods is valued more than sum of values of individual goods : V({a,b})>V({a})+V({b})

• e.g. having a VCR and a TV together

– Substitutability• Combination of goods is valued less than sum of

values of individual goods : V({a,b})<V({a})+V({b})• e.g. having a Dell or a Gateway computer

• One formulation: Combinatorial Auctions

Bidding in Simultaneous Auctions

• Goods are traded independently• Different rules for each auction (potentially)

• Main issue: Participants need to speculate on behavior of other agents

• How aggressively does one bid, when and what for?

• Having a plan flexible enough to handle contingencies

• Best solution is relative to other players strategies

Trading Agent Competition (TAC)

• General problem capturing several issues of bidding in simultaneous auctions

• Provides a universal testbed for researchers

• Travel agents– Working on behalf of 8 customers each– Arranging for a trip to Tampa

• round-trip flight tickets• hotel accommodations• entertainment tickets

– GOAL: Maximize profit

TAC

url://www.sics.se/tac

White Bear General Architecture

Follows the SMPA architecture (loosely)

While (not end of game){ Get price quotes Calculate estimates & statistics Planner (Formulate desired plan) Bidder (Bid to implement plan)}Plan : how many goods of each type it is desirable to

allocate to each customer

Decomposing the Problem

Optimizer / Planner

AuctionType 1

PartialBidding

Strategy 1

AuctionType 2

PartialBidding

Strategy 2

AuctionType k

PartialBidding

Strategy k

Agent

Agent Components

• OPTIMIZER– INPUT: Price information from bidders

(and client preferences from original game data)– OUTPUT: Quantities of each good to be bought– METHOD: Solve optimization problem

• BIDDERS (for each auction type)– INPUT: Quantities to be bought and

pricing information from auctions

– OUTPUT: Bid Price and Bid Placement Time– METHOD: Determine strategies and experiment

to find “best” strategy profile

Determining Partial Strategies

• Determine “boundary strategies”– E.g. minimum and maximum price for the

bid, if bid price is the issue

• Determine “intermediate strategies”– By modifying boundary strategies– By combining boundary strategies– By using a strategy that constitutes an

equilibrium for a simpler but similar game

Bidding Strategies – HotelsISSUE: Bid Price

Dilemma:• If not aggressive, could get outbid and lose

rooms needed– will get outbid by other agents and lose utility

for not implementing the plan and for unused resources

• If too aggressive, prices will skyrocket and the agent’s score will get hurt more than other agents’ scores– All agents’ scores are hurt– But this hurts the agent more, since rooms it

desires will have an increased price

Bidding Strategies – Hotels (cont.)

1. Low aggressiveness : (boundary str.) Bids higher than the current ask price by an

increment2. High aggressiveness : (boundary str.)

Bids for all rooms progressively closer to the marginal utility

3. Medium aggressiveness : (intermediate str.) Combines two previous strategies For critical rooms (rooms with high marginal

utility) the bid is close to the marginal utility For all other rooms it bids an increment above

the current price (the increment increases as time passes)

Bidding – Plane TicketsISSUE: Time of Bid Placement

Dilemma:– To bid early in order to get the cheapest tickets– Or to bid later in order not to limit its options

Solution:• Bid for some of the tickets at the beginning• Bids for the rest after some hotel room auctions have

closed• Strategies: Which tickets are bought at the beginning

Bidding – Plane Tickets (cont.)

1. Late Bidder: (boundary str.) Buy at the beginning only tickets that are

“certain” to be used Buying nothing at the beginning is a clearly

inefficient strategy in this setting, so it is not used as a boundary strategy

2. Early Bidder: (boundary str.) Buy all tickets at the beginning

3. Strategic Bidder : (intermediate str.) Modifies “Early Bidder” boundary strategy Uses “Strategic Demand Reduction” [Weber

’97] Buy all tickets at the beginning, except the

ones that are “highly likely not to be used”

Exploring Strategy Space• Determine the best partial strategy for one

particular auction type– Keep all other partial strategies fixed– Use a fixed number of agents using intermediate

strategies– Vary the mixture of agents using boundary

strategies

• Explore strategy space systematically– Use several experiments to evaluate the

strategies for different auction types– Use the best partial strategies found in the

previous experiments as the strategies that are kept fixed in each experiment

– Stop when experiments “converge”

Experiment 1

0

500

1000

1500

2000

2500

3000

Less Aggressive More Aggressive Agents

Av

g S

co

re

Low Aggressiveness

Medium Aggressiveness

High Aggressiveness

A mildly aggressive agent usually performs better than agents with high or low aggressiveness

Experiment 2

1800

1900

2000

2100

2200

2300

2400

2500

0 2 4 6 Numbe r of Early-bidding age nts

Av

g. S

co

re

s

Late-bidding(med. aggr)

Late-bidding(high aggr)

Strategic(med. aggr)

Strategic(high aggr)

Early-bidding(med. aggr)

Early-bidding(high aggr)

The strategically bidding agents perform best overall

Experiment 3

2300

2350

2400

2450

2500

2550

2600

2 4 6 Num be r of Aggre s s ive Age nts

Avg

. Sco

re

M ed. A ggr(Strategic)

M ed. A ggr(Early B idder)

High A ggr(Strategic)

High A ggr(Early B idder)

The medium aggressiveness agent performs best overall

However the difference is not always significant

Some Comments

Overall the medium and high aggressiveness versions perform the best– But the medium aggressiveness agent is

more consistent in general Overall the strategic agent versions

perform the best– The early bidder is significantly better than

the late bidder In general you win when you are “going

against the tide”, i.e. being aggressive when most other agents are not

White Bear General Observations

• Planner is adaptive, versatile, fast and robust• Agent uses both principled methods and

approaches guided by the knowledge acquired by observing the behavior of the games and combines both seamlessly

• The agent used in TAC was the strategic agent with medium aggressiveness

• Agent White Bear always ranks in the top three agents in all the competition rounds of the Trading Agent Competition

TAC 2002 Final Scores

# Agent Score

1 WhiteBear 3556

2 Southampton 3492

3 Thalis 3351

4 UMBCTAC 3321

5 Walverine 3316

6 livingagents 3310

7 kavayaH 3250

8 cuhk 3248

• 19 institutions in the preliminaries

• 16 in the semi-finals

• 8 in the finals

• White Bear was 1st in the final

Related Work

• Examined the behavior of agents bidding for N similar items in an Nth price auction to find Bayes-Nash equilibria for the bid prices

• Examined the effect that better price prediction has on the performance of the agent– Using historical price information definitely improves

performance– More intelligent price prediction showed minimal

improvement

• Examined ways to reduce the number of games per experiment needed in order to derive accurate conclusions