Milgrom-Stokey No-Trade Theorem
The no-trade theorem says that in a fully rational market, private information by itself does not generate trade: if everyone knows everyone is rational and trading voluntarily, then an order to buy/sell is itself informative, so the other side updates and becomes unwilling to trade at the quoted price.
The core logic is that trades reveal information. If a trader is willing to buy at price , that willingness is evidence they believe the asset is worth more than . Once the counterparty accounts for this inference, the “deal” should disappear unless there is some other motive to trade.
For the theorem to bite, the environment has to be very clean:
- Common priors + rational Bayesian updating: disagreements come from information, not different baseline beliefs.
- Common knowledge of rationality and voluntary trade: everyone expects others to interpret orders strategically.
- No non-informational motives: no liquidity needs, hedging demands, taxes, constraints, rebalancing, etc.
- No noise or bounded rationality: prices and order flow are not contaminated by “irrelevant” shocks.
The practical implication is not that “markets have zero volume,” but rather: persistent volume requires something beyond pure information. Real markets trade because there are liquidity shocks, risk-sharing motives, institutional constraints, heterogeneous beliefs, bounded rationality, or noise trading (i.e., reasons someone might trade even if the other side infers something from the trade).
In behavioral finance, the theorem is used as a discipline device: if a model predicts lots of trading, it must clearly specify what breaks the no-trade logic (noise, overconfidence, disagreement, constraints, etc.).
In Baker’s story, traders face uncertainty about others’ information and reliability, so they form trusted networks to reduce search and verification costs. Those networks improve information quality within the clique, but they also segment the market, so information travels imperfectly across groups and traders can become stuck in locally shared views, sustaining belief dispersion and noise.