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Markets in Uncertainty: Risk, Gambling, and Information Aggregation

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Real-money markets: Examples & evaluations. Iowa Electronic Market. Options ... Play-money markets. AAAI'04 July 2004. MP1-4. Pennock/Wellman. Outline ... – PowerPoint PPT presentation

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Title: Markets in Uncertainty: Risk, Gambling, and Information Aggregation


1
Markets in UncertaintyRisk, Gambling, and
Information Aggregation
  • a tutorial by
  • David M. Pennock Michael P.
    Wellman pennockd_at_yahoo-inc.com
    wellman_at_umich.edu
  • dpennock.com
    ai.eecs.umich.edu/people/wellman
  • presented at the 19th National Conference on
    Artificial Intelligence, July 2004, San Jose, CA,
    USA

MP1-1
2
Outline
  • Overview tour 15 minWhat is a market in
    uncertainty?
  • Background 30 min
  • Single agent perspective
  • Subjective probability
  • Utility, risk, and risk aversion
  • Decision making under uncertainty
  • Multiagent perspective
  • Trading/allocating risk
  • Pareto optimality
  • Securities Markets in uncertainty

3
Outline
  • Mechanisms, examples andempirical studies
    45 min
  • What how Instruments mechanisms
  • Real-money markets Examples evaluations
  • Iowa Electronic Market
  • Options
  • TradeSports Effects of war
  • Horse racing, sports betting
  • Play-money markets

4
Outline
  • Lab experiments and theory 20 min
  • Laboratory experiments, field tests
  • Theoretical underpinnings
  • Rational expectations
  • Efficient markets hypothesis
  • No-Trade Theorems
  • Information aggregation

5
Outline
  • Characterizing information 20 minaggregation
  • Market as an opinion pool
  • Market as a composite agent
  • Market belief, utility
  • Market Bayesian updates
  • Market adaptation, dynamics
  • Paradoxes, impossibilities
  • Opinion pool impossibilities
  • Composite agent non-existence

6
Outline
  • Computational aspects 60 min
  • Combinatorics
  • Compact securities markets
  • Combinatorial securities markets
  • Compound securities markets
  • Market scoring rules
  • Dynamic pari-mutuel market
  • Policy Analysis Market
  • Distributed market computation
  • Legal issues miscellaneous 5 min
  • Discussion, QA 15 min

7
1. Overview tour
  • What is a market in uncertainty ?

8
A market in uncertainty
  • Take a random variable, e.g.
  • Turn it into a financial instrument payoff
    realized value of variable

US04Pres Bush?
2004 CAEarthquake?
9
Aside Terminology
  • Key aspect payout is uncertain
  • Called variously asset, security, contingent
    claim, derivative (future, option), stock,
    prediction market, information market, gamble,
    bet, wager, lottery
  • Historically mixed reputation
  • Esp. gambling aspect
  • A time when options were frowned upon
  • But when regulated serve important social roles...

10
Why? Reason 1
  • Get information
  • price ? expectation of random variable(in
    theory, lab experiments, empirical studies,
    ...more later)
  • Do you have a random variable whose expectation
    youd like to know?A market in uncertainty can
    probably help

11
Why?Reason 1 Information
  • Information market financial mechanism
    designed to obtain estimates of expectations of
    random variables
  • Easy as 1, 2, 3
  • Take a random variable whose expectation youd
    like to know
  • Turn it into a financial instrument (payoff
    realized value of variable)
  • Open a market in the financial instrument
  • ? price(t) ? EtX (in many cases, ... more later)

12
Getting information
  • Non-market approach ask an expert
  • How much would you pay for this?
  • A 5/36 ? 0.1389
  • caveat expert is knowledgeable
  • caveat expert is truthful
  • caveat expert is risk neutral, or RN for 1
  • caveat expert has no significant outside stakes

13
Getting information
  • Non-market approach pay an expert
  • Ask the expert for his report r of the
    probability P( )
  • Offer to pay the expert
  • 100 log r if
  • 100 log (1-r) if
  • It so happens that the expert maximizes expected
    profit by reporting r truthfully
  • caveat expert is knowledgeable
  • caveat expert is truthful
  • caveat expert is risk neutral, or RN
  • caveat expert has no significant outside stakes

logarithmic scoring rule, a proper scoring
rule
14
Getting information
  • Market approach ask the publicexperts
    non-experts alikeby opening a market
  • Let any person i submit a bid order an offer to
    buy qi units at price pi
  • Let any person j submit an ask order an offer
    to sell qj units at price pj(if you sell 1 unit,
    you agree to pay 1 if )
  • Match up agreeable trades (many poss. mechs...)

15
Getting information
  • Market approach ask the publicexperts
    non-experts alikeby opening a market
  • If, at any time, for any bidder i and ask-er j,
    pi pj, then ij trade min(qi,qj) units at price
    ?pj,pi
  • In equilibrium (no trades)
  • max bid pi
  • bounds aggregate public opinion of expectation

16
Aside Mechanism alternatives
  • This is the continuous double auction (CDA)
  • Many other market auction mechanisms work
  • call market
  • pari-mutuel market
  • market scoring rules
  • CDA w/ market maker
  • Vegas bookmaker, others
  • Key Market price aggregate estimate of
    expected value

Hanson 2002
17
(Real) Great expectations
  • For dice example, no need for market Ex is
    known no one should disagree
  • Real power comes for non-obvious expectations of
    random variables, e.g.

