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Market Games for Mining Custome

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					              Research Labs
Y!RL Spot Workshop on
New 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 Labs

Distinguished guests (thanks!)
• Edward Castronova
  Prof. Economics, Cal State Fullerton
• John Ledyard
  Prof. Econ & Social Sciences, CalTech
• Justin Wolfers
  Prof. Economics, Stanford
             Research Labs

Schedule
11am-noon    Castronova on the Future of
             Cyberspace Economies
noon-1pm     Lunch provided
1pm-2pm      Ledyard on ~ Information Markets
             and Experimental Economics
2pm-3pm      Wolfers on ~ Prediction Markets,
             Play Money, & Gambling
3pm-3:30pm   Pennock on Dynamic Pari-Mutuel
             Market for Hedging, Speculating
3:30pm-4pm   Roundtable Discussion
                    Research Labs


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

paper to appear EC’04, New York
               Research Labs
Economic 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
               Research Labs

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
              Research Labs

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
                       Research Labs
 What is a financial
 “prediction market”?
 • Take a random variable, e.g.
 2004 CA               US’04Pres =          =6?
Earthquake?              Bush?
 • Turn it into a financial instrument
   payoff = realized value of variable
   I am entitled to:


      $1 if            =6    $0 if     6
                   Research Labs


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
         Research Labs

Updating on new information
                    Research Labs

The flip-side of prediction: Hedging
E.g. options, futures, insurance, ...
• Allocate risk (“hedge”)       • Aggregate information
   • insured transfers risk        • price of insurance
     to insurer, for $$               prob of catastrophe
   • farmer transfers risk         • OJ futures prices yield
                                     weather forecasts
     to futures speculators
                                   • prices of options
   • put option buyer                encode prob dists
     hedges against stock            over stock
     drop; seller assumes            movements
     risk                          • market-driven lines
                                     are unbiased
                                     estimates of
                                     outcomes
                                   • IEM political forecasts
                  Research Labs
Continuous double auction
CDA
• 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://www.biz.uiowa.edu/iem   http://us.newsfutures.com/
           Research Labs

Running comparison
          no risk   liquidity     info
                                aggreg.
 CDA        x                       x
 CDAwMM
 PM
 DPM
               Research Labs


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/
                  Research Labs


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
           Research Labs

Running comparison
          no risk   liquidity     info
                                aggreg.
 CDA        x                       x
 CDAwMM                x          x
 PM
 DPM
              Research Labs

What is a pari-mutuel market?
                             A B

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

What is a pari-mutuel market?
                             A B

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

What is a pari-mutuel market?
                             A B

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

What is a pari-mutuel market?
                               A B

• E.g. horse racetrack style wagering
• Two outcomes:      A                 B
• 2 equivalent
  ways to consider            1+ $ on B = 1+ 8 =$3
                                 $ on A      4
  payment rule
  • refund + share of B          total $ = 12 = $3
  • share of total               $ on A     4
                  Research Labs


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
           Research Labs

Running comparison
          no risk   liquidity     info
                                aggreg.
 CDA        x                       x
 CDAwMM                x          x
 PM         x          x
 DPM
               Research Labs

Dynamic pari-mutuel market
Basic 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
                  Research Labs

Dynamic pari-mutuel market
Example Interface
                        A B                A B

• Outcomes:           A                      B
• Current payoff/shr: $5.20                  $0.97
                              $3.27
                              $3.27
                             $3.27                  $3.27
                                                    $3.27
                   sell 100@ $3.25                 $3.27
                                        sell 100@ $0.85
  market maker     sell 100@ $3.00      sell 100@ $0.75
        traders     sell 35@ $1.50         sell 3@ $0.50
                   buy 4@ $1.25       buy 200@ $0.25
                  buy 52@ $1.00
                 Research Labs

Dynamic pari-mutuel market
Setup & Notation
                        A B        A B

•   Two outcomes:       A            B
•   Price per share:    pri1         pri2
•   Payoff per share:   Pay1         Pay2
•   Money wagered:      Mon1         Mon2
                         (Tot=Mon1+Mon2)
• # shares bought:      Num1         Num2
             Research Labs

How are prices set?
• A price function pri(n) gives the
  instantaneous price of an infinitesimal
  additional share beyond nthe nth

                          
• Cost of buying n shares: pri (n)dn
                          0
• Different assumptions lead to different
  price functions, each reasonable
              Research Labs

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
             Research Labs

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

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


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

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)
             Research Labs

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
             Research Labs

Deriving the price function
• Solve the differential equation
  dm/dn = pri1(n) = Pay2
          = (Mon1+m)/Num2
  where m is dollars spent on n shares

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

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
  •   ...
              Research Labs

Price function II
• Suppose: pri1/pri2 = Mon1/Mon2
  also natural, reasonable
• Implies

   MPr(A) =         Mon1 Num1
              Mon1 Num1 + Mon2 Num2
              Research Labs

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
                        2   N 1 n
                                    2
                                       N1      
  cost1(n) = m =   Mon1e     N2       N2
                                             1
                       
                                              
                                               
                                                   N 1 n    N1
                             Mon1          2              2
  pri1(n) = dm/dn =                      e          N2       N2

                        ( Num1  n) Num2
             Research Labs

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

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

• Market probability
         MPr(A) = pri1 / Pay1
                           Research Labs

Price function III
• Suppose: pri1/pri2 = Mon1/Mon2
• Implies
  • MPr(A) =                   Mon1 Num1
                         Mon1 Num1 + Mon2 Num2

                                                  ( Mon1  m) Mon2  Tot
  • pri1(m) = (Mon1 m)Mon2Num1 (Mon2  m)Mon2Num2  Tot(Mon1 m)Num2  ln Tot(Mon1 m) 
                                                                                 Mon1(Tot  m) 
                                                                                               


     cost1(m) =             m( Num1  Num2) Num2(Tot  m)  Tot( Mon1  m) 
                                                              Mon1(Tot  m) 
                                                          ln                
                                  Tot          Mon2                          
              Research Labs

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
                 Research Labs

Aftermarkets
•   Losing money redistributed: Each
    share is different. Composed of:
    1. Original price refunded
       priI(A)
       where I(A) is indicator fn
    2. Payoff
       PayI(A)
                   Research Labs

Aftermarkets
•       Can sell two parts in two
        aftermarkets
•       The two aftermarkets can be
        automatically bundled, hiding the
        complexity from traders
    •     New buyer buys priI(A)+PayI(A) for pri
          dollars
    •     Seller of priI(A) gets $ priMPr(A)
    •     Seller of PayI(A) gets $ pri(1-MPr(A))
                   Research Labs
Alternative “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 $3I(A) ; limits loss to $3 or $0
                   Research Labs

Running comparison
                  no risk   liquidity     info
                                        aggreg.
 CDA                x                       x
 CDAwMM                        x          x
 PM                 x          x
 DPM                x          x          x


 MSR                           x          x
  [Hanson 2002]
            Research Labs

Pros & cons of DPM types
          Losing money       All money
           redistributed    redistributed

   Pros      Winning        Aftermarket
          wagers never     trivial, natural
           lose money
  Cons    Aftermarket        Winning
          complicated       wagers can
                           lose money!
                  Research Labs

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
             Research Labs

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

				
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posted:4/7/2010
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