market games for mining customer information
TRANSCRIPT
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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
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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
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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
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http://tradesports.com
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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
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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))
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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