I am entitled to
1 if
0 otherwise
I am entitled to
x if interest rate x on Jan 1, 2004
18
I am entitled to
max(0,x-k) if MSFT xon Jan 1, 2004
call option
I am entitled to
f(future weather)
weather derivative
I am entitled to
Bin Ladencaptured
1 if
0 otherwise
I am entitled to
1 if Kansas beats Marq.by 4.5 points 0
otherw.
19
http//tradesports.com
20
(No Transcript)
21
Play moneyReal expectations
http//www.hsx.com/
22
http//us.newsfutures.com/
http//www.ideosphere.com
Cancercuredby 2010
Machine Gochampionby 2020
23
Does it work?Yes...
  • Evidence from real markets, laboratory
    experiments, and theory indicate that markets are
    good at gathering information from many sources
    and combining it appropriately e.g.
  • Markets like the Iowa Electronic Market predict
    election outcomes better than pollsForsythe
    1992, 1999Oliven 1995Rietz 1998Berg
    2001Pennock 2002
  • Futures and options markets rapidly incorporate
    information, providing accurate forecasts of
    their underlying commodities/securitiesSherrick
    1996Jackwerth 1996Figlewski 1979Roll
    1984Hayek 1945
  • Sports betting markets provide accurate forecasts
    of game outcomes Gandar 1998Thaler
    1988Debnath EC03Schmidt 2002

24
Does it work?Yes...
  • E.g. (contd)
  • Laboratory experiments confirm information
    aggregationPlott 198219881997Forsythe
    1990Chen, EC-2001
  • And field tests Plott 2002
  • Theoretical underpinnings rational
    expectationsGrossman 1981Lucas 1972
  • Procedural explanation agents learn from
    pricesHanson 1998Mckelvey 1986Mckelvey
    1990Nielsen 1990
  • Proposals to use information markets to help
    science Hanson 1995, policymakers, decision
    makers Hanson 1999, government Hanson 2002,
    military DARPA FutureMAP, PAM
  • Even market games work! Servan-Schreiber
    2004Pennock 2001

25
Why? Reason 2
  • Manage risk
  • If is horribly terrible for
    youBuy a bunch of and if
    happens, you are
    compensated

26
Why? Reason 2
  • Manage risk
  • If is horribly terrible for
    youBuy a bunch of and if
    happens, you are
    compensated

I am entitled to
1 if
0 if
27
The flip-side of prediction Hedging (Reason 2)
  • 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

28
Reason 2 Manage risk
  • What is insurance?
  • A bet that something bad will happen!
  • E.g., Im betting my insurance co. that my house
    will burn down theyre betting it wont. Note we
    might agree on P(burn)!
  • Why? Because Ill be compensated if the bad thing
    does happen
  • A risk-averse agent will seek to hedge (insure)
    against undesirable outcomes

29
E.g. stocks, options, futures, insurance, ...,
sports bets, ...
  • 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
  • sports bet may hedge against other stakes in
    outcome
  • 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

30
Examples
  • I buy MSFT stock at s. Im afraid it will go
    down. I buy a put option that pays Max0,k-s k
    is strike price. If s goes down below k, my
    stock investment goes down, but my option
    investment goes up to compensate
  • Im a farmer. Im afraid corn prices will go too
    low. I buy corn futures to lock in a price today.

31
Examples
  • I own a house in CA. Im afraid of earthquakes. I
    pay an insurance premium so that, if an
    earthquake happens, I am compensated.
  • I am an Oscar-nominated actor. Im afraid Im
    going to lose. I bet against myself on an
    offshore gambling site. If I do lose, I am
    compensated. (Except that the offshore site
    disappears and refuses to pay?)

32
What am I buying?
  • When you hedge/insure, you pay to reduce the
    unpredictability of future wealth
  • Risk-aversion All else being equal, prefer
    certainty to uncertainty in future wealth
  • Typically, a less risk-averse party (e.g., huge
    insurance co, futures speculator) assumes the
    uncertainty (risk) in return for an expected
    profit

33
On hedging and speculating
  • Hedging is an act to reduce uncertainty
  • Speculating is an act to increase expected future
    wealth
  • A given agent engages in a (largely inseparable)
    mixture of the two
  • Both can be encoded together as a maximization of
    expected utility, where utility is a function of
    wealth, ... more later

34
On trading
  • Why would two parties agree to trade in a market
    in uncertainty?
  • They disagree on expected values (probs)
  • They differ in their risk attitude or exposure
    they trade to reallocate risk
  • Both (most likely)
  • Aside legality is murky, though generally (2) is
    legal in the US while (1) often is not. In
    reality, it is nearly impossible to differentiate.

35
On computational issues
some
?
  • Information aggregation is a form of distributed
    computation
  • Agent level
  • nontrivial optimization problem, even in 1
    marketultimately a game-theoretic question
  • probability representation, updating algorithm
    (Bayes net)
  • decision representation, algorithm (POMDP)
  • agent problems computational complexity,
    algorithms, approximations, incentives

36
On computational issues
some
?
  • Mechanism level
  • Single market
  • What can a market compute?
  • How fast (time complexity)?
  • Do some mechanisms converge faster (e.g.,
    subsidy)
  • Multiple markets
  • How many securities to compute a given fn? How
    many secs to support sufficient social
    welfare?(expressivity and representational
    compactness)
  • Nontrivial combinatorics (auctioneers
    computational complexity algorithms
    approximations incentives)

37
On computational issues
some
?
  • Machine learning, data mining
  • Beat the market (exploiting combinatorics?)
  • Explain the market, information retrieval
  • Detect fraud

38
2. Background
  • Single agent perspective
  • Subjective probability
  • Utility, risk, and risk aversion
  • Decision making under uncertainty
  • Multiagent perspective
  • Trading/allocating risk
  • Pareto optimality
  • Securities markets in uncertainty

39
Decision making under uncertainty
  • How should agents behave (make decisions, choose
    actions) when faced with uncertainty?
  • Decision theory Prescribes maximizing expected
    utility

40
Why reason about uncertainty?
  • Propositional logic No uncertaintyCould never
    explain seatbelt use
  • Decisions D - drive car S - wear seatbelt
  • Events A - accident occurs
  • A ? ?D
  • ?A ? ?S
  • Cant explain DS
  • Key A is uncertain

41
Why Bayesian uncertainty?
  • E.g. You can buy skis for bOr you can rent for
    b/k, k1
  • Worst-case analysisRent for k days, then
    buyYoull spend at most 2b
  • But what if you strongly believe youll skimore
    than k times? ? Buy earlier
  • That k1st time is your last? ? Dont buy
  • Expected (utility) case often more appropriate

42
Decision making under uncertainty, an example
ABC TVs Who Wants to be a Millionaire?
43
Decision making under uncertainty, an example
  • v15 1,000,000 if correct 32,000 if
    incorrect500,000 if walk away

44
Decision making under uncertainty, an example
  • if you answer
  • Ev15 1,000,000 Pr(correct)32,000
    Pr(incorrect)
  • if you walk away
  • 500,000

45
Decision making under uncertainty, an example
  • if you answer
  • Ev15 1,000,000 0.532,000 0.5
  • 516,000
  • if you walk away
  • 500,000
  • you should answer, right?

