A Multi-Agent Prediction Market Based on

Boolean Network Evolution

Janyl Jumadinova., Mihaela T. Matache and Prithviraj DasguptaWI-IAT.2011

Presenter: Yu Hsiang HuangDate: 2011-12-09

Outline

• Introduction• Related work• Boolean Network based prediction market• Experiment result• Conclusion

Introduction

• Prediction market• Multi-Agent system• Boolean Network (BN) – Boolean rule(0/1)

• BN vs. LMSR– Eliminate the frequently fluctuating price

Related work

• Prediction Markets• Outcome geopolitical events – US presidential elections• Outcome of sporting events• Predicting the box office performance of Hollywood movies

– Belief• Opinion of individual trader about the outcome of a future event• Market price

Boolean Network-Based Prediction Market

• A. Prediction Market Preliminaries– Major participants in agent-based prediction market

• A set of trading agents• A market maker agent – central entity

– Outcome of an event is binary (will happen/won’t happen)– Trading agent

• At time t• Bet security (bought/sold/held) discrete quantities

– Market maker agent• Aggregate the price at which securities of event traded by agents• Market price – probability of the outcome of the event• Compare market price with actual decision in real world cost

Trading agents

Market maker agent

Trading period t

bet

bet

bet

bet bet

Quantity=10Security(bought)

Quantity=8Security(held)

Quantity=5Security(bought)

Quantity=7Security

(sold)

Quantity=10Security(bought)

Market price

Actual decision

vs.

cost

cost

Boolean Network-Based Prediction Market(cont.)

• B. BN-based Prediction Market– Major participants in BN-based prediction market

• Trading agent buy and sell securities on behalf of human traders

• Market maker agent• Information sources

– Based on traditional prediction market’s operation• Belief

– Outcome of security corresponding to the event– Used to calculate the market price

• State– In BN, used to represent belief– Updated using Boolean function– 1 or ON : trading agent believes the event will happen– 0 or OFF : trading agent believes the event won’t happen

Tradition PM

BN-based PM

1

2

2

34

4

Boolean Network-Based Prediction Market (cont.)

• C. Trading Agents’ Boolean Belief Update

Market price State Information signal

Threshold

trust

Boolean Network-Based Prediction Market (cont.)

• D. Mean-field Analysis for Calculating the Aggregated Market Price by Market Maker agents

– Market price• Density of ones• Fraction of trading agents in state 1

– Mean field• Recursive mathematical model for the density of ones

– , are the same for all agents• Drop the trading index n

(1)

(5)

A

B

C

D

E

F

𝑝𝑟 (𝑡)

1)

2)

3) Bernoulli random variable 1 / 0

Boolean Network-Based Prediction Market (cont.)

– Mean field mathematical model• For the density of ones• Aggregated market price• Analyze the dynamics of prediction market

– Map• Fixed point – p

– attract all other points close enough to p , as – repels all the orbits starting at x in neighborhood of p–

» [A ,F ] always stable in 0 / 1» -- [ D ] stable in q» -- [ C ] all points are fixed points , frozen from beginning , unstable

A

D

F

C

Experimental results• A. Learning the trust values by trading agents– Back propagation neural network

• – Initial weights are set randomly– Find the best

• Input – – – - set to 0 or 1 based on the value of q

• Output– market price at trading period t+1

• Over 200 different combinations of values of z and q parameters– z threshold parameter– q probability that Bernoulli random variable is 1

Experimental results(cont.)• B. Patterns and validation of the mean-field based price aggregation mechanism

– Pattern formation plot– Arranging nodes representing the trading agents in one dimensional array left to right– State : 1 black plot– State : 0 neutral plot

Experimental results(cont.)

q probability that Bernoulli random variable is 1z threshold parameter

Experimental results(cont.)

A DF C

Experimental results(cont.)• C. Comparison to Conventional Prediction Markets – LMSR vs. BN

Experimental results(cont.)• D. Robustness to noise – Affect prediction market

• Disturbances in the form of manipulation by trading agent• Untruthfully beliefs• Noise can stabilize a certain type of BN for a wide range of parameters

– Flip• Noise procedure• Randomly select j trading agents and flip their state at time t

•

Experimental results(cont.)

stable

Experimental results(cont.)• E. Scalability– The number of trading agents v.s. model ‘s accuracy

Conclusion• Boolean network– Behavior of trading agent

• Aggregated market price• Past beliefs• Information flow

• BN v.s. LMSR– Less fluctuation of the market price– Analyze and predict the dynamics of prediction market– Simpler

• Future• Variation of weight and threshold parameters• More possible state• Limit untruthful belief