本文探讨了跨市场套利对账户余额的影响。假设在预测市场A和B中存在价格差异，通过在A市场购买NO，在B市场购买YES进行套利。理论上，无论事件结果如何，总收益为a-b，其中a和b分别是两个市场的价格。如果两个市场的概率估计平均值等于事件的真实概率，利润将在两个市场平均分配。但如果市场存在偏差，更准确的市场会获得更多利润，套利行为实际上是将资金从不准确的市场转移到更准确的市场。持续套利会导致不准确的市场资金流失，而准确的市场资金流入。

💰跨市场套利的核心在于利用不同市场对同一事件的定价差异，通过在价格较低的市场购买，在价格较高的市场卖出，从而实现无风险盈利。

⚖️当两个市场的概率估计平均值接近事件的真实概率时，套利利润会在两个市场之间平均分配。这表明市场在一定程度上是有效的，价格差异反映了真实概率。

📉如果市场存在偏差，即一个市场的概率估计更接近真实值，那么套利者在该市场获得的利润会相对较少。套利行为会将资金从不准确的市场转移到更准确的市场，这是一种市场自我纠正的机制。

💸持续的套利操作，会导致不准确的市场资金不断流出，而更准确的市场资金不断流入，最终可能会使不准确的市场因资金耗尽而无法继续交易。

Published on January 21, 2025 3:44 AM GMT

Also, why one account keeps running dry when you try to arbitrage two markets.

I was thinking about how inter-market arbitrage might affect one's account balances & the total amount of money on the markets arbitraged.

## The arbitrage. 

Let's say I have accounts on prediction markets A and B, and I have discovered an arbitrage opportunity for an event that has a price/probability of a on A and b on B such that a>b.

This price difference allows us to arbitrage the markets by buying shares of NO on market A and buying shares of YES on market B. So currently our accounts would look like:

Cost:

Market A: (1-a) dollars spent

Market B: b dollars spent

Let the "true" probability of the event happening be p. Then, when the market resolves, we profit on:
- Market A: (1-p) dollars, in expectation
- Market B: p dollars, in expectation

So we can expect to make
- (1-p) - (1-a) = a-p dollars on market A
- p-b dollars on market B

The arbitrage works because a-p + p-b = a-b which is positive, and there is no risk because we always get 1 dollar back regardless of whether the event happens or not.

## The flow of money

If the two markets' probability estimates of the events average to the true probability of the event (such that (a+b)/2 = p), then we can expect our profit to be split evenly between market A and B, since if a+b=2p, then a-p = p-b.

If the markets are skewed such that A is more correct than B, then we can expect to make less money on A than B, as a-p < p-b when 2p < a+b. [^1]

So in effect, by performing the arbitrage, we are draining money from the less accurate prediction market, and feeding into the more accurate one.

If we were to try to continue the arbitrage, we will have to withdraw money from B and feed it into A, draining money from the less accurate market and putting money into the more accurate one.

[^1]: Without loss of generality, the same applies if market B had a close-to-true probability estimate than A

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