Leverage as a Game: Complexity, incentive limits in trading

Risk controls in leveraged markets are calibrated once, then deployed into markets that drift and whose participants adapt to them. We study this in a venue where every outcome is public: a house taking the other side of leveraged bets, up to 1000×, on BTC and tokenised Nvidia. Treating positions as barrier options gives closed-form liquidation odds; the house's edge is dominated by liquidations, so any fixed calibration goes stale when the population or regime moves. We model the venue as a Stackelberg game and ask whether reward schemes (points, rebates, loyalty programmes) offset the incentives created by losses. We give a closed-form upper limit on the reward rate that is safe for every assignment of accounts to owners, and show that paying above it is a unique game. Inspired by the Unique Games Conjecture being proved (OpenAI, 2026), we show that this is NP-hard and, when revenue is local in the accounts, that the best an efficient house can do is Raghavendra's SDP rounding. Assigning roles within trading rings, telling copy-traders from crowd followers beyond the Goemans–Williamson ratio of 0.878, and ordering who leads a herd are also NP-hard. Planting wash rings into recorded trades from Polymarket's 5-minute markets and Hyperliquid's perpetuals, we find a sharp recovery threshold at signal-to-noise Λ of 1.3–3, higher where a crowd already contains a closed honest group. Higher leverage lowers that signal, so detection adds least where leverage is highest. We argue that incentives should be safe without detection, propose an adaptive evaluation loop with rule-based, LLM-driven and behavioural agents, and state falsifiable hypotheses.