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Consider a prediction market with two outcomes (Yes and No) and a scoring rule based on Hansons’s LMSR, i.e. ln(ea+eb), where a and b are the number of Yes resp. No shares sold.

Assume that I have previously bought 10 Yes shares, but now I changed my mind and want to bet on the other side. I have the option to either sell my 10 yes shares, or buy 10 no shares.

When should I choose one or the other option? Is it always the same, or does it depend on, say, the current market?

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For the market it does not matter, the prices/chances change exactly the same: ea-10/(ea-10+eb) = ea/(ea+eb+10).

For you as the trader, selling 10 yes shares is preferable. It means you get your money out and can invest it elsewhere.

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