46
Decision making under uncertainty, an example
  • Most people wont answer risk averse
  • U(x) log(x)
  • if you answer
  • Eu15 log(1,000,000) 0.5log(32,000)
    0.5
  • 6/24.5/2 5.25
  • if you walk away
  • log(500,000) 5.7

47
Decision making under uncertainty, an example
  • Maximizing Eui for i

Q7, L1,3
walk
answer
L1
L3
Q7, L3
? 0.4
X 0.6
log(2k)
walk
answer
L3
log(1k)
Q8, L1,3
? 0.8
X 0.2
log(2k)
log(1k)
Q8, L3
48
Decision making under uncertainty, in general
?set of all possible future states of the world
49
Decision making under uncertainty, in general
  • ? are disjoint exhaustivestates of the world
  • ?i rain tomorrow Bush elected Y! stock up
    car not stolen ...
  • ?j rain tomorrow Bush elected Y! stock up
    car stolen ...

?1
?2
?3
?i
?
?
??
50
Decision making under uncertainty, in general
  • Equivalent, more natural
  • Ei rain tomorrowEj Bush elected
  • Ek Y! stock up
  • El car stolen
  • ?2n

E1
E2
?
Ei
En
Ej
51
Decision making under uncertainty, in general
  • Preferences, utility
  • ??i?j ? u(?i) u(?j)
  • Expected utility
  • Eu ?? Pr(?)u(?)
  • Decisions (actions) can affect Pr(?)
  • What you should dochoose actions to maximize
    expected utility
  • Why? To avoid being a money pump de
    Finetti74, among other reasons...

52
Preference under uncertainty
  • Define a prospect, ? p, ?1 ?2
  • Given the following axioms of ?
  • orderability (?1 ? ?2) ? (?1 ? ?2) ? (?1 ?2)
  • transitivity (?1 ? ?2) ? (?2 ? ?3) ? (?1 ? ?3)
  • continuity ?1 ? ?2 ? ?3 ? ? p. ?2 p, ?1 ?3
  • substitution ?1 ?2 ? p, ?1 ?3 p, ?2 ?3
  • monotonicity ?1 ? ?2 ? pq ? p, ?1 ?2 ? q,
    ?? ?2
  • decomposability
  • p, ?1 q, ?2 ?3 q, p, ?1 ?2 p, ?1
    ?3
  • Preference can be represented by a real-valued
    expected utility function such that
  • u(p, ?1 ?2) p u(?1) (1p)u(?2)

53
Utility functions
  • (??? a probability distribution over ?)
  • Eu ????represents preferences,
  • Eu(?) ? Eu(??) iff ??? ???
  • Let ?(?) au(?) b, a0.
  • Then E?(?) Eaub(?) a Eu(?) b.
  • Since they represent the same preferences, ? and
    u are strategically equivalent (? u).

54
Utility of money
  • Outcomes are dollars
  • Risk attitude
  • risk neutral u(x) x
  • risk averse (typical) u concave (u??(x) all x)
  • risk prone u convex
  • Risk aversion function
  • r(x) u??(x) / u?(x)

55
Risk aversion hedging
  • Eu.01 (4).99 (4.3) 4.2980
  • Action buy 10,000 of insurance for 125
  • Eu4.2983
  • Even better, buy 5974.68 of insurance for 74.68
  • Eu 4.2984 ? Optimal

?1 car stolenu(?1) log(10,000)
?2 car not stolenu(?2) log(20,000)
u(?1) log(19,875)
u(?2) log(19,875)
u(?1) log(15,900)
u(?2) log(19,925)
56
Securities market s
  • Note that, in previous example, risk-neutral
    insurance company also profitsEv
    .01(-5,900) 0.99(74.68) 14.93Both parties
    gain from bilateral agreement
  • Securities market generalizes this to
  • arbitrary states
  • more than two parties
  • Market mechanism to allocate risk among
    participants

57
Pareto optimality
  • An allocation is Pareto optimal iff there does
    not exist another solution that is
  • better for one agent and
  • no worse for all the rest.

a minimal (and maximal?) condition for social
optimality, or efficiency.
58
What is traded Securities
  • Specifies state-contingent returns, r
    (r1,,r?) in terms of numeraire (e.g., )
  • Examples
  • (1,,1) riskless numeraire (1)
  • (0,,0,1,0,,0) pays off 1 in designated state
    (Arrow security for
    that state)
  • ri 1 if ?i?E1, ri 0 otherwise

1 if E1
59
Terms of trade Prices
  • Price p associated with security
  • Relative prices dictate terms of exchange
  • Facilitate multilateral exchange via bilateral
    exchange
  • defines a common scale of resource value
  • Can significantly simplify a resource allocation
    mechanism
  • compresses all factors contributing to value into
    a single number
  • A default interface for multiagent systems

1 if Ei
60
Equilibrium
  • General (competitive, Walrasian) equilibrium
    describes a simultaneous equilibrium of
    interconnected markets
  • Definition A price vector and allocation such
    that
  • all agents making optimal demand decisions
    (positive demand buy negative demand sell)
  • all markets have zero aggregate demand(buy
    volume equals sell volume)

