The ultimatum and dictator games, explained

The ultimatum game is a two-player bargaining test in which a proposer offers a split of a fixed sum and a responder either accepts it or rejects it, leaving both with nothing. The dictator game removes the veto: the dictator simply decides how much to give. Werner Güth, Rolf Schmittberger and Bernd Schwarze reported the first ultimatum experiments in the December 1982 Journal of Economic Behavior and Organization. Under material self-interest, a responder should accept any positive offer, so a proposer should offer almost nothing. People do not play that way. A 2013 survey by Güth and Martin Kocher reports that the equal split is the most common offer and calls that finding extremely reliable.

The 1982 Cologne experiments

In the 1982 "easy games," player 1 stated a demand from an amount to be divided. If player 2 accepted, player 1 got the demand and player 2 the rest. Otherwise both got zero. The subjects were graduate economics students at the University of Cologne, and the authors thought it almost sure that none knew game theory. After pilots in the summer semester of 1978, the main experiments ran early in the next winter semester.

Each main session had 21 games, three at each amount from 4 to 10 Deutsche marks (DM). In the first, naive session, conflict occurred in only 2 of the 21 games. The experiment was repeated one week later, and conflict rose to 6 games. The average demand of players 1 rose from DM 4.38 to DM 4.75, and the authors judged players 1 more daring the second time. In a third experiment, all 37 subjects played both roles over DM 7. In more complex "complicated games" with colored chips, players 1 proposed the equilibrium solution in 6 of 17 games, and in 9 of 15 a week later with higher payoffs.

What later studies found

The 2013 survey summarizes three decades of results. On average, proposers offer around 40 to 50 percent of the pie in the standard game, and such offers are almost always accepted. Acceptance falls with smaller offers and approaches zero quite quickly below 20 percent. Taking actual rejection rates into account, either the equal split or offers around 40 percent maximize the proposer's payoff. A small number of responders even reject rare offers above half.

Camerer and Thaler's 1995 Journal of Economic Perspectives column found that ultimatum results changed little with the stakes or with the players' nationality. Responders rejected offers only when the offers were known to be proportionally stingy and chosen by the proposer.

Stakes do matter at large enough sizes. Andersen, Ertaç, Gneezy, Hoffman and List, in the December 2011 American Economic Review, ran the game with 458 responders in eight villages in Meghalaya, India. Stakes ran from 20 to 20,000 rupees, where 100 rupees was roughly a day's wage. Instructions were worded to draw out low offers, and the median offer was 20 percent of the pie, against an average of 40 percent in the literature. At the highest stakes, only 1 of 24 responders rejected.

The dictator game as a control

The dictator game separates fairness from fear of rejection. Mei and colleagues, discussed below, describe the dictator game as a test of altruism and the ultimatum game as a test of fairness and spite. Forsythe, Horowitz, Savin and Sefton, in the May 1994 Games and Economic Behavior, tested whether fairness alone explains why proposers make nontrivial offers. They varied the game and whether players were paid. With pay, outcomes of the ultimatum and dictator games were significantly different, so fairness alone could not explain the offers. Doubling the money did not change that result. Both games replicated when players were paid, but the ultimatum game did not replicate when they were unpaid.

Camerer and Thaler add that dictator games, unlike ultimatum games, are sensitive to many design features. A dictator result therefore depends on how that particular game was set up.

Language models in the games

Mei, Xie, Yuan and Jackson, in a February 2024 Proceedings of the National Academy of Sciences (PNAS) article, had ChatGPT-3 and ChatGPT-4 play six games, including the dictator and ultimatum games. The human comparison came from the MobLab classroom platform: 88,595 game players from more than 50 countries, mostly college and high school students. In their Turing test, one action drawn from a chatbot and one from a person were compared for which was more likely under the human distribution. ChatGPT-4 was picked as more human-like than a random person in 5 of the 8 game comparisons and on average. ChatGPT-3 was in 2 of 8 and not on average.

ChatGPT-4 proposed a strictly equal split both as dictator and as ultimatum proposer. Neither chatbot ever gave $0 as dictator, which a significant share of people did. As responder, fewer than a fifth of humans would accept as little as $1, yet that was ChatGPT-4's most common response, with a second peak at $50. Prompted to play as a mathematician, ChatGPT-4 accepted $1 in most cases. As a legislator, it demanded $50 in the majority of cases. The authors note that the human data come from students, that a chatbot's spread is within one subject while the human spread is across people, and that the results are illustrative, not broadly representative.

What to check

• Does a result report the full distribution of offers and rejections, or only a mean?
• Were the stakes large enough to matter to the players, as in the 20,000-rupee games?
• Was there a dictator-game control to separate fairness from fear of rejection?
• Were players paid? The 1994 ultimatum results did not replicate without pay.
• For an AI agent, is the spread from repeated queries of one model being compared with a spread across many people?
• Which persona or framing did the prompt use, given the shift between the mathematician and legislator prompts?

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 analysis of ultimatum bargaining · Güth, Schmittberger and Schwarze, Journal of Economic Behavior and Organization 3(4), December 1982 (scan in David K. Levine's economics archive)
2. 2More than thirty years of ultimatum bargaining experiments: Motives, variations, and a survey of the recent literature · Güth and Kocher, Jena Economic Research Papers 2013-035, August 21, 2013
3. 3Fairness in simple bargaining experiments · Forsythe, Horowitz, Savin and Sefton, Games and Economic Behavior 6(3), May 1994 (Iowa Research Online record and abstract)
4. 4Anomalies: Ultimatums, Dictators and Manners · Camerer and Thaler, Journal of Economic Perspectives 9(2), 1995
5. 5Stakes Matter in Ultimatum Games · Andersen, Ertaç, Gneezy, Hoffman and List, American Economic Review 101, December 2011 (UC San Diego copy)
6. 6A Turing test of whether AI chatbots are behaviorally similar to humans · Mei, Xie, Yuan and Jackson, PNAS 121(9), February 22, 2024 (PubMed Central)

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.