Beyond
Binary.
A quantitative framework for the LMSR-PM Hybrid architecture. Solving the microstructure dilemma.
The Microstructure
Dilemma.
Traditional continuous prediction markets are fatally constrained by liquidity depth requirements and unmitigated protocol bankruptcy risk against sharps.
Pure order-book designs fail in long-tail scalar markets due to fractured liquidity across hundreds of price ticks. Traditional solutions attempt to graft standard Automated Market Makers (AMMs) onto continuous probability distributions.
However, scalar AMMs incur theoretically infinite liability exposure. If a sharp whale identifies a mispriced outlier tail event before consensus adjusts, the protocol absorbs the entirety of the toxic flow, paying out massive multiples natively minted by the mathematical slippage function, essentially causing protocol insolvency.
Temporal
Separation.
The Hybrid engine isolates price discovery entirely away from liability settlement using an explicit temporal boundary.
Phase 1: LMSR (Price Discovery). Intraday trading is governed by a standard Logarithmic Market Scoring Rule:
C(q) = b × ln(Σ exp(q_i / b)).
Trades are priced continuously, offering deep liquidity and the ability to exit early into a counterparty-free automated curve.
Phase 2: PM Settlement (Liability Ring-Fencing). At timestamp t_end, the AMM function is aggressively deprecated. The aggregate sum of all historical Phase 1 entries strictly dictates the maximum gross payable liability. It becomes a pure Winner-Takes-All Pari-Mutuel vault. The protocol's risk reduces to absolute zero.
Asymmetric
Dual-Fees.
Maximizing intraday velocity while violently taxing the high-frequency MEV space and generating terminal protocol yield.
A naked LMSR allows pathological MEV volume spoofing at zero economic friction.
By implementing a 4% exit tax explicitly applied only on Phase 1 exit legs (sells), we simultaneously generate revenue to subsidize institutional-grade deep liquidity ($b = 20,000$) while making artificial algorithmic wash-trading strictly expected-value (EV) negative. Retail traders experience true zero-slippage entry, and only pay the tax when extracting realized profit.
The core terminal fee (3%) is extracted exclusively as a management layer atop the Phase 2 Pari-Mutuel vault, operating without intruding upon the Phase 1 bid-ask spread liquidity.
The protocol permits frictionless 0-fee transfers between outcome positions to facilitate fluid mid-game strategizing. A common concern is whether late-game transferring dilutes early backers unfairly.
The LMSR cost function $C(q)$ mathematically neutralizes this vector. A trader transferring from a losing to a winning position late in a match must sell their old position at the collapsed marginal AMM price (e.g., $0.02) taking a realized loss, and simultaneously buy the new position at the heavily favored premium (e.g., $0.98).
This dynamic strictly restricts the number of new "winning units" they can acquire, ensuring the aggregate PM payout ratio for early backers remains protected. Our internal simulations demonstrate net dilution under adversarial transfer scenarios is constrained to nominal variance (~1.2% ROI impact).
The Arbitrage
Docking Phase.
The AMM Spot Price natively converges to the Pari-Mutuel Expected Return via explicit algorithmic arbitrage.
Because the Phase 1 Early Exit Tax is 4%, but the terminal Phase 2 Treasury fee is 3%, holding a winning ticket to the final whistle is mathematically incentivized.
Quantitative traders aggressively identify mispriced AMM Spot Prices. They inject capital into Phase 1 to capture localized EV, knowing exactly what the net PM payout will be minus 3%. If the Spot Price spikes beyond their target, they may still dump into the 4% exit tax to secure guaranteed absolute returns rather than risk the final settlement edge. This continuous tension between the 4% automated exit and the 3% terminal payout strictly bounds the AMM curve against the underlying PM vault.