61
Complete securities market
  • A set of securities is complete if rank of
    returns matrix ? ?1
  • For example, set of ? ?1 Arrow securities
    Arrow-Debreu securities market
  • Market with complete set of securities guarantees
    a Pareto optimal allocation of risk, under
    classical conditions

62
Incomplete markets
  • Securities do not span states of nature (always
    the case in practice)
  • Equilibria may exist, but may not be Pareto
    optimalExample missed insurance opportunity
  • More Theory of Incomplete Markets, Magill
    Quinzii, MIT Press, 1998

63
Why trade securities?
  • Profit from perceived mispricings
  • Price p differs significantly enough from
    traders belief Pr(E1)
  • speculation
  • Insure against risk
  • Traders marginal value for wealth in E1,
    relative to p, differs from that in other
    states
  • e.g., home fire insurance
  • hedging

64
Societal roles of security markets
  • From speculation
  • Aggregate beliefs
  • Disseminate information
  • From hedging
  • Allocate risk

65
Summary Background
  • General equilibrium framework for market-based
    exchange
  • Incorporate uncertainty through securities
  • Agents trade securities in order to optimize
    expected utility, thereby
  • Allocating risk
  • Reaching consensus probabilities

66
3. Mechanisms, examples empirical studies
  • What howInstruments mechanisms
  • Real-money marketsExamples evaluations
  • Iowa Electronic Market
  • Options
  • TradeSports Effects of war
  • Horse racing, sports betting
  • Play-money markets

67
Building a market in uncertainty
  • What is being traded?the good
  • Define
  • Random variable
  • Payoff function
  • Payoff output
  • How is it traded?the mechanism
  • Call market
  • Continuous double auction
  • Continuous double auction w/ market maker
  • Pari-mutuel
  • Bookmaker
  • Combinatorial (later)

68
What is being traded?
  • Underlying statistic / random variable
  • Binary Discrete
  • Continuous interest rate, dividend flow
  • Clarity e.g., Saddam out, House burns,Gore
    wins, Buchanan wins
  • Payoff function
  • Arrow (0,0,0,1,0) Portfolio (2,4,0,1,0)
  • Dividends, options Max0,s-k, arbitrary
    (non-linear) fn
  • Payoff output
  • dollars, fake money, commodities

6
69
How is it traded?
  • Call market
  • Orders are collected over a period of time
    collected orders are matched at end of period
  • One-time or repeated
  • Pre-defined or randomized stopping time/rule
  • Mth price auction
  • M1st price auction
  • k-double auction
  • lim period?0 Continuous double auction

70
A note on selling
  • In a securities market, you can sell what you
    dont have you agree to pay according to terms
  • Binary case sell 1 if A for 0.3
  • Receive 0.3 (now, or contractually later), pay
    1 if A
  • Exactly equivalent to buying 1 if A for 0.7
  • sell 1 if A _at_ 0.3
  • buy 1 if A _at_ 0.7
  • Alternative Market institution always stands
    ready to buy/sell exhaustive bundle for 1.00
  • Iowa Electronic Market

A occurs A occurs-1.3 -.7 0.3 .3 0 -.7
-.7 1 -.7 .3
71
Mth price auction
  • N buyers and M sellers
  • Mth price auction
  • sort all bids from buyers and sellers
  • price the Mth highest bid
  • let n of buy offers price
  • let m of sell offers
  • let x min(n,m)
  • the x highest buy offers and x lowest sell offers
    transact

72
Call market
  • Buy offers (N4)
  • Sell offers (M5)

0.30
0.15
0.17
0.12
0.13
0.09
0.11
0.05
0.08
73
Mth price auction
  • Buy offers (N4)
  • Sell offers (M5)

1
0.30
0.17
2
0.15
3
?
0.13
4
price 0.12
0.12
5
?
0.11
?
0.09
0.08
?
0.05
  • Matching buyers/sellers

74
M1st price auction
  • Buy offers (N4)
  • Sell offers (M5)

1
0.30
0.17
2
0.15
3
?
0.13
4
0.12
5
?
price 0.11
0.11
?
6
0.09
0.08
?
0.05
  • Matching buyers/sellers

75
k-double auction
  • Buy offers (N4)
  • Sell offers (M5)

1
0.30
0.17
2
0.15
3
?
0.13
4
price 0.11 0.01k
0.12
5
?
0.11
?
6
0.09
0.08
?
0.05
  • Matching buyers/sellers

76
Continuous 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

77
http//tradesports.com
78
http//www.biz.uiowa.edu/iem
http//us.newsfutures.com/
79
CDA with market maker
  • Same as CDA, but with an extremely active, high
    volume trader (often institutionally affiliated)
    who is nearly always willing to buy at some price
    p and sell at some 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

80
CDA with market maker
  • E.g. World Sports Exchange (WSE)
  • Maintains 5 differential between bid ask
  • Rules Markets are set to have 50 contracts on
    the bid and 50 on the offer. This volume is
    available first-come, first-served until it is
    gone. After that, the markets automatically move
    two dollars away from the price that was just
    traded.
  • The depth of markets can vary with the contest.
  • Also, WSE pauses market adjusts prices
    (subjectively?) after major events (e.g., goals)
  • http//www.wsex.com/about/interactiverules.html

81
CDA with market maker
  • E.g. Hollywood Stock Exchange (HSX)
  • Virtual Specialist automated market maker
  • Always willing to buy sell at a single point
    price ? no bid-ask spread
  • Price moves when buys/sells are imbalanced
  • Fake money, so its OK if Virtual Specialist
    loses money in fact it does Brian Dearth,
    personal communication
  • http//www.hsx.com/

82
http//www.wsex.com/
http//www.hsx.com/
83
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 probs
  • 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

