Dictator Game

The setup

Two participants sit in separate cubicles, unable to see one another. The experimenter hands one of them — chosen by coin flip — an endowment of X (twenty dollars is a common amount). That subject, the dictator, decides how much of X, if any, to transfer to the other subject, the recipient. Whatever the dictator does not give away she keeps. The recipient learns the dictator's decision after the fact and walks out with whatever was sent. The recipient does not bid, negotiate, accept, reject, or reciprocate. The game lasts exactly one round, and the two players are strangers.

That is the entire mechanism. There is no information asymmetry, no repeated play, no future shadow. The dictator's choice is a closed-form one-shot allocation between her own pocket and a stranger's. Economists call such tasks non-strategic: the optimal action does not depend on any expectation about what the other player will do, because the other player cannot do anything.

Why the game was invented

The dictator game was not the starting point — the ultimatum game was. Werner Güth, Rolf Schmittberger and Bernd Schwarze (1982) had shown that in the ultimatum bargaining task, where the recipient can reject the proposed split and force both players to zero, proposers typically offer 40 to 50 percent and recipients reliably reject low offers. The puzzle was: how much of that fair-looking behaviour was strategic — fear of rejection — and how much was a genuine taste for fair allocations?

Forsythe, Horowitz, Savin and Sefton's 1994 paper in Games and Economic Behavior proposed the dictator game as the clean control. Strip away the rejection option, hold everything else constant, and measure what remains. If ultimatum offers were entirely strategic, dictator transfers should collapse to zero. They did not. Dictators in Forsythe et al. gave on average about 23 percent of a five- or ten-dollar pie, with substantial mass at 50 percent. The conclusion was that fairness in the ultimatum game is real, not just strategic — but the strategic component is also large, since transfers in the dictator game are roughly half those in the ultimatum game.

What three decades of data say

Christoph Engel's 2011 meta-analysis aggregated 616 dictator-game treatments — covering roughly 20,813 subjects across labs in Europe, North America, Asia, Africa and Latin America. The headline distribution looks like this:

Statistic	Value	Notes
Mean transfer	≈ 28.4 % of endowment	Aggregated across all treatments
Median transfer	≈ 20 %	Distribution skewed left by zero-givers
Share giving 0 %	≈ 36 %	Modal but not majority response
Share giving exactly 50 %	≈ 17 %	Second peak — egalitarians
Share giving > 50 %	≈ 5 %	"Hyper-fair" — small but persistent
Share giving between 0 and 50 %	≈ 42 %	The intermediate mass

The distribution is therefore bimodal at zero and at fifty, with the mean dragged down toward 28 percent by the heavy left mass. About a third of subjects look like the textbook self-interested agent. About a sixth look like strict egalitarians. The remainder occupy intermediate positions that are most parsimoniously explained by smoothly varying social preferences.

What moves dictator giving

The mean transfer is not a constant of nature — it slides up and down in response to features of the protocol. The big drivers, all robustly replicated:

• Anonymity (double-blind). When neither the experimenter nor other subjects can attach choices to identities, giving roughly halves. Hoffman, McCabe, Shachat and Smith (1994): 24 percent → 10 percent. The interpretation is that a substantial share of laboratory generosity is image management — the dictator is partly paying for how she appears to the experimenter, and that incentive disappears under double-blind.
• Earned endowment. If the dictator earned the X (by completing a task, winning a quiz, or arriving early), transfers fall sharply. Cherry, Frykblom and Shogren (2002) report near-zero giving under earned-and-double-blind. The intuition is moral entitlement: my money is sticker than found money.
• Deserving recipient. Replace the anonymous subject with a named charity (a children's hospital, the Red Cross, the local food bank) and giving rises markedly — often by ten to twenty percentage points. The recipient's identifiability and apparent need both matter.
• Identity revealed. If the dictator sees a photograph or learns a name (the "identifiable victim effect"), transfers rise. Pure abstraction depresses giving; concrete particularity raises it.
• Cost of giving. In modified protocols where transferring one dollar costs the dictator k dollars (k > 1) or yields the recipient k dollars (k > 1), demand-curve-style logic holds: cheaper giving produces more giving, consistent with a positive but bounded preference for the recipient's welfare.
• Audience effects. Telling the dictator the experimenter will (or won't) see the choice nudges transfers up (or down) by several percentage points even before full double-blind.
• Framing. "Take" frames (the dictator decides how much to take from the recipient's pre-allocated endowment) produce lower giving than "give" frames at the same effective allocation. The reference point matters — a classic prospect-theory result.

Three theories of why people give

The leading non-strategic explanations:

• Pure altruism. The dictator's utility includes a term in the recipient's payoff. Classical "warm-list" altruism: I care directly about your money. Predicts positive but possibly small giving; predicts that any change in the recipient's outside option matters (since it changes how much my dollar helps).
• Warm glow (Andreoni 1990). The dictator gets utility not from the recipient's payoff per se but from the act of giving itself — a psychological reward for the choice. Predicts that giving is robust to changes in recipient outside options (the warm glow does not depend on the recipient's welfare) but sensitive to how generous the dictator feels. Differs empirically from pure altruism in tasks that decouple "amount given" from "amount received".
• Distributional / inequity aversion (Fehr-Schmidt 1999; Bolton-Ockenfels 2000). The dictator dislikes unequal allocations, with stronger weight on inequality that disadvantages her than on inequality that disadvantages the recipient. Predicts mass at 50 percent (the inequality-minimising point) and mass at zero (subjects with low β just keep everything). Reproduces the bimodal distribution.

