Self-Enforcing Strategic Demand Reduction

Paul S. A. Reitsma1, Peter Stone2, János A. Csirik3, Michael L. Littman4

1Brown University 2U. Texas at Austin 3AT&T Research 4Stowe Research

00.511.522.533.544.55

Bill

ions

of d

olla

rs

Normal PRSDR

Bidding Strategy

Total Profit

Overview

• Complex, high-stakes auctions

• Complex, realistic simulations

• Highly effective strategy

• Robust, stable, simple

• Theoretical issues

Auctions Important

• Tiny toys to giant resources

• Commercial interest

• Theoretical interest– testbed for ideas

• Agents appearing in auctions

FCC Auction #35

• 422 licenses (spectrum blocks)

• 195 markets (major US cities)

• 80 bidders

• 101 rounds

• Dec 12 – Jan 26 2001

FCC Rules

• Theory: more information more efficient– all bids known– current winners known

• Bids: only 1 to 9 bid increments– 10% - 20% of current price

• Eligibility requirements• i.e., complex scenario

Auction Simulator

• FAucS

• Faithful to published rules

• Client-server architecture

• Runs auctions with agents and/or humans

FAucS Agents

• 5 important bidders– modeled individually– input from actual bidder team

• Other 75 served to raise prices– model as 5 secondary bidders– same role price floor 75%

Agent Goals

• Utility is profit

• Separate values per market– based on Merril Lynch data, real bidder input,

real auction analysis– per-agent

• Desire 0-2 licenses per market

• Assume no inter-market dependencies

Uncertain Knowledge

• Estimate other agents’ goals, budget– budget: within 20%– license valuations: within 20%

• per-license, per-agent

– desired licenses / market: 25% chance wrong• even one error can double perceived total desires

General Agent Strategy

• Each round:1. Get prices from server

2. Compute remaining budget, eligibility

3. Compute market values, costs

4. Choose desired licenses within constraints

5. Submit bids to server

Bidding Strategies

• Self-Only– knapsack approach effective

• Strategic Bidding (consider others)– threats– budget stretching– Strategic Demand Reduction (SDR)– explicit communication not allowed…

Randomized SDR

• Determine allocations dynamically– bid for desired licenses– tie-breaking creates allocation– respect allocation; no competition– ignore secondary bidders– don’t waste profit– great expected results

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Mill

ions

of d

olla

rs

1 2 3 4 5

Per-Agent Profit

Normal PRSDR

Luck

• Great expected results

• Random luck

• Unlucky winning little of desires– low satisfaction

• Incentive to defect– lowers expected profits

Fairing

• Unlucky bidder takes licenses until satisfaction near average

• Also bias compensation

• Equitable distribution– Yet, incentive to defect again!

Crime and Punishment

• Temptation to take too much– big profit gain– destroys fairness, destabilizes strategy

• Punish cheater to remove all profit gain– removes incentive– stabilizes strategy– Punishing RSDR

Detection

• Should take licenses only if:1. Low satisfaction rating

2. Punishing a cheater– i.e., focused

• Cheater takes when satisfied

• Cheater takes indiscriminately

• Flawless detection

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Pro

fit

vs. b

asel

ine

Missed Caught

Detection Results

Enforcement EffectsDefector PRSDR

Enforcement Effects

• Large win for uncaught cheater

• All extra profit lost when cheater caught– strong disincentive

• Slight enforcement cost– raises expected profit by dissuading cheating– less aggressive punishment scheme possible– people willing to pay to punish cheaters

Alternative Scenarios

• Change price floor

• PRSDR preserves profit nearly optimally– larger profit margin larger absolute and

relative profit from PRSDR

• Large numbers of defectors– drop back to all-Knapsack without loss

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0.05

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0.35

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0.45

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Fra

ctio

n w

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85% 75% 50%

Price Floor

Wasted Profit

Knapsack PRSDR

Algorithm Overview

1. Bid on desired licenses

2. Tie-breaking creates allocation

3. No competition

4. Fairing balance

5. Auto-punish defectors

6. Punishment removes defection incentive

Improved Auction Design

• Information sources:1. via low prices

2. from auctioneer

• Traditionally, more info greater efficiency• However, more info more strategies

– PRSDR hard to thwart

– less efficiency?

– tradeoffs in auction design

Game Theory

• Analyze as 3-option Prisoner’s Dilemma:1. Cooperate (RSDR)

2. Hedge (PRSDR)

3. Defect (Knapsack)

• Pure Nash equilibrium

• Suggestive, not conclusive, for auction

3 3 0

3 3 2

5 1 1

Real-World Application

• Relies on few assumptions:1. Bidders desire maximum profit

2. Bidders know of PRSDR, benefits

3. Bidders willing to try, risk-free

4. Information available

Conclusions

• Effective• Realistic

– related real strategies– safe to try

• Stable– self-enforcing

• Robust• Fair

Questions?