It seems you cannot simply use this: C = b * ln(eq1/b+eq2/b) as with the market with 2 discrete outcomes, as the “higher than market” and “lower than market” bets are placed at different market price points.

I second the thoughts that this blog makes implementation of LMSR easy to understand.. thanks!..

I have problem with its implementation in dynamically changing price markets. Let’s say the question is “How much will X sell” and you started with 1000. People can bet higher or lower than market price and this is expected to change the market price in return. New bets come in based on the updated price (ie 1055). How do you calculate the up-to-date price in this case – what is the logic/formula behind the scenes? Inkling, for instance, offers this option.

It seems you cannot simply use this: C = b * ln(eq1/b+eq2/b) as with the market with 2 discrete outcomes, as the “higher than market” and “lower than market” bets are placed at different market price points.

Any comments/links will be appreciated! Thank you!

Very good explanation of Hanson’s scoring rule. Have couple of questions: 1) How do you chosse a value for b for a given market. Does it depend on the market size (i.e number of participants?). I understand your explanation that it controls the maximum money that the market maker can loose (for a 2 outcome case it is b* ln2). So, for example, if I set b = 100, then the max loss = $69, if I choose b = 50, the max loss = $34.5; How do i know which value is correct, because “b” also impacts the price functions? Does it depend on the initial play money? 2) How to choose the correct initial play money for a market?

Thank you.

I am writing a research paper on http://www.Hubdub.com, and I’m still confused on how they calculate their Payments, outcome Percentage etc. for Hubdub $$.

I was wondering if you could spare a few minutes and check out Hubdub, and briefly explain to how their system works.

Again, thank you.

Frederic wrote:

> I recently stumbled upon your article “Implementing Hanson’s Market
> Maker ” which was really interesting (I had read both Hanson’s
> articles and couldn’t really figure out everything it contained, nor
> extract the ‘implementation guides’ I would have wanted).
>
> I have a few questions, though, and would be glad if you could spare a
> few minutes to answer me (I know that the article is already almost 3
> years old).
>
> Basically, the cost function is C = b * ln(exp(q1)/b+exp(q2)/b)
>
> – Would this generalize, for n outcomes to C = b *
> ln(exp(q1)/b+exp(q2)/b+exp(q3)/b+…+exp(qn)/b)?
> – If a trader sells short some shares for q1, does this mean that, in
> fact, the amount of q2 will increase? (or q2,q3, … in the
> generalized case?) Because I don’t see negative values in your example
> (and negative values will just make the exp(q1) close to 0). Or is the
> short selling forbidden by this model?

I answered:

* Yes, it generalizes easily and I believe that’s the correct formula (didn’t check completely). See this book chapter for the exact formula: http://blog.oddhead.com/2007/09/17/computational-aspects-of-prediction-markets-book-chapter-and-extended-bibliography/

* “short” selling is a poor concept for a standard type of prediction market where each winning share pays $1 (or any fixed amount). It’s much clearer to think of “buy not q1″ rather than “short sell q1″. It’s perfectly fine to “buy not q1″ which is equivalent to “buy q2, q3, q4, etc.” for all securities. See: http://blog.oddhead.com/2009/03/17/kiss-prediction-market-lingo-goodbye/