84
Pari-mutuel mechanism
  • Common at horse races, jai alai games
  • n mutually exclusive outcome (e.g., horses)
  • M1, M2, , Mn dollars bet on each
  • If i wins all bets on 1, 2, , i-1,i1, , n
    lose
  • All lost money is redistributed to those who bet
    on i in proportion to amount they bet
  • That is, every 1 bet on i gets1 1/Mi
    (M1, M2, ,Mi-1, Mi1, , Mn) 1/Mi (M1,
    M2, , Mn)

85
Pari-mutuel market
  • E.g. horse racetrack style wagering
  • Two outcomes A B
  • Wagers

86
Pari-mutuel market
  • E.g. horse racetrack style wagering
  • Two outcomes A B
  • Wagers

?
87
Pari-mutuel market
  • E.g. horse racetrack style wagering
  • Two outcomes A B
  • Wagers

?
88
Pari-mutuel market
  • E.g. horse racetrack style wagering
  • Two outcomes A B
  • 2 equivalentways to considerpayment rule
  • refund share of B
  • share of total

?
89
Pari-mutuel market
  • Before race begins, odds are reported, or the
    amount you would win per dollar if betting ended
    now
  • Horse A 1.2 for 1 Horse B 25 for 1 etc.
  • Normalized odds consensus probabilities
  • Actual payoffs depend only on final odds, not
    odds at time of bet incentive to wait
  • In practice track takes 17 first, then
    redistributes what remains

90
Examples of markets
  • Continuous double auction (CDA)
  • Iowa Electronic Market (IEM)
  • TradeSports, experimental Soccer market
  • Financial markets stocks, options, derivatives
  • CDA with market maker
  • World Sports Exchange (WSE)
  • Hollywood Stock Exchange (HSX)
  • Pari-mutuel horse racing
  • Bookmaker NBA point spread betting

91
Example IEMIowa Electronic Market
http//www.biz.uiowa.edu/iem
US Democratic Pres. nominee 2004
1 if other wins
1 if Kerry wins
1 if Lieberman wins
1 if Gephardt wins
1 if H. Clinton wins
priceECPr(C)0.056
as of 4/22/2003
92
Example IEMIowa Electronic Market
http//www.biz.uiowa.edu/iem
US Presidential election 2004
1 if Democrat votes Repub
1 if Republican votes Dem
priceERPr(R)0.494
as of 7/25/2004
93
IEM vote share market
US Pres. election vote share 2004
1 ? 2-party vote share of Bush v. other
1 ? 2-party vote share of other Dem
1 ? vote share of Bush v. Kerry
1 ? vote share of Kerry
priceEVS for K0.148
as of 4/22/2003
94
IEM vote share market
US Pres. election vote share 2004
1 ? 2-party vote share of Kerry
1 ? vote share of Bush v. Kerry
priceEVS for B v. K0.508
1 ? vote share of Dean
1 ? vote share of Bush v. Dean
as of 7/25/2004
95
Example IEM 1992
Source Berg, DARPA Workshop, 2002
96
Example IEM
Source Berg, DARPA Workshop, 2002
97
Example IEM
Source Berg, DARPA Workshop, 2002
98
Example IEM
Source Berg, DARPA Workshop, 2002
99
Example IEM
Source Berg, DARPA Workshop, 2002
100
Speed TradeSports
Source Wolfers 2004
Contract Pays 100 if Cubs win game 6 (NLCS)
Price of contract (Probability that Cubs win)
Fan reaches over and spoils Alous catch. Still
1 out.
Cubs are winning 3-0 top of the 8th1 out.
The Marlins proceed to hit 8 runs in the 8th
inning
Time (in Ireland)
101
The marginal trader Forsythe 1992,1999 Oliven
1995 Rietz 1998
  • Individuals in IEM are biased, make mistakes
  • Democrats buy too many Democratic stocks
  • Arbitrage is left on the table
  • When there are multiple equivalent trades, the
    cheapest is not always chosen
  • Yet market as a whole is accurate, efficient
  • Why? Prices are set by marginal traders, not
    average traders
  • Marginal traders are active traders, price
    setters, unbiased, better performers

102
Forecast error bounds Berg 2001
  • Single market gives Ex
  • IEM winner takes all P(candidate wins) P(C)
  • IEM vote share Ecandidate vote share EV
  • Can we get error bounds? e.g. Varx?
  • Yes combine the two markets

103
Evaluating accuracyRecall log scoring rule
  • Logarithmic scoring rule(one of several proper
    scoring rules)
  • Pay an expert approach
  • Offer to pay the expert
  • 100 log r if
  • 100 log (1-r) if
  • Expert should choose rPr(A), given caveats

104
Evaluating accuracy
  • Log score gives incentives to be truthful
  • But log score is also an appropriate measure of
    experts accuracy
  • Experts who are better probability assessors will
    earn a higher avg log score over time
  • We advocate evaluate the market just as you
    would evaluate an individual expert
  • For a given market (person), compute average log
    score over many assessments

105
? log score ? information
  • Log score dynamics also shows speed of
    information incorporation
  • Expected log score P(A) log P(A) P(A) log
    P(A) - entropy
  • Actual log score at time t
  • - amount market is surprised by true outcome
  • - of bits of info provided by revelation of
    true outcome
  • As bits of info flow into market, log score ?

