Topics in Game Theory - Prediction Markets - A Presentationlcm.csa.iisc.ernet.in/eclwiki/images/0/09/Perspectives_pres.pdf · Topics in Game Theory - Prediction Markets A Presentation

Topics in Game Theory - Prediction MarketsA Presentation

PhD Student: Rohith D VallamFaculty Advisor: Prof Y. Narahari

Department of Computer Science & AutomationIndian Institute of Science, Bangalore

Bengaluru, India.

Dept of CSA (IISc) Prediction Markets October 14, 2010 1 / 26

Outline of the Presentation

Organization of the PresentationPrediction Markets: IntroductionResearch Directions in Prediction MarketsImportant Prediction Market Mechanisms

Automated Market MakersDynamic Parimutuel MarketsMarket Scoring Rule

Wagering mechanismsCollective revelation

Scope for future work


Prediction Markets: Motivation

How do people predict ?

Popular Prediction TechniquesAutomated market makers / Prediction Markets - aggregateinformation from agents with diverse informationWagering mechanisms - players wager and are rewarded basedon prediction accuracyCollective revelation - infer private information of all agentsProper scoring rules - single agent, single event scenarioPeer-prediction methods - predict about what others are predictingSimple polls - simple tool for aggregating informationsDelphi methods - structured discussion through many rounds



Searching the roots: Origin of Prediction Markets

Hayek Hypothesis(1940)Price system in a competitive market is a very efficient mechanismto aggregate dispersed information among market participants.In an efficient market, price of a security almost instantlyincorporates all available information.Market price summarizes all relevant information across traders.Market price is market participants’ consensus expectation aboutthe future value of the security.

The Wisdom of Crowds: James Surowiecki (2004)Why the Many Are Smarter Than the Few and How Collective WisdomShapes Business, Economies, Societies and Nations



What is a Prediction Market?

Intuition through an exampleLet us say we want to predict the outcome about who the next Prime Minister of India will be. Specifically, we want to know ifDr. Manmohan Singh will continue to be the next Prime Minister !A prediction market can trade a ’Dr. Manmohan Singh Security’ , a share of which pays the following after the election:

Value of 1 share =

Re.1 if Dr. Manmohan Singh becomes the PM0 otherwise

Let W represent the event that Dr. Manmohan Singh wins the election. Now, the expected payoff of a share of ’Manmohan Singhsecurity’ is

p = Pr(W )× 1 + [1− Pr(W )]× 0 (1)

where p is the price of ’Manmohan Singh’ security.

For instance, if current price of the security is Re. 0.6, it means that market traders believe that, with probability 0.6, Dr.Manmohan Singh will beat, say, Mr. Narendra Modi . This probability will become consensus among the marketparticipants.

If some market traders possess crucial information that leads them to believe that Dr. Manmohan Singh only has halfchances to win, they will sell their security holdings at the current price, which in turn drives down the price.



What is a Prediction Market?

Knowledge Integration and Price discoveryEliciting and aggregation of information from diverse andfrequently self-interested sources.A market designed primarily for price discovery.For example, the market operator may be happy to pay for theinformation it seeks, instead of enforcing neutral or positiverevenue.



Advantages of Prediction Markets over otherapproaches of information aggregation

Compared with statistical forecasting methodsCan incorporate real-time information, which was not contained inhistorical data.

Compared with eliciting expert opinionsLess constrained by space and time.Eliminate the effort of identifying experts and soliciting theirparticipation.Less expensive in practice.They do not need to deal with conflicting opinions.



Prediction Markets At Work

Online Prediction Market ExamplesThe Iowa Electronic Markets (IEM) are real-money futures markets to predict economic and political events such aspresidential elections

Hollywood Stock Exchange (HSX) trades securities to forecast future box office proceeds of new movies

MIT’s Innovation Futures predict important business and technology trends

Tech Buzz Game aims at both forecasting high-tech trends and testing a new market mechanism

Case study: Iowa Electronic Markets



Broad Areas of Research in Prediction Markets

Accuracy, Effectiveness and Scope of Prediction MarketsCompare with Expert Aggregation (Experiments with 2003 USNational Football League games)

Computational Aspects of Prediction MarketsEquilibrium price of a financial security reflects all of the informationregarding the security’s value

Design of Prediction market mechanismsMechanisms are usuallly pari-mutuel in the sense that the winnersare generally paid out by the stakes of the losers.

Truthful prediction market mechanisms


Automated Market Makers

Through the looking glass: Thin Markets-An issue inPrediction markets

Thin Markets - A chicken-or-egg problem

Continuous Double Auction: A double auction is a process of buying andselling goods when potential buyers submit their bids and potentialsellers simultaneously submit their ask prices to an auctioneer, and thenan auctioneer chooses some price p that clears the market: all thesellers who asked less than p sell and all buyers who bid more than pbuy at this price p.

