market games for mining customer information

Research LabsResearch LabsY!RL Spot Workshop onNew Markets, New Economics• Welcome!• Specific examples of new trends in

economics, new types of markets• virtual currency• prediction (“idea”) markets• experimental economics

• Interactive, informal• ask questions• rountable discussion wrap-up

Research LabsResearch Labs

Distinguished guests (thanks!)• Edward Castronova

Prof. Economics, Cal State Fullerton• John Ledyard

Prof. Econ & Social Sciences, CalTech• Justin Wolfers

Prof. Economics, Stanford


Schedule11am-noon Castronova on the Future of

Cyberspace Economiesnoon-1pm Lunch provided1pm-2pm Ledyard on ~ Information Markets

and Experimental Economics2pm-3pm Wolfers on ~ Prediction Markets,

Play Money, & Gambling3pm-3:30pm Pennock on Dynamic Pari-Mutuel

Market for Hedging, Speculating3:30pm-4pm Roundtable Discussion


A Dynamic Pari-Mutuel Market for Hedging, Wagering, and Information AggregationDavid M. Pennock

paper to appear EC’04, New York

Research LabsResearch LabsEconomic mechanisms for speculating, hedging• Financial

• Continuous Double Auction (CDA)stocks, options, futures, etc

• CDA with market maker (CDAwMM)• Gambling

• Pari-mutuel market (PM)horse racing, jai alai

• Bookmaker (essentially like CDAwMM)• Socially distinct, logically the same• Increasing crossover


Take home message

• A dynamic pari-mutuel market (DPM)• New financial mech for speculating on

or hedging against an uncertain event; Cross btw PM & CDA

• Only mech (to my knowledge) to• involve zero risk to market institution• have infinite (buy-in) liquidity• continuously incorporate new info;

allow cash-out to lock in gain, limit loss


Outline• Background

• Financial “prediction” markets• Pari-mutuel markets• Comparing mechs:

PM, CDA, CDAwMM, MSR• Dynamic pari-mutuel mechanism

• Basic idea• Three specific variations; Aftermarkets• Open questions/problems


What is a financial“prediction market”?• Take a random variable, e.g.

• Turn it into a financial instrument payoff = realized value of variable

= 6 ?

= 6$1 if 6$0 ifI am entitled to:

US’04Pres =Bush?

2004 CAEarthquake?


Real-time forecasts• price expectation of random variable

(in theory, in lab, in practice, ...huge literature)

• Dynamic information aggregation• incentive to act on info immediately• efficient market

today’s price incorporates all historical information; best estimator

• Can cash out before event outcome• BUT, requires bi-lateral agreement


Updating on new information


The flip-side of prediction: HedgingE.g. options, futures, insurance, ...

• Allocate risk (“hedge”)• insured transfers risk

to insurer, for $$• farmer transfers risk

to futures speculators• put option buyer

hedges against stock drop; seller assumes risk

• Aggregate information• price of insurance

prob of catastrophe• OJ futures prices yield

weather forecasts• prices of options

encode prob dists over stock movements

• market-driven lines are unbiased estimates of outcomes

• IEM political forecasts

Research LabsResearch LabsContinuous double auctionCDA• k-double auction

repeated continuously• buyers and sellers

continually place offers• as soon as a buy offer

a sell offer, a transaction occurs

• At any given time, there is no overlap btw highest buy offer & lowest sell offer

http://tradesports.com

http://us.newsfutures.com/http://www.biz.uiowa.edu/iem


Running comparisonno risk liquidity info

aggreg.CDA x x

CDAwMM

PM

DPM


CDA with market maker• Same as CDA, but with an extremely active,

high volume trader (often institutionally affiliated) who is nearly always willing to sell at some price p and buy at price q p

• Market maker essentially sets prices; others take it or leave it

• While standard auctioneer takes no risk of its own, market maker takes on considerable risk, has potential for considerable reward

http://www.wsex.com/

http://www.hsx.com/


Bookmaker• Common in sports betting, e.g. Las Vegas• Bookmaker is like a market maker in a CDA• Bookmaker sets “money line”, or the amount you

have to risk to win $100 (favorites), or the amount you win by risking $100 (underdogs)

• Bookmaker makes adjustments considering amount bet on each side &/or subjective prob’s

• Alternative: bookmaker sets “game line”, or number of points the favored team has to win the game by in order for a bet on the favorite to win; line is set such that the bet is roughly a 50/50 proposition



aggreg.CDA x x

CDAwMM x x

PM

DPM


What is a pari-mutuel market?

• E.g. horse racetrack style wagering• Two outcomes: A B• Wagers:

AA BB


What is a pari-mutuel market?

• E.g. horse racetrack style wagering• Two outcomes: A B• 2 equivalent

ways to considerpayment rule• refund + share of B• share of total

AA BB

$ on B 8$ on A 41+ = 1+ =$3

total $ 12$ on A 4= = $3


What is a pari-mutuel market?• Before outcome is revealed, “odds” are

reported, or the amount you would win per dollar if the betting ended now• Horse A: $1.2 for $1; Horse B: $25 for $1; … etc.