106
Avg log score dynamics
IEM
FX
WSE bball
HSX
WSE soccer
107
Avg log score22 IEM political markets
Average log score ?i log (pi)/N pi ith
winners normalized price
108
Example options
  • Options prices (partially) encode a probability
    distribution over their underlying stocks
  • Arbitrary derivative ? P(underlying asset)

payoff
10
20
30
40
50
stock price s
109
Example options
  • Options prices (partially) encode a probability
    distribution over their underlying stocks
  • Arbitrary derivative ? P(underlying asset)

butterfly spread
payoff
10
20
30
40
50
stock price s
- 2call30
110
Example options
  • Options prices (partially) encode a probability
    distribution over their underlying stocks
  • Arbitrary derivative ? P(underlying asset)

payoff
10
20
30
40
50
stock price s
- 2call40
111
Example options
  • call10 - 2 call20 call30 2.13
    relative
  • call30 - 2 call30 call40 5.73 likelihood
    of falling
  • call30 - 2 call40 call50 3.54 near
    center

payoff
2.13
5.73
3.54
10
20
30
40
50
stock price s
112
Example options
  • More generally, uses prices as constraintsEMax0
    ,s-10p10 EMax0,s-20p20 ... etc.
  • Fit to assumed distribution or maximize
    entropy, smothness, etc. subject to constraints

Jackwerth 1996
probability
10
20
30
40
50
stock price s
113
Example TradeSports
Source Wolfers 2004
114
Source Wolfers 2004
115
Source Wolfers 2004
116
Source Wolfers 2004
117
State Price Distribution
Source Wolfers 2004
118
State Price Distribution War and Peace
Source Wolfers 2004
119
Example horse racing
  • Pari-mutuel mechanism
  • Normalized odds match objective frequencies of
    winning very closely
  • 31 horses win about twice as much as 61 horses,
    etc.
  • Slight favorite-longshot bias (favorites are
    better bets extremely rarely Ereturn 0)
  • Ali 77 Rosett 65 Snyder 78 Thaler 88
    Weitzman 65

120
Example horse racing
  • Tracks can be biased, e.g., Winning Colors,a S
    Californian horse, 1988 Kentucky Derby
  • 1 paid in MA 10.60, ..., in FL 10.40,
    ...,KY 8.80,..., MI 7.40, ..., N.CA 5.20,
    ..., S.CA 4.40 Wong 2001
  • Some teams apparently make more than a decent
    living beating the track using computer models
    e.g., Bill Benters team in Hong Kong
  • logistic regression standard now SVMs Edelman
    2003
  • http//www.unr.edu/gaming/confer.asp
  • http//www.wired.com/wired/archive/10.03/betting_p
    r.html

121
Example sports betting
  • US NBA Basketball
  • Closing lines set by market are unbiased
    estimates of game outcomes?better than opening
    lines set by experts Gandar 98
  • Soccer (European football)Experimental market in
    Euro 2000 Championship Schmidt 2002
  • Market prediction betting odds random
  • Market confidence statistically meaningful

122
World Sports Exchange WSE
  • Online in-game sports betting markets
  • Trading allowed continuously throughout game as
    goals are scored, penalties are called, etc. ?
    i.e. as information is revealed!
  • National Basketball Association (NBA)
  • Soccer World Cup
  • MLB, NHL, golf, others
  • http//wsex.com
  • Debnath, EC-2003

Same concept,better site
123
Soccer World Cup 2002
  • 15 Soccer markets (June 715, 2002)
  • Several 1st round and 2nd round games
  • All games ended without penalty shoot-out
  • Scores recorded from www.LiveScore.com
  • Sampled the stream of price and score
    information every 10 seconds

124
Ex Price reaction to goals
  • Sweden vs. Nigeria (Final score 2-1, goals scored
    at 31st (0-1), 39th (1-1) and 83rd (2-1)
    minutes. Yellow bars indicate goals.

125
Ex Price reaction to goals
  • Denmark vs. France (Final Score 2-0, goals
    scored at the 22nd (1-0) and 85th (2-0) minute of
    the game) Yellow bars indicate goals

126
Avg log score entropy
127
Delay Calculation
Where Timestamp of scoring Timestamp of
price update Delay in updating score
network delay Delay in updating the price
network delay
128
Reaction time after goals
129
NBA 2002
  • 18 basketball markets during 2002 Championships
    (May 631, 2002)
  • Score recorded from www.SportsLine.com
  • Sampled the stream of price and score
    information every 10 seconds

130
Correlation between price and score
  • San Antonio vs. LA Lakers (May 07, 2002, Final
    Score 88-85, Correlation 0.93).

131
Correlation between price and score
132
Avg log score entropy
133
Soccer vs. NBA
Soccer World Cup 2002
NBA Championship 2002
134
Soccer vs. NBA
  • Soccer characteristics
  • Price does not change very often
  • Price change is abrupt immediate after goal
  • Average entropy decreases gradually toward 0
  • Comebacks less likely?more surprising when they
    occur
  • Basketball characteristics
  • Price changes very often by small amounts
  • Price is well correlated with scoring
  • More uncertainty until late in the games
  • entropy 0.7 for 77 of game 0.8 for 55.5 of
    game
  • More exciting late?outcome is unclear until
    near end

135
Basketball as coin flips
  • Model scoring as a series of coin flips
  • tails Boston 1
  • heads Detroit 1
  • Current scores Bt,Dt
  • Final scores BT,DT
  • ComputeP(BT-DT 5.5 Bt,Dt)
  • ED B 180
  • EB - D 5.5
  • EB92.75ED87.25
  • p P(tails) P(Boston) 92.75/180
    0.515

May10 505 DETROIT o/u 180 0700 506 BOSTON -5.5
180-Bt-Dt
180-Bt-Dtj
? ( )pj (1-p)(180-Bt-Dt-j)
j93-Bt
136
Basketball as coin flips
137
Explain the marketParallel IR
Pennock 2002
IEM Giuliani NY Senate 2000
Use expected entropy lossto determine the key
wordsand phrases that bestdifferentiate between
textstreams before and after thedate of interest
138
Explain the marketParallel IR
us.politics
IEM Gore US Pres 2000
florida, ballots, recount, palm
beach, ballot, beach county, palm beach
county
FX Extraterrestrial Life
sci.space.news
meteorite, life, evidence, martian
meteorite,primitive, gibson, organic, of
possible,martian, life on mars, ...
139
Applications future work
  • Monitoring dynamics
  • Automatic explanations
  • Low probability event detection
  • Sporting events auto highlights, auto summary,
    attention scheduling, finding turning points,
    most exciting games/moments, modeling different
    sports...

