diff --git a/docs/learn/parimutuel.md b/docs/learn/parimutuel.md new file mode 100644 index 00000000..38b6e92e --- /dev/null +++ b/docs/learn/parimutuel.md @@ -0,0 +1,154 @@ +--- +id: parimutuel +title: Parimutuel +--- + +## Overview + +The term _parimutuel_ refers to a particular market making and payout mechanism +used on Zeitgeist for extra casual markets. + +These are "losers pay winners" market makers: Any informant can bet any amount +at any time. Their bet amount goes into the _pot_ and they receive tokens which +represent their share of the pot. After the market is resolved, the entire pot +is distributed amongst those who wagered on the outcome that materialized, +proportional to what their share of the pot is. + +Although parimutuels work with scalar markets, Zeitgeist currently only supports +parimutuel for categorical markets. + +## Example + +Let's imagine a simple prediction market based on a horse race. There are five +horses running in this race: A, B, C, D and E. People are placing bets on which +horse they believe will win. + +Suppose that at this point, the total amount of money wagered on these horses is +as follows: + +- A: $200 +- B: $300 +- C: $100 +- D: $250 +- E: $150 + +Altogether, the total pool of money that's been wagered is $1,000. + +If you bet on Horse A, and Horse A wins, for each dollar you bet, you'd get the +total bets on all horses ($1,000) divided by the total amount bet on Horse A +($200). So for every dollar you bet, you would get $5 back - this includes the +return of your original dollar plus $4 in winnings. If you bet $100, then you'd +receive a total of $500 from the pot. The market predicts the probability of A +winning the race as 20% (or 1:4). + +Similarly, if you bet on Horse B, and Horse B wins, for each dollar you bet, +you'd get the total bets on all horses ($1,000) divided by the amount bet on +Horse B ($300). So for every dollar you bet, you would get roughly $3.33 back - +this includes the return of your original dollar plus about $2.33 in winnings. +The market predicts the probability of B winning the race as 30%. + +And so on for the rest of the horses... + +### Advantages and Disadvantages + +Unlike automatic market makers (AMM) or continuous double-auction (CDA), the +parimutuel market maker does not require any liquidity, and shares the property +of AMM that it can fill any order at any time. It is essentially a "bring your +own liquidity" market maker. + +However, it does suffer several disadvantages compared to the other mechanisms +on Zeitgeist: + +- The odds are not fixed when tokens are bought. For example, if an informant + fills an ask at a price of 0.33 on an order book, then they know that they'll + get a 300% payoff if they're right. That's not the case at a parimutuel. If + more people buy your outcome, your payoff gets worse. This makes it impossible + to properly reward traders that have moved the price in the right direction + and have done so early and incentivizes informants to withhold information + until close to the end of the market. + + But a particularly vexing symptom of this problem is that, if a market becomes + trivialized (some outcome $X$ has materialized before the end of the market) + and at least two agents have bet on the winning outcome, then it's a winning + strategy to keep pumping more money into the market to dilute the other + agent's stake. + +- No selling of contracts. Once you've bought a contract, you have to hold it. + You can't just take back your bet. This means that parimutuels are really only + suited for markets which resolve very quickly. + +As such, parimutuel markets are perfectly suited for short-lived markets where +the market's outcome is published at a predefined time or where odds are +considered comparatively stable. + +## Parimutuel Markets on Zeitgeist + +### Betting + +Every parimutuel market uses a special account as the pot. If an informant +places a bet, they send `x` units of collateral to the pot and receive `x` units +of the corresponding type of _parimutuel shares_. Informants must observe a +minimum bet size defined in the parimutuel pallet when placing their bets. + + + +External fees are paid when users buy parimutuel shares in the usual fashion: If +Alice buys parimutuel shares for a certain amount of collateral, then the +external fees are deducted from this amount before the rest of the transaction +is executed. The amount Alice is left with after fees are deducted must satisfy +the minimum bet size requirement. + +### Claiming Rewards + +Suppose an informant holds $x$ units of the parimutuel share for the outcome +$A$. If the market resolves to some outcome not equal to $A$, then the +informants shares are completely worthless; if the market resolves to $A$, then +the informant receives $xr$ units of collateral from the pot, where $r$ is the +ratio between the amount wagered on $A$ and the total amount wagered on any +outcome. A detailed outline of the math is presented further below. + +If the unlikely event occurs that the winning token has a total issuance of zero +but the pot is not empty, each informant can redeem _any_ parimutuel share for +its original price, one unit of collateral. This avoids confusion on markets +with very low participation ("I bet $100 on A, no one else was interested, B won +and now my money is gone?! Why?"). + +## Details: Expected Payoff in Categorical Markets + +If you believe an outcome has a probability p of occurring, then the fair return +on a winning bet should be $1/p$. This is because, over many repetitions, you'd +expect to win once every $1/p$ times. For example, if you believe that +$p = 0.25$, then fair odds would be 4:1. This means for every dollar you bet, +you'd expect a return of $4 on a win. + +We consider a denote the amount wagered on each outcome $i$ by $w_i$. In the +parimutuel system, the return for each dollar bet on $i$ is +$r_i = \sum_k w_k +/w_i$. For this return to be considered "fair" based on your +belief about the outcome's probability, it should match the inverse of your +believed probability. In other words, if you think there's a 25% chance of an +outcome, you'd expect the system to give you 4:1 odds (or a return of $4 for +every $1 bet) for it to be a fair bet. + +If the system offers odds that are better than your believed probability, then +you'd consider the bet to have positive expected value (you expect to make a +profit in the long run). If the odds are worse, then the bet has negative +expected value (you expect to lose money in the long run). + +In essence, for a bet to be "fair", the expected value should be zero: you +neither expect to make nor lose money in the long run. This happens when the +system's offered odds match your personal beliefs about the probability of the +outcome. + +Long story short, given a pot balance $w$, the return $r_i(w)$ of a fair bet on +$i$ would match the inverse of the probability $p_i(w)$ of $i$. Thus, the +prediction/spot price of $i$ is $p_i(w) = r_i(w)^{-1}$. + +## Bibliography & Further Reading + +- Abraham Othman, Tuomas Sandholm, David M. Pennock, Daniel M. Reeves, + [A practical liquidity-sensitive automated market maker](https://www.researchgate.net/publication/221445031_A_practical_liquidity-sensitive_automated_market_maker), + ACM Transactions on Economics and Computation 1(3), pp. 377-386 (2010) +- D. M. Pennock, "A dynamic pari-mutuel market for hedging, wagering, and + information aggregation," in Proceedings of the 5th ACM Conference, 2004. DOI: + 10.1145/988772.988799 diff --git a/sidebars.js b/sidebars.js index 305b8013..a0e1301f 100644 --- a/sidebars.js +++ b/sidebars.js @@ -22,6 +22,7 @@ const sidebars = { items: [ "learn/prediction-markets", "learn/liquidity", + "learn/parimutuel", "learn/using-zeitgeist-markets", "learn/betting-strategy", "learn/market-rules",