1.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
A Multi-Agent Prediction Market based on
Partially Observable Stochastic Game
Janyl Jumadinova, Raj Dasgupta
C-MANTIC Research Group
Computer Science Department
University of Nebraska at Omaha, USA
ICEC 2011
1 / 37
2.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Outline
Problem: Traders’ behavior in a prediction market and
its impact on the prediction market’s behavior
Solution: A multi-agent system that formalizes the
strategic behavior and decision making by market’s
participants based on a partially observable stochastic
game
Experimental validation: Comparison with other
trading approaches
1 / 37
3.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
A Prediction market is
a market-based mechanism used to
- combine the opinions on a future event from diﬀerent
people and
- forecast the possible outcome of the event based on the
aggregated opinion
2 / 37
4.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
3 / 37
5.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
4 / 37
6.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
5 / 37
7.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
6 / 37
8.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
7 / 37
9.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
8 / 37
10.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
9 / 37
11.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
10 / 37
12.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
11 / 37
13.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
12 / 37
14.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
13 / 37
15.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Prediction Market
Main Features
A prediction market is run for a real-life unknown event
Each event has a ﬁnite duration
Each event’s outcome has a security associated with it
Traders buy and sell the securities based on their beliefs
about the outcome of the event
Traders’ beliefs are expressed as probabilities
Market maker aggregates the probabilities from all the
traders into a single probability, market price
Market price of a security represents the probability of
the outcome of an event associated with that security
happening
Traders get paid according to their reported beliefs
14 / 37
16.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
A Multi-Agent Prediction Market
Software trading agents perform calculations and trade
on behalf of human traders
Provides testbed for modeling diﬀerent strategic
behaviors of traders through simulations with trading
agents15 / 37
17.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Do Prediction Markets Work?
Yes, evidence from real markets, laboratory experiments, and theory
I.E.M. beat political polls 451/596 [Forsythe 1999, Berg
2001, Pennock 2002]
HP market beat sales forecast 6/8 [Plott 2000]
Sports betting markets provide accurate forecasts of
game outcomes [Debnath 2003, Schmidt 2002]
Market games work [Pennock 2001]
Laboratory experiments conﬁrm information
aggregation [Forsythe 1990, Plott 1997, Chen 2001]
Theory of Rational Expectations [Lucas 1972, Grossman
1981]
and more...
16 / 37
18.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Research Problem Addressed
Develop a formal, game-theoretic model of the trading
agent behavior in prediction markets including
- impact of information from external sources on trading
agent decisions/behavior,
- a solution concept for calculating the equilibrium
strategies of the trading agents
Research Questions:
How does diﬀerent traders’ behaviors aﬀect market
prices?
What trading strategies give the highest utilities to the
traders?
How can prediction markets incentivize traders to
participate and report their beliefs truthfully in order to
achieve a higher prediction accuracy?
17 / 37
19.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Our Solution
A partially observable stochastic game with information
(POSGI)-based model of the trading agent behavior
A correlated equilibrium (CE)-based solution to
determine equilibrium strategy in the POSGI
representation
18 / 37
20.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Partially Observable Stochastic Game with
Information (POSGI)
19 / 37
21.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Partially Observable Stochastic Game with
Information (POSGI)
- Logarithmic Market Scoring Rule (LMSR) [Hanson
2007] gives formula to calculate aggregate market price
from the outstanding quantity of a security
19 / 37
22.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Partially Observable Stochastic Game with
Information (POSGI)
- Belief state is updated using a Bayesian model of past
beliefs, past actions and current observation
20 / 37
23.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Partially Observable Stochastic Game with
Information (POSGI)
- Information signal can be {−1, 0, 1} representing
