" Market Games for Mining Custome"
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 = Mon1e 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 2 • pri1(m) = (Mon1 m)Mon2Num1 (Mon2 m()Mon12NumMonTotTot 1 m)Num2 ln Tot(Mon1 m) Mon m) 2 ( Mon 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 priI(A) where I(A) is indicator fn 2. Payoff PayI(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 priI(A)+PayI(A) for pri dollars • Seller of priI(A) gets $ priMPr(A) • Seller of PayI(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 $3I(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