Market Games for Mining Customer Information
Transcript of 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
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Distinguished guests (thanks!)• Edward Castronova
Prof. Economics, Cal State Fullerton• John Ledyard
Prof. Econ & Social Sciences, CalTech• Justin Wolfers
Prof. Economics, Stanford
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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
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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
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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
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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
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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?
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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
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Updating on new information
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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
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Running comparisonno risk liquidity info
aggreg.CDA x x
CDAwMM
PM
DPM
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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/
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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
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Running comparisonno risk liquidity info
aggreg.CDA x x
CDAwMM x x
PM
DPM
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What is a pari-mutuel market?
• E.g. horse racetrack style wagering• Two outcomes: A B• Wagers:
AA BB
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What is a pari-mutuel market?
• E.g. horse racetrack style wagering• Two outcomes: A B• Wagers:
AA BB
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What is a pari-mutuel market?
• E.g. horse racetrack style wagering• Two outcomes: A B• Wagers:
AA BB
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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
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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
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Running comparisonno risk liquidity info
aggreg.CDA x x
CDAwMM x x
PM x x
DPM
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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
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$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
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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
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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
)(
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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
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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)
!!
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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)
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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
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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
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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• ...
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Price function II• Suppose: pri1/pri2 = Mon1/Mon2
also natural, reasonable• Implies
MPr(A) = Mon1 Num1 Mon1 Num1 + Mon2
Num2
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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
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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
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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
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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
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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)
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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
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Running comparisonno risk liquidity info
aggreg.CDA x x
CDAwMM x x
PM x x
DPM x x x
MSR x x[Hanson 2002][Hanson 2002]
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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!
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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
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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