positive, neutral, or negative information
21 / 37
24.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Partially Observable Stochastic Game with
Information (POSGI)
22 / 37
25.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Two Agent Trading Scenario with 1 security
Example
Actions = to buy, sell, or hold one security
Market state is denoted by q
C(q) is the cost function calculated by LMSR, that
reﬂects the total money collected by the market maker
Can construct a normal form game to capture the
decision problem for each agent
23 / 37
26.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Correlated Equilibrium (CE)
Set up
Let N be the set of trading agents
Let Ai be the set of actions for agent i ∈ N
Let Φi be the set of mixed strategy proﬁles deﬁned over
Ai
Joint strategy space is then Φ = ×
|N|
i=1Φi
Let φ ∈ Φ be a strategy proﬁle and φi denote agent i’s
component in φ
Let ui(φ) be the utility of agent i from joint strategy φ
24 / 37
27.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Correlated Equilibrium (CE)
Correlated Equilibrium is a probability distribution p on
Φ such that
for all agents i and all strategies φi, φi
if all agents follow a strategy proﬁle φ,
agent i has no incentive to play another strategy φi
instead
The Chicken-Dare Game
Assume there is a trusted third party that draws a
strategy for each player and announces it to each player
separately
Players agree to follow the strategy suggested by the
third party
Players get higher payoﬀs when use CE than NE
25 / 37
28.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Correlated Equilibrium (CE) Algorithm
CE algorithm applied to our POSGI model is based on
the method proposed by Papadimitriou [2008]
CE algorithm of the POSGI gives the action (buy or
sell; quantity) for each agent at each time step
Time complexity of our CE algorithm is O(|N| × |Φi|2)
26 / 37
29.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Correlated Equilibrium (CE)
with Trading Agents’ Risk Preferences
The beliefs and risk preferences of traders are directly
correlated [Kadane 1988, Dimitrov 2008]
Use constant relative risk averse (CRRA) utility function
To ﬁnd CE in the market with risk-averse trading
agents:
- Find the set of all Pareto optimal strategy proﬁles
- Check whether a Pareto optimal strategy proﬁle satisﬁes
CE constraints
27 / 37
30.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Correlated Equilibrium (CE)
with Trading Agents’ Risk Preferences
A strategy proﬁle φP is Pareto optimal if there does not
exist another strategy proﬁle φ such that
ui(φ ) ≥ ui(φP )∀i ∈ N with at least one inequality
strict
Pareto optimal strategy is found by maximizing
weighted utilities and solving the maximization problem
using Lagrangian method
Proposition
If p is a correlated equilibrium and φP is a Pareto optimal
strategy proﬁle calculated by p in a prediction market with
risk averse agents, then the strategy proﬁle φP is incentive
compatible, that is each agent is best oﬀ reporting truthfully
28 / 37
31.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Set up
Default values for market related parameters came from
Iowa Electronic Marketplace (IEM) movie market
Assume there is one event with two outcomes
Consider only disjoint events
Report utilities and market price for the security
corresponding to the outcome of the event being 1
29 / 37
32.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Set up
We use the following strategies for comparison of the trading
agents’ and market’s behavior
1 ZI (Zero Intelligence) - each agent submits randomly
calculated quantity to buy or sell
2 ZIP (Zero Intelligence Plus) - each agent selects a quantity
to buy or sell that satisﬁes a particular level of proﬁt
3 CP (by Preist and Tol) - each agent adjusts its quantity to
buy or sell based on past prices and tries to choose that
quantity so that it is competitive among other agents
4 GD (by Gjerstad and Dickhaut) - each agent maintains a
history of past transactions and chooses the quantity to buy
or sell that maximizes its expected utility
5 DP (Dynamic Programming solution for POSG game) - each
agent uses dynamic programming solution to ﬁnd the best
quantity to buy or sell [Hansen 2004]
30 / 37
33.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Risk-neutral Agents
(a) DP strategy has the highest percentage of adoption of
some CE
(b) Prediction market with trading agents using CE strategy
result in more accurate market prices
(c) Trading agents using CE strategy obtain 38% more
utility than the agents following the next best
performing strategy DP
31 / 37
34.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Risk-neutral Agents
(a) DP strategy has the highest percentage of adoption of
some CE
(b) Prediction market with trading agents using CE strategy
result in more accurate market prices
(c) Trading agents using CE strategy obtain 38% more
