The double auction: Vernon Smith's market experiments

A double auction is a market in which buyers call out bids and sellers call out offers at the same time, and any trader may accept a standing quote to close a contract. Vernon Smith used it in a series of classroom markets, reported in the April 1962 Journal of Political Economy, to test competitive price theory. Each trader knew only a private limit price, yet contract prices moved close to the price where the induced supply and demand schedules crossed. In 2002 the Royal Swedish Academy of Sciences shared the economics prize between Smith and Daniel Kahneman, citing Smith "for having established laboratory experiments as a tool in empirical economic analysis." The design is a yardstick for artificial intelligence (AI) trading agents because its answer is known in advance.

How Smith's market worked

Smith ran the experiments over six years beginning in 1955, mostly with sophomore and junior engineering, economics, and business majors. Subjects were split at random into buyers and sellers. Each buyer received a card with a number known only to that buyer: the most the buyer could pay for one unit. Each seller's card gave the least the seller could accept. Profit was the gap between the contract price and the card. The cards defined supply and demand schedules that no subject ever saw.

Trading was open outcry. Any trader could raise a hand at any time and call a bid or offer within the limit on the card, and any trader on the other side could accept it. The pair then left the market for that period. Periods ran five to ten minutes, and in experiments 1 to 8 each trader could make only one contract per period. The same cards came back each period, so the market repeated under fixed conditions.

The Academy's scientific background calls this a double oral auction, a mechanism used in many financial and commodity markets. Edward Chamberlin, Smith's teacher at Harvard, had reported classroom markets with pairwise bargaining in 1948.

Convergence to the competitive equilibrium

Smith measured convergence with a "coefficient of convergence," alpha: the standard deviation of contract prices around the predicted equilibrium price, divided by that price, as a percentage. In test 1 the schedules crossed at $2.00 and six units. Card values ran from $0.75 to $3.25, yet over five periods contracts ranged only from $1.70 to $2.25. Average prices were $1.80, $1.86, $2.02, $2.03, and $2.03, and alpha fell from 11.8 to 8.1, 5.2, 5.5, and 3.5.

Alpha tended to decline in every test except test 8. In test 8 only sellers could quote, a rough model of a retail market, and alpha rose from 2.9 percent in the second period to 7.4 and 7.0 in the last two. When buyers were allowed to quote again, prices moved toward equilibrium at once.

Smith's tentative conclusion was that competitive equilibrium tends to form even with small numbers, provided collusion is prohibited and all bids, offers, and contracts are public. He reported that the subjects were highly motivated without monetary payoffs. The background adds that Plott and Smith (1978) found slower convergence when traders had to post one price for a whole period.

Allocative efficiency as a measure

Smith named an early form of the measure: a market's ability to ration out submarginal buyers and sellers, those who should not trade at the equilibrium price. In test 1, period 4, one submarginal buyer and one submarginal seller traded, and volume rose to seven against a prediction of six.

The modern definition, as stated in a 2026 replication, divides the total profit buyers and sellers actually realize by the total gains from trade available at equilibrium. The score equals 1 only when every profitable trade happens and no unit goes to a lower-value buyer or a higher-cost seller. Smith's 2002 prize lecture cites work finding that the continuous double auction converges faster and is more efficient than posted-offer pricing.

The same lecture describes the Gode and Sunder result that efficiency stays high even with "zero" intelligence robot traders that bid at random within loss-free limits. Gjerstad and Shachat dispute the reading. In their comparison, the median price standard deviation was 8.53 in constrained zero-intelligence simulations against 1.70 in human sessions, and they argue that the loss-free limit is itself individual rationality. Efficiency and price convergence are separate tests.

Language-model traders in Smith's market

Struski and colleagues rebuilt Smith's symmetric test with 11 buyers and 11 sellers, cards from $0.75 to $3.25 in $0.25 steps, an equilibrium of $2.00 and six trades, and five rounds. They ran 10 simulations each for three model populations from two providers. No condition converged fully, and alpha stayed above the human figure in every round. The best population cut alpha from 27.6 to 11.7 and raised efficiency from 0.79 to 0.91. Another averaged 2.2 to 3.8 trades per round, with efficiency of 0.36 to 0.67, because its agents kept improving quotes by $0.01 without closing the spread. The authors advise validating language-model stand-ins against human and theoretical benchmarks.

The 2002 press release credits Smith with laboratory "wind-tunnel tests" of new market designs before they are used in practice. A separate June 2026 study compared market rules for language-model agents, holding the agents fixed and changing only the rules. Call markets realized 88.6 percent of efficient surplus, continuous double auctions 71.5 percent, and bilateral bargaining 56.4 percent.

What to check

• Does a market result report price convergence, such as Smith's alpha, as well as allocative efficiency, or only one of them?
• Is efficiency measured against the maximum gains from trade at the induced equilibrium, and are submarginal trades counted?
• Which rules applied: two-sided quoting, sellers-only quoting as in test 8, or posted prices for a whole period?
• Does a claim that agents trade well compare them with Smith's human benchmark, an alpha of 3.5 by the fifth period of test 1?
• Were agents run with enough rounds and repeated seeds, as in the 10 simulations per condition of the 2026 replication?

Azcuna's CALIBER puts AI agents in practice markets with play money and a news feed whose truth is known, and measures from their trades whether they are gullible, follow the crowd, overpay, or can be steered. It was proposed to DARPA under SBIR Phase I topic DPA26BZ06-DV026, and the proposal was submitted on October 21, 2026.

Sources

1. 1An Experimental Study of Competitive Market Behavior · Vernon L. Smith, Journal of Political Economy 70(2), 1962, via Chapman University Digital Commons
2. 2Press release: The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel 2002 · Royal Swedish Academy of Sciences, October 9, 2002
3. 3Foundations of Behavioral and Experimental Economics: Daniel Kahneman and Vernon Smith · Royal Swedish Academy of Sciences, advanced information, December 17, 2002
4. 4Constructivist and Ecological Rationality in Economics · Vernon L. Smith, Prize Lecture, December 8, 2002
5. 5Individual Rationality and Market Efficiency · Gjerstad and Shachat, Krannert School of Management, Purdue University, Paper No. 1204, August 2007
6. 6Competitive Market Behavior of LLMs · arXiv (Struski, Swistak, Okulska and Biecek), September 2026
7. 7Artificial Institutions: How Institutional Design Shapes LLM Simulations · arXiv (Chupilkin), June 2026

Where this shows up in our work

• CALIBER, the market testbed for AI agents measures from an AI agent's trades whether it is gullible, herds, overpays, or can be steered.
• LEDGER, auditable Army acquisition decisions turns a trade study into a package where every number cites its source and AI drafts but never decides.