This market was inspired by my previous chaos theory markets. The problem with those was that they each resolved themselves, so the markets were more about finding a fixed point than actual chaos.
I am correcting this by making a sequence of markets. At the end of each month the market will close. Then the market for that month will resolve, and the rest of the markets will re-open.
The January 2024 market resolves to 50%.
Each market after that resolves to 3.56995*x*(1-x) rounded to the nearest percent, where x is the displayed value (as a fraction) of the market for the prior month, before it resolves.
So, for example, if the January 2024 market is trading at 40% at the end of January, and the market closes, the January 2024 market will then resolve to 50% at that time, and a month later, the February 2024 market will resolve to 86% ~ 85.68 = 3.56995*0.4*(1-0.4).
Anyone can extend by adding more months. Please match the format and don't make a month unless the prior month already exists, otherwise I will N/A.
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I feel this won’t be too chaotic either. The current month resolution is fixed, and people will price the next one or two accordingly, and ignore the far future. The only way to win is to snipe the close, which isn’t too much fun imo. Also, the rounding kills much of the potential for indeterminacy.
Finally, seems to me allowing the parameter (3.56995) to vary somehow based on trader behavior is key to getting chaotic prices, as it opens up the full logistic map as a canvas for manipulation, instead of just sniping the close.