utility than the agents following the next best
performing strategy DP
31 / 37
35.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Risk-neutral Agents
(a) DP strategy has the highest percentage of adoption of
some CE
(b) Prediction market with trading agents using CE strategy
result in more accurate market prices
(c) Trading agents using CE strategy obtain 38% more
utility than the agents following the next best
performing strategy DP
31 / 37
36.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Risk-neutral Agents
(a) Trading agents using CE strategy obtain more utility
than trading agents using ZIP strategy
(b) Trading agents using CE strategy obtain more utility
than trading agents using CP strategy
32 / 37
37.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Risk-neutral Agents
(a) Trading agents using CE strategy obtain more utility
than trading agents using ZIP strategy
(b) Trading agents using CE strategy obtain more utility
than trading agents using CP strategy
32 / 37
38.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Risk-neutral Agents
(c) Trading agents using CE strategy obtain more utility
than trading agents using GD strategy
(d) Trading agents using CE strategy obtain more utility
than trading agents using DP strategy
33 / 37
39.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Risk-neutral Agents
(c) Trading agents using CE strategy obtain more utility
than trading agents using GD strategy
(d) Trading agents using CE strategy obtain more utility
than trading agents using DP strategy
33 / 37
40.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Risk-averse Agents
(a) DP strategy has the highest percentage of adoption of
some CE
(b) Prediction market with risk-averse trading agents using
CE strategy result in more accurate market prices
(c) Risk-averse trading agents using CE strategy obtain
41% more utility than the agents following the next
best performing strategy DP
34 / 37
41.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Risk-averse Agents
(a) DP strategy has the highest percentage of adoption of
some CE
(b) Prediction market with risk-averse trading agents using
CE strategy result in more accurate market prices
(c) Risk-averse trading agents using CE strategy obtain
41% more utility than the agents following the next
best performing strategy DP
34 / 37
42.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Experimental Results
Risk-averse Agents
(a) DP strategy has the highest percentage of adoption of
some CE
(b) Prediction market with risk-averse trading agents using
CE strategy result in more accurate market prices
(c) Risk-averse trading agents using CE strategy obtain
41% more utility than the agents following the next
best performing strategy DP
34 / 37
43.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Conclusions and Future Work
In this work we have:
- described a novel multi-agent based representation of
the prediction market using POSG
- developed a CE solution for solving POSG
- empirically compared diﬀerent agent behavior strategies
in the prediction market
- showed how CE can be obtained in the prediction
market with risk averse agents
35 / 37
44.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Conclusions and Future Work
In this work we have:
- described a novel multi-agent based representation of
the prediction market using POSG
- developed a CE solution for solving POSG
- empirically compared diﬀerent agent behavior strategies
in the prediction market
- showed how CE can be obtained in the prediction
market with risk averse agents
In the future we plan to:
Conduct experiments in an n-agent scenario using richer
commercial data sets
Investigate the dynamics evolving from multiple
prediction markets that interact with each other
35 / 37
45.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
References
1 Y. Chen, D. Pennock. Utility Framework for
Bounded-Loss Market Maker. Proc. of the 23rd
Conference on Uncertainty in Artiﬁcial Intelligence (UAI
2007), pages 49-56, 2007.
2 E. Hansen, D. Bernstein, S. Zilberstein. Dynamic
programming for partially observable stochastic games.
In Proceedings of the 19th National Conference on
Artiﬁcial Intelligence, pages 709-715, 2004.
3 R. Hanson. Logarithmic Market scoring rules for
Modular Combinatorial Information Aggregation.
Journal of Prediction Markets, 1(1):3-15, 2007.
4 Iowa Electronic Marketplace. URL:
www.biz.uiowa.edu/iem/
5 C. Papadimitriou, T. Roughgarden. Computing
correlated equilibria in multi-player games. Journal of
ACM, 55(3):1-29, 2008.36 / 37
46.
A Multi-Agent
Prediction Market
based on Partially
Observable
Stochastic Game
Janyl Jumadinova,
Raj Dasgupta
Outline
Introduction
Research Problem
POSGI
Trading Agents’
Strategy
Experimental
Results
Future Work
Thank You!
Questions?
jjumadinova@unomaha.edu
C-MANTIC Research Group
http://cmantic.unomaha.edu/
37 / 37
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