A research report from Andromeda Computer comparing three payout mechanisms for Trepa, a one-minute forecasting game on Solana where participants submit numerical BTC/USD estimates and are rewarded by proximity to the true outcome: (A) the current median-error cutoff with water-filling, (B) a continuous accuracy-proportional distribution with no cutoff, and (C) a hybrid design keeping the cutoff but adding a consolation floor for losers. Multi-agent equilibrium simulations across 540 configurations show no mechanism is universally optimal — the median cutoff yields higher equilibrium private-signal weight on average (0.375 vs 0.297), the continuous design matches or beats it for low risk-aversion agents, and the cutoff dominates for high risk-aversion agents — while a hybrid with a 0.5F consolation floor outperforms both pure designs in 70% of cases, raising private-signal weight while eliminating total-loss trauma and improving Sybil resistance. Recommends a segmented pool strategy, with open-source simulation code for independent verification.

Classical theory ties forecasting accuracy to trading profit, but only for automated market makers; on central limit order book exchanges, informed forecasters routinely lose money while uninformed heuristics profit. The authors prove a formal equivalence that works in both settings: for any strictly proper scoring rule, a "proper betting" strategy depending only on your prediction and the market price earns positive expected profit whenever your forecast beats the price, and it is essentially the only strategy with such a robust guarantee. Across thousands of AI model forecasts, proper betting is the only strategy that reliably converts accuracy into profit, with optimal play varying by forecasting persona. A month-long live deployment on Kalshi returned +80.33% with a Sharpe ratio of 3.35.

Binary prediction markets compress continuous probability distributions into yes/no outcomes, discarding variance, skew, and tail information that forecasters naturally produce. functionSPACE analyzes 622 mutually exclusive bracket events on Polymarket and finds that less than half price a coherent probability distribution. The piece argues for continuous market design as the primitive that finally matches how both institutional analysts and prediction market traders actually reason about uncertainty.

Analyzes Trepa's high-frequency forecasting contest on Solana and shows its current design (median error cutoff, steep accuracy weights) induces a Keynesian beauty contest equilibrium that underweights private information. Introduces the orthogonal precision multiplier, a mechanism that rewards accurate forecasts decorrelated from the consensus, transforming Trepa into a tunable second-order oracle. Proves equilibrium existence via potential game theory, quantifies information gain through mutual information, and addresses practical vulnerabilities including oracle latency, median instability, and collusion.

Explains the SKC (Srinivasan, Karger, Chen) mechanism for prediction markets on unverifiable outcomes. Markets resolve using crowd consensus as the outcome, with delta-based scoring rewarding participants for moving markets toward final consensus. Enables markets for subjective questions lacking ground truth.

Educational thread on the game-theoretic foundations of prediction markets. Explains why truth-telling is the dominant strategy through incentive compatibility, details how LMSR works as a proper scoring rule, and argues prediction market builders need economists and game theory experts on their teams.

Academic survey of prediction mechanism design from a mechanism design perspective. Covers scoring rules, market scoring rules (LMSR), cost-function-based market makers, dynamic parimutuel markets, incentive compatibility, combinatorial markets, and peer prediction systems for subjective events where ground truth doesn't exist.

Proposes a mechanism for prediction markets where outcomes cannot be objectively verified. Uses the last reporter's prediction as a reference point, creating incentives for truthful reporting through negative cross-entropy payments. Proves truthful reporting is a perfect Bayesian equilibrium.

Investigates combinatorial prediction markets, which extend the standard model to support forecasts on conditional events (e.g., A given B) and Boolean combinations of events rather than only base events. Reports experimental results comparing combinatorial versus flat market structures on forecasting accuracy and calibration. Co-authored by Robin Hanson, whose LMSR underpins most automated prediction markets.