A CDA only matches willing traders, and so poses no risk whatsoever forthe market institution.

But a CDA can suffer from illiquidity if trading is light and thus marketsare thin.

Thin markets lead to a ’chicken and egg’ problem where few traders careto participate because other traders are scarce, potentially spiraling themarket into failure.Dept of CSA (IISc) Prediction Markets October 14, 2010 10 / 26

Automated Market Makers

Through the looking glass: Thin Markets-An issue inPrediction markets

Automated Market MakersAn automated market maker can improve the liquidity of a prediction market. The market maker continually announcesprices offering both to buy and to sell some quantity of the security, adjusting his prices in programmatic response totrader demand.

Should run into predictable /bounded loss

Informed traders should have incentive to trade whenever their information would change the price

After any trade, computing new prices should be tractable

A prediction market maker may subsidize a market maker that expects to lose some money, in return for improving traderincentives, liquidity, and price discovery .

Approaches to forming Market makersContinuous Double Auction with Market Maker (CDAwMM): have built-in liquidity, but the market maker is exposed tosignificant risk of large monetary losses.

Hanson Scoring Rule (HSR)

Dynamic Pari-mutuel markets(DPM)



Automated Market Makers: Dynamic Pari-mutuelmarkets(DPM)

An artist’s impressionPari-mutuel markets

Pari-mutuel markets effectively have infiniteliquidity:

Pari-mutuel markets also involve no risk forthe market institution.

Since there is a strong disincentive forplacing bets until either (1) all information isrevealed, or (2) the market is about to close.

Pari-mutuel market participants cannot ’buylow and sell high’


Hybrid between mutuel market and CDA.

Pari-mutuel by nature - acts to redistribute money from some traders to another.

A subsidy needed to start the market

Has infinite liquidity: The essential characteristic of a liquid market is that there are ready and willing buyers and sellers atall times.



DPM - Key points

Mechanism for wagering on a future uncertain eventSatisfies 3 important properties

Guaranteed No Risk Continuous incorporationLiquidity for the market maker information

CDA No Yes YesCDAwMM Yes No Yes

MSR Yes No YesDPM Yes Yes Yes

DPM acts as an automated market maker willing to accept infinitebuying orders at some pricePrice functions derived which encode how prices changecontinuosly as shares are purchasedPossibility of an aftermarket wherein traders can cash out of themarket early to lock in their gains or limit their losses.


Scoring rules

Proper Scoring rules

Ω = 1,2, ...,m - Outcome spaceP = p ∈ Rm : 0 < pi < 1,

∑mi=1 pi = 1

Reported Probability distribution : p ; True Probability distribution : p

DefinitionA scoring rule is a function s : P× Ω→ R. For each report p ∈ P andeach outcome i ∈ Ω, it specifies a payment s(p, i).

The expected payment s under the scoring rule is given by

s(p,p) =m∑

i=1

s(p, i)× pi

DefinitionA scoring rule s : P× Ω→ R is (weakly) proper if ∀p, p ∈ P,

s(p,p) ≥ s(p,p).


Scoring rules

Proper Scoring rules - Single Event Scenario

Suppose we want to incentivize a single agent to truthfully reportits subjective probability pE that event E will take place. We needto pay the agent some amount of money that depends on thereported probability pE and on whether the event actuallyhappens.Proper Scoring Rule : s(pE , xE ) where xE = 1 if the event occursand xE = 0 otherwisep = arg maxp (p × s(p,1) + (1− p)× s(p,0)) where p is the trueestimate of the agent’s probability.Quadratic Scoring Rule : s(pE , xE ) = 1− (xE − pE )2

Logarithmic Scoring Rule :s(pE , xE ) = (xE × logpE ) + (1− xE )× log(1− pE )


Scoring rules

Market Scoring rules

Basically using proper scoring rule in the setting of multipleagents.Current Estimate of the probability - pE

At any point of time, agent can change it to p′

E

After event is realized, agent will be paid: s(p′

E , xE )− s(pE , xE )(may be negative)In some sense, this gives right incentive to agent as it cannotaffect s(pE , xE )

Nice property: Net payment made by the rule :s(pf

E , xE )− s(p0E , xE ) where pf

E is the final probability and p0E is the

initial probability.


Truthful Mechanisms

Truthful Mechanisms for Prediction Markets

Wagering Mechanisms - Setting

Operate in 2 stepsEach player announces a report chosen from a certain set ofpossible reports R and wagers any positive amount of moneyAfter realization of experiment, the common pot is divided amongthe players based on their performance

DefnitionA Wagering mechanism is a tuple (R,Ω,Π) where R is set of allowedreports, Ω is outcome space, and Π = (Πi(r,m, ω))i∈N is the vector ofpayout functions Πi : RN × [0,+∞)N × Ω 7→ [0,+∞) withΠi(r,m, ω) = 0 if mi = 0


Truthful Mechanisms


Examples - Wagering MechanismsPari-mutuel betting markets

Wager on mutually exclusive and exhaustive events i.e.,E1, ...,EmPlayers lose their wagers when the true outcome is not what theybet.Winning players share money in proportion to their own wager.