140
Play-money market games
http//www.hsx.com/
http//www.newsfutures.com/
http//www.100world.com/
http//www.ideosphere.com/
http//www.ipreo.com/
http//www.incentivemarkets.com/
141
Play-money market games
  • Many studies show that prices in real-money
    markets provide accurate likelihoods
  • Researchers credit monetary incentives/risk
  • Can play money markets provide accurate
    forecasts?
  • Incentives in market games may derive from
    entertainment value, educational value,
    competitive spirit, bragging rights, prizes

142
Market games analyzed
  • Hollywood Stock Exchange (HSX)
  • Play-money market in movies and stars
  • Movie stocks movie options
  • Award options (e.g., Oscar options)
  • Foresight Exchange (FX)
  • Market game to bet on developments in science
    technology e.g., Cancer cured by 2010 Higgs
    boson verified Water on moon Extraterrestrial
    life verified
  • NewsFutures
  • Newsworthy events items of pop interest

143
Put-call parity
  • stock price s - call price put price strike
    price k

payoff
10
20
30
40
50
stock price s
144
Internal coherence HSX
  • Prices of movie stocks and options adhere to
    put-call parity, as in real markets
  • Arbitrage loopholes disappear over time, as in
    real markets

145
Internal coherenceHSX vs IEM
  • Arbitrage closure for HSX award options
  • Arbitrage closure on IEM qualitatively similar to
    HSX, though quantitatively more efficient

146
Forecast accuracy HSX
  • 0.94 correlation
  • Comparable to expert forecasts at Box Office Mojo

147
Combining forecasts
  • HSX Box Office Mojo (expert forecast)
  • Correlation of errors 0.818

148
Probabilistic forecastsHSX
  • Bins of similarly-priced options
  • Observed frequency? average price
  • Analysis similar for horse racing markets
  • Error bars 95 confidence intervals assuming
    events are indep Bernoulli trials

149
Avg logarithmic score
HSX Oscar options 2000
forecast source avg log score Feb 19 HSX
prices -0.854 DPRoberts -0.874 Fielding -1.04 e
xpert consensus -1.05 Feb 18 HSX
prices -1.08 Tom -1.08 John -1.22 Jen -1.25
150
Probabilistic forecastsFX
  • Prices 30 days before expiration
  • Similar results
  • 60 days before
  • specific date
  • Average logarithmic score

FX
151
Real marketsvs. market games
IEM
HSX
averagelog score
arbitrageclosure
152
Real marketsvs. market games
HSX
FX, F1P6
forecast source avg log score F1P6 linear
scoring -1.84 F1P6 F1-style scoring -1.82 betting
odds -1.86 F1P6 flat scoring -2.03 F1P6 winner
scoring -2.32
expectedvalueforecasts489 movies
153
Does money matter? Play vs real, head to head
  • Experiment
  • 2003 NFL Season
  • Online football forecasting competition
  • Contestants assess probabilities for each game
  • Quadratic scoring rule
  • 2,000 experts, plus
  • NewsFutures (play )
  • Tradesports (real )
  • Used last trade prices
  • Results
  • Play money and real money performed similarly
  • 6th and 8th respectively
  • Markets beat most of the 2,000 contestants
  • Average of experts came 39th

Forthcoming, Electronic Markets, Emile
Servan-Schreiber, Justin Wolfers, David Pennock
and Brian Galebach
154
(No Transcript)
155
Does money matter? Play vs real, head to head
StatisticallyTS NFNF Avg TS Avg
156
Market games summary
  • Online market games can contain a great deal of
    information reflecting interactions among
    millions of people
  • Naturally attract well-informed and
    well-motivated players
  • Game players tend to be knowledgeable and
    enthusiastic
  • Internet polls - skewed demographic
  • Polls typically ask questions of the form What
    do you want?
  • Games ask questions of the form What do you
    think will happen?

157
Market games discussion
  • Are incentives strong enough?
  • Yes (to a degree)
  • Manifested as price coherence, information
    incorporation, and forecast accuracy
  • Reduced incentive for information discovery
    possibly balanced by better interpersonal
    weighting
  • Statistical validations show HSX, FX, NF are
    reliable sources for forecasts
  • HSX predictions expert predictions
  • Combining sources can help

158
Applications
  • Obtain information from existing games
  • Build new games in areas of interest
  • Alternative to costly market research
  • Easy/inexpensive to setup compared to real
    markets
  • Few regulations compared to real markets
  • Worldwide audience

159
Future work
  • Data mining and fusion algorithms can improve
    predictions
  • Weight users by expertise, reliability, etc.
  • Controlling for manipulation
  • Merging with other sources
  • Box office prediction (market chat groups,
    query logs, movie reviews, news, experts)
  • Weather forecasting (futures, derivatives
    experts, satellite images)
  • Privacy issues and incentives

160
4. Lab experiments theory
  • Laboratory experiments, field tests
  • Theoretical underpinnings
  • Rational expectations
  • Efficient markets hypothesis
  • No-Trade Theorems
  • Information aggregation

161
Laboratory experiments
  • Experimental economics
  • Plott and decendents Ledyard, Hanson, Fine,
    Coughlan, Chen, ... (and others)
  • Controlled tests of information aggregation
  • Participants are given information, asked to
    trade in market for real monetary stakes
  • Equilibrium is examined for signs of information
    incorporation

162
Plott Sunder 1982
  • Three disjoint exhaustive states X,Y,Z
  • Three securities
  • A few insiders know true state Z
  • Market equilibrates according to rational
    expectations as if everyone knew Z

163
Plott Sunder 1982
  • Three disjoint exhaustive states X,Y,Z
  • Three securities
  • Some see samples of joint can infer P(Zsamples)
  • Results less definitive

164
Plott Sunder 1988
  • Three disjoint exhaustive states X,Y,Z
  • Three securities
  • A few insiders know true state is not X
  • A few insiders know true state is not Y
  • Market equilibrates according to rational
    expectations Z true

