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Implementing Hanson's Market Maker states:

If the market maker wants to quote a "current price", he can. The current price for outcome 1 is:

$$ \mbox{price1} = \frac{e^{\frac{q1}{b}}}{e^{\frac{q1}{b}} + e^{\frac{q2}{b}}} $$

Why this is the case? Is it just some simple "see-saw" algorithm? Exert pressure on one side and it will simply radiate across into the corresponding +/- price change?

I am asking in the context of writing a simple market-making algorithm to offer bids and quotes (on a virtual market), but this seems too simple.

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    $\begingroup$ Is this related to your university project? $\endgroup$
    – chrisaycock
    Apr 24 '13 at 19:55
  • $\begingroup$ Its related to the algorithm I linked to in the question. $\endgroup$
    – user997112
    Apr 24 '13 at 20:33
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It does create a see-saw. This can be reduced by having it charge a slightly bigger spread, which gets contributed to b. In this way, b effectively becomes a market making fund, and volatility decreases as trade volume increases. This makes the LMSR market maker liquidity sensitive.

This makes the market more efficient as spreads decrease over time as trading imparts price knowledge and subsidizes liquidity.

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