How concentrated LP bands work

A plain-language walk through the idea behind Tessera's DC-LMSR. For the exact math and definitions, read the whitepaper, section 5.

1. A flat LMSR market

A prediction market on a yes/no question needs someone to quote a price at every probability from near 0 to near 1. A logarithmic market scoring rule (LMSR) does that with one liquidity parameter, b. The price of "yes" moves along a smooth logistic curve as traders buy and sell.

In a flat LMSR, the capital behind the market is committed across the whole range. That includes prices a market rarely visits. A question that trades between 40% and 60% for weeks still has capital reserved for 2% and 98%.

2. What a band changes

In Tessera, a liquidity provider picks a price range, a band, such as 45% to 55%. Inside that band the market uses the same LMSR curve traders already know. The LP commits capital for that band only, not for the whole range.

Traders see the same kind of curve. The difference is on the LP side: a narrower band means less capital is needed to provide the same depth inside it.

3. What the band does not do

• It does not remove risk. If the price leaves the band, the LP's position stops earning from trades there and the LP can end up holding one side.
• It does not guarantee returns. LPs in a resolving market face informed traders, which the whitepaper discusses in its adverse selection section.
• It does not change the question. The market still resolves to yes or no.

4. Where this stands

Tessera is a research prototype. The reference simulator and the contracts run on the Base Sepolia test network only. There is no audit and no mainnet deployment, and nothing on this site is an offer or advice. Capital efficiency (η) is defined in the whitepaper as ln 2 divided by the logit width of the band, divided by max(p_b, 1 - p_a). With that formula a band of 49% to 51% gives about 16.99 times a flat LMSR, 45% to 55% gives about 3.14 times, and a wide 5% to 95% band gives about 0.124 times. These are results from the formula, not measured returns.

Questions or corrections are welcome: contact@tesserafoundation.com.