Such a market is a wagering mechanism with R = E1, ...,Em andpayout

Πi = 1ω∈ri

mi∑j mj1ω∈rj

∑j

mj


Truthful Mechanisms


Distribution properties

A distribution property Γ(P) is a function that assigns a real value toany probability distribution P in a given convex domain.Examples

Probability of an eventthe expectation, the variancemedians/quantiles, moments, skewness, kurtosis, etc.

Strictly proper scoring rules - RecapA score function for a vector of distribution propertiesΓ = (Γ1, Γ2, ..., Γk ) is a real-valued function s(r , ω) with r = (r1, r2, ..., rk )and ri the report for property Γi . Strictly proper when

EP [s(r , ω)] < EP [s(Γ(P), ω)]


Truthful Mechanisms


Weighted Score mechanisms

A weighted-score mechanism is a wagering mechanism (Ω,R,Π)asscociated with a vector of properties Γ = (Γ1, Γ2, ..., Γk ). Π is thevector of payout functions with the payout of player i defined as

Πi(r ,m, ω) = mi

(1 + s(ri , ω)−

∑j s(rj , ω)mj∑

j mj

)

where s is a strictly proper score function for Γ taking values in [0,1]

Reference

N. S. Lambert, J. Langford, J. Wortman, Y. Chen, D. Reeves, Y. Shoham, and D. M. Pennock, “Self-financed wagering mechanisms

for forecasting,” in Proceedings of the 9th ACM Conference on Electronic Commerce (EC ’08). New York, NY, USA: ACM, 2008,

pp. 170–179.


Truthful Mechanisms


Desirable PropertiesBudget-balance : if market generates neither profit or lossAnonymity : if payouts does not depend on the playerTruthfulness : if players maximize their expected payout whenreporting true property values.Normality : relative performance of a player should increase ifplayer’s absolute performance increases or when absoluteperformance of another player decreases.Sybilproofness : if immune to multiple identities.Individual rationality :Monotonicity : if increase in wagers lead to increase in expectedpayoff.


Truthful Mechanisms


TheoremAll weighted score mechanisms satisfy these properties.

Proof: (Truthfulness)

EP [Πi (r, m, ω)] = mi

(1 + EP [s(ri , ω)]

(1−

mi∑j mj

)−∑

j 6=i EP [s(rj , ω)mj ]∑j mj

)

Since s is a strictly proper for Γ, EP [s(ri , ω)] is maximized only at ri = Γ(P), so

EP [Πi ((r−i , ri ), m, ω)] < EP [Πi ((r−i , Γ(P)), m, ω)]

for all ri 6= Γ(P)

TheoremWeighted score mechanisms are unique mechanisms which satisfiesthese properties.


Truthful Mechanisms


Goel et al. have recently proposed a mechanism which satisfies keyproperties such as

Incentive compatibility - incentivizes the participants to be truthful.Information weighted - incorporates the fact that some agents arebetter than the other.Self verifying - the payoff of agents are decided before theobjective observations.Budget balanced - external subsidy is not required

Reference

S. Goel, D. M. Reeves, and D. M. Pennock, “Collective revelation: a mechanism for self-verified, weighted, and truthful predictions,”

in Proceedings of the 10th ACM Conference on Electronic Commerce (EC ’09). New York, NY, USA: ACM, 2009, pp. 265–274.


Future Work

The Path Ahead

Research Directions - A broad perspectiveTheoretical Examination: Why do information market work? Willan information market converge to a consensus equilibrium?What is the best possible equilibrium?Experimental Evaluation: To what extent, are theoretical models ofinformation markets valid?Empirical Analysis: How well do information market work? Howwell do information markets perform compared with otherforecasting methods, especially opinion pools?Design and Development: How to develop an effective informationmarkets? When to choose information markets over otherforecasting methods?


Future Work

The Path Ahead

Research Directions - A narrow perspectiveDeveloping and understanding multi-round wagering mechanismsby using techniques like delphi method, etc.Study performance of prediction market mechanisms like marketscoring rules, etc through experiments using some open sourceprediction markets like Zocalo.There exists deep mathematical connections between marketscoring rules, prediction markets and no-regret learning . Thereexists potential to define new prediction mechanisms based onlearning algorithm.


Thank You

THANK YOU !!


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Topics in Game Theory - Prediction Markets - A Presentationlcm.csa.iisc.ernet.in/eclwiki/images/0/09/Perspectives_pres.pdf · Topics in Game Theory - Prediction Markets A Presentation