165
Plott Sunder 1988
  • Three disjoint exhaustive states X,Y,Z
  • One security
  • A few insiders know true state is not X
  • A few insiders know true state is not Y
  • Market does not equilibrate according to rational
    expectations

166
Forsythe and Lundholm 90
  • Three disjoint exhaustive states X,Y,Z
  • One security
  • Some know not X
  • Some know not Y
  • As long as traders are sufficiently knowledgeable
    experienced, market equilibrates according to
    rational expectations

1 if Z
not X
not Y
1
price of Z
0
time
167
Small groups
  • In small, illiquid markets, information
    aggregation can fail
  • Chen, Fine, Huberman EC-2001 propose a two
    stage process
  • Trade in a market to assess participants risk
    attitude and predictive ability
  • Query participants probabilities using the log
    score compute a weighted average of
    probabilities, with weights derived from step 1

168
Small groups
Source Fine DARPA Workshop, 2002
169
Field test Hewlett Packard
  • Plott Chen 2002 conducted a field test at
    Hewlett Packard (HP)
  • Set up a securities market to predict, e.g. next
    months sales (in ) of product X
  • 1 iff 0 20K
  • 1 iff 10K 30K
  • Employees could trade at lunch, weekends, for
    real
  • Market predictions beat official HP forecasts

170
Why does it work?Rational expectations
  • Theory Even when agents have asymmetric
    information, market equilibrates as if all agents
    had all info Grossman 1981 Lucas 1972
  • Procedural explanation agents learn from prices
    Hanson 98 Mckelvey 86 Mckelvey 90 Nielsen 90
  • Agents begin with common priors, differing
    information
  • Observe sufficient summary statistic (e.g.,
    price)
  • Converge to common posteriors
  • In compete market, all (private) info is revealed

171
Efficient market hypotheses (EMH)
  • Internal coherenceprices are self-consistent or
    arbitrage-free
  • Weak form Internal unpredictabilityfuture
    prices unpredictable from past prices
  • Semi-strong form Unpredictabilityfuture prices
    unpredictable from all public info
  • Strong form Expert-level accuracyunpredictable
    from all public private infoexperts cannot
    outperform naïve traders
  • More

stronger assumps
http//www.investorhome.com/emh.htm
172
How efficient are markets?
  • Good question as many opinions as experts
  • Cannot prove efficiency can only detect
    inefficiency
  • Generally, it is thought that large public
    markets are very efficient, smaller markets
    questionable
  • Still, strong form is sometimes too strong
  • There is betting on Oscars until winners are
    announced
  • Prices do not converge completely on eventual
    winners
  • Yet aggregating all private knowledge in the
    world (including Academy members votes) would
    yield the precise winners with certainty

173
No-trade theorems
  • Why trade? These markets are zero-sum games
    (negative sum w/ transaction fees)
  • For all money earned, there is an equal (greater)
    amount lost am I smarter than average?
  • Rational risk-neutral traders will never trade
    Milgrom Stokey 1982Aumann 1976. Informally
  • Only those smarter than average should trade
  • But once below avg traders leave, avg goes up
  • Ad infinitum until no one is left
  • Or If a rational trader is willing to trade with
    me, he or she must know something I dont know

174
But... Trade happens
  • Volume in financial markets, gambling is high
  • Why do people trade?
  • 1. Different risk attitudes (insurance, hedging)
    Cant explain all volume
  • 2. Irrational (boundedly rational) behavior
  • Rationality arguments require unrealistic
    computational abilities, including infinite
    precision Bayesian updating, infinite
    game-theoretic recursive reasoning
  • More than 1/2 of people think theyre smarter
    than average
  • Biased beliefs, differing priors, inexperience,
    mistakes, etc.
  • Note that its rational to trade as long as some
    participants are irrational

175
A theory of info aggregationNotation
Pennock 2002
  • Event A (event negation A)
  • Security
  • Probability Pr(A)
  • Likelihood L(A) Pr(A)/(1-Pr(A))
  • Log-likelihood LL(A) ln L(A)
  • Price of at time t pt
  • Likelihood price lt pt/(1-pt)
  • Log-likelihood price llt ln lt

1 if A
1 if A
176
Assumptions
  • Efficiency assumptionLet pt be the price of
    at time tThen
  • Pr(Apt,pt-1,pt-2,,p0) pt
  • (Markov assumpt. accuracy assumpt.)

1 if A
177
Consequences
  • Eptpt-1 x xexpected price at time t
    is price at t-1
  • log-likelihood price is e? as likely to go up
    by ? in worlds where A is true, as it is to go up
    ? in worlds where A is false

178
Consequences
  • Pr(ptyA,pt-1x) Pr(ptypt-1x)price
    is y/x times as likely to go from x to y in
    worlds where A is true
  • given A is true, expected price at time t is
    greater than price at t-1 by an amount prop. to
    the variance of price

EptA,pt-1x x
179
Empirical verification
Distribution of changes e in log-likelihood price
over 22 IEM markets, consistent with theory
Distribution of changes e in log-likelihood price
of winning candidates divided by losing
candidates. Line is ee, as predicted by theory
180
Avg log score dynamics
IEM
FX
WSE bball
HSX
WSE soccer
181
Applications future work
  • Better understanding of market dynamics
    assumptions required for predictive value
  • Closeness of fit to theory is a measure of market
    forecast accuracy could serve as an evaluation
    metric or confidence metric
  • Explaining symmetry, power-law dist in IEM

182
Coin-flip model
  • Previous theory minimalist assumptions no
    explicit notion of evidence
  • Coin-flip model of evidence incorporation
  • A ? occurrence of n/2 tails out of n flips
  • Release of info ? revelation of flip outcomes
  • At time t it tails have occurred out of kt flips
  • For A to occur, n/2-it more tails are needed

183
Avg log score dynamics
IEM
FX
WSE bball
coin flip model
HSX
WSE soccer
184
5. Characterizin
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