• Strong incentive to wait• payoff determined by final odds; every $ is same• Should wait for best info on outcome, odds• No continuous information aggregation• No notion of “buy low, sell high” ; no cash-out



aggreg.CDA x x

CDAwMM x x

PM x x

DPM


Dynamic pari-mutuel marketBasic idea

• Standard PM: Every $1 bet is the same• DPM: Value of each $1 bet varies

depending on the status of wagering at the time of the bet

• Encode dynamic value with a price• price is $ to buy 1 share of payoff• price of A is lower when less is bet on A• as shares are bought, price rises; price is

for an infinitesimal share; cost is integral


$3.27$3.27$3.27

Dynamic pari-mutuel marketExample Interface

• Outcomes: A B• Current payoff/shr: $5.20

$0.97

AA BB AA BB

$1.00$1.25

$1.50$3.00

sell 100@sell 100@sell 35@

buy 4@buy 52@

$3.25$3.27$3.27$3.27

$0.25

$0.50$0.75

sell 100@sell 100@

sell 3@

buy 200@

$0.85market maker

traders


Dynamic pari-mutuel marketSetup & Notation

• Two outcomes: A B• Price per share: pri1 pri2• Payoff per share: Pay1Pay2• Money wagered: Mon1 Mon2

(Tot=Mon1+Mon2)• # shares bought: Num1 Num2

AA BB AA BB


How are prices set?• A price function pri(n) gives the

instantaneous price of an infinitesimal additional share beyond the nth

• Cost of buying n shares:

• Different assumptions lead to different price functions, each reasonable

n

dnnpri0

)(


Redistribution rule• Two alternatives

• Losing money redistributed. Winners get: original money refunded + equal share of losers’ money

• All money redistributed. Winners get equal share of all money

• For standard PM, they’re equivalent• For DPM, they’re significantly different


Losing money redistributed• Payoffs: Pay1=Mon2/Num1 Pay2=.• Trader’s exp pay/shr for shares:

Pr(A) E[Pay1|A] + (1-Pr(A)) (-pri1)

• Assume: E[Pay1|A]=Pay1 Pr(A) Pay1 + (1-Pr(A)) (-pri1)

!!


Market probability• Market probability MPr(A)• Probability at which the expected

value of buying a share of A is zero• “Market’s” opinion of the probability• MPr(A) = pri1 / (pri1 + Pay1)


Price function I• Suppose: pri1 = Pay2 pri2=Pay1

natural, reasonable, reduces dimens., supports random walk hypothesis

• Implies

MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2


Deriving the price function• Solve the differential equation

dm/dn = pri1(n) = Pay2 = (Mon1+m)/Num2where m is dollars spent on n shares

• cost1(n) = m(n) = Mon1[en/Num2-1]• pri1(n) = dm/dn = Mon1/Num2 en/Num2


Interface issues• In practice, traders may find costs as

the sol. to an integral cumbersome• Market maker can place a series of

discrete ask orders on the queue, e.g.• sell 100 @ cost(100)/100• sell 100 @ [cost(200)-cost(100)]/100• sell 100 @ [cost(300)-cost(200)]/100• ...


Price function II• Suppose: pri1/pri2 = Mon1/Mon2

also natural, reasonable• Implies

MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2

Num2


Deriving the price function• First solve for instantaneous price

pri1=Mon1/Num1 Num2• Solve the differential equation

dm/dn = pri1(n) = Mon1+m (Num1+n)Num2

cost1(n) = m =

pri1(n) = dm/dn = 212

212

2)1(1 N

NNnN

eNumnNum

Mon

11 212

212

NN

NnN

eMon


All money redistributed• Payoffs: Pay1=Tot/Num1 Pay2=.• Trader’s expected pay/shr for

shares:

Pr(A) (Pay1-pri1) + (1-Pr(A)) (-pri1)

• Market probabilityMPr(A) = pri1 / Pay1


Price function III• Suppose: pri1/pri2 = Mon1/Mon2• Implies

• MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2 Num2

• pri1(m) =

cost1(m) =

)(1)1(ln2)1(22)2(12)1(

2)1(

mTotMonmMonTotNummMonTotNumMonmMonNumMonmMon

TotMonmMon

)(1)1(ln

2)(2)21(

mTotMonmMonTot

MonmTotNum

TotNumNumm


Aftermarkets• A key advantage of DPM is the ability

to cash out to lock gains / limit losses• Accomplished through aftermarkets• All money redistributed: A share is a

share is a share. Traders simply place ask orders on the same queue as the market maker


Aftermarkets• Losing money redistributed: Each

share is different. Composed of:1. Original price refunded

priI(A)where I(A) is indicator fn

2. PayoffPayI(A)


Aftermarkets• Can sell two parts in two

aftermarkets• The two aftermarkets can be

automatically bundled, hiding the complexity from traders

• New buyer buys priI(A)+PayI(A) for pri dollars

• Seller of priI(A) gets $ priMPr(A)• Seller of PayI(A) gets $ pri(1-MPr(A))

Research LabsResearch LabsAlternative “psuedo” aftermarket• E.g. trader bought 1 share for $5• Suppose price moves from $5 to $10

• Trader can sell 1/2 share for $5• Retains 1/2 share w/ non-negative value,

positive expected value• Suppose price moves from $5 to $2

• Trader can sell share for $2• Retains $3I(A) ; limits loss to $3 or $0



aggreg.CDA x x

CDAwMM x x

PM x x

DPM x x x

MSR x x[Hanson 2002][Hanson 2002]


Pros & cons of DPM typesLosing money redistributed

All money redistributed

Pros Winning wagers never lose money

Aftermarket trivial, natural

Cons Aftermarket complicated

Winning wagers can lose money!


Pros & cons of DPMs generally• Pros

• No risk to mechanism• Infinite (buying) liquidity• Dynamic pricing / information aggregation

Ability to cash out• Cons

• Payoff vector indeterminate at time of bet• More complex interface, strategies• One sided liquidity (though can “hedge-sell”)• Untested


Open questions / problems• Is E[Pay1|A]=Pay1 reasonable?

Derivable from eff market assumptions?

• DPM call market• Combinatorial DPM• Empirical testing

What dist rule & price fn are “best”?• >2 discrete outcomes (trivial?)

Real-valued outcomes

market games for mining customer information

Documents