Prediction markets trade individual events — will this team win, will this candidate prevail. But a trader who believes two events are correlated has no way to express this. Buying both contracts separately doesn't tell the market about the dependence. The joint distribution remains invisible.
Rana, Nadkarni, Moshrefi, and Viswanath (arXiv:2603.22596) build ParlayMarket, an automated market maker that prices parlay-style joint contracts alongside individual ones. The mechanism consolidates liquidity into a single pool and maintains coherent pricing across all combinations. Under repeated trading, the system converges to the true joint distribution.
The key finding is that parlay trades improve the market's estimate of dependence between events, reducing estimation error beyond what individual market trades alone can achieve. A bet on “A and B both happen” directly encodes information about their correlation. The same trader making separate bets on A and B would move both prices but leave their dependence structure untouched.
The market maker's error and losses scale predictably with the number of base markets, providing theoretical guarantees on convergence.
The structural insight is about what trades communicate. An individual bet is a marginal statement — “I think this probability is wrong.” A parlay bet is a joint statement — “I think these events are related in a way the market doesn't reflect.” The second kind of bet carries strictly more information about the world's structure. Markets that can't accept joint bets are systematically blind to dependence, even when every individual price is correct.