These models are not mutually exclusive and the empirical mass is best fit by a population with heterogeneous mixtures of all three.

The Fehr-Schmidt model in detail

Ernst Fehr and Klaus Schmidt's 1999 paper writes the dictator's utility as

u_i(π_i, π_j) = π_i − α_i · max(π_j − π_i, 0) − β_i · max(π_i − π_j, 0)

where π_i is the dictator's own monetary payoff, π_j is the recipient's, α_i ≥ 0 captures the dictator's aversion to disadvantageous inequality (being behind), and β_i ≥ 0 captures aversion to advantageous inequality (being ahead). The constraint α_i ≥ β_i and β_i < 1 is standard: people dislike being behind more than being ahead, and being ahead by a dollar is not worse than not getting that dollar at all.

In the dictator game the dictator chooses x ∈ [0, X] to give. Her own payoff is X − x; the recipient's is x. Since X − x ≥ x for any "fair" or less-than-fair split, the relevant inequality term is the β term. Optimising:

u_dict(x) = (X − x) − β · ((X − x) − x)
         = (X − x) − β · (X − 2x)
         = (X − x)(1 − β) + β · x        (algebra)
∂u/∂x   = −(1 − β) + β · 2 − 0
         = 3β − 1                         (for x < X/2)

The optimum is x = X/2 when β > 1/3 and x = 0 when β < 1/3. So Fehr-Schmidt with a binary β distribution would generate a bimodal split between 0 % givers and 50 % givers — close to what we observe, modulo the intermediate mass. Adding heterogeneity in β (or noise) fills in the middle. Two parameters per agent reproduce dictator, ultimatum, public-goods and trust-game stylised facts simultaneously.

Dictator versus ultimatum, side by side

Feature	Dictator game	Ultimatum game
Recipient can reject	No	Yes (rejection → both get 0)
Strategic motive to give	None	Strong (avoid rejection)
Standard-theory prediction	0 % offer	Smallest positive offer the recipient won't reject
Typical proposer offer	≈ 28 % mean	≈ 40 – 50 % mean
Pure altruism component	All of it	≈ 28 percentage points of the offer
Strategic / rejection-avoidance component	None	≈ 12 – 22 percentage points of the offer
Best identifies	Social preferences	Joint test of social preferences + strategic foresight

The dictator–ultimatum spread is the standard way economists decompose ultimatum offers into their "real fairness" and "strategic" components. The fact that dictator offers are non-zero is the cleanest existence proof that human laboratory subjects have non-pecuniary preferences over distributions.

Cross-cultural and developmental evidence

Henrich, Boyd, Bowles and colleagues (2001, 2005) ran the dictator game in fifteen small-scale societies — Amazonian foragers, East African pastoralists, New Guinean horticulturalists — and found means broadly in the 25 – 40 percent band, with considerable variance. The Machiguenga of Peruvian Amazonia gave the least (about 26 percent); the Lamalera whale-hunters of Indonesia gave the most (above 50 percent on average), seemingly reflecting a cultural norm of large-scale cooperative sharing. Mean giving across societies is similar; the variance and the modal response differ. Universal "fairness as 50/50" is not a thing — but universal positive giving is.

Developmentally: four-year-olds tested with stickers or candies typically give very little, and most behave as pure egoists. By age seven or eight, the modal response has shifted to an even split. Fehr, Bernhard and Rockenbach (2008) showed that the rise in giving with age co-occurs with the development of in-group preferences — children share more with their own school class than with strangers. The egalitarian peak at 50 percent is a developmental achievement, not an innate baseline.

Critiques and limits

• External validity. Lab dictators give to anonymous strangers in front of an experimenter for stakes that are small compared with their wealth. List (2007) argued that field analogues — where the choice is whether to keep money you'd otherwise have, against a real third party — produce essentially zero giving. The pure-altruism story may be more constrained outside the lab.
• Demand effects. Subjects know they are being observed in an experiment about generosity. Bardsley (2008) showed that adding a "take" option (the dictator can subtract money from the recipient) shifts the distribution to look much less generous, which is hard to reconcile with stable underlying preferences and instead suggests "experimenter demand" — people gauge what the experimenter wants.
• Stake-size scepticism. Doubling the stakes from $10 to $100 leaves relative giving roughly constant in most studies — but the absolute amount given grows correspondingly. Some scholars argue truly large stakes would erode generosity; the few studies at multiple-hundred-dollar stakes give mixed results.
• Heterogeneity, not a typical agent. Reporting "the average dictator gives 28 percent" hides the fact that no single subject is well described by 28 percent. The population is a mixture of egoists, egalitarians and intermediates. Most behavioural-economics models are now mixture models for that reason.

Where the dictator game shows up outside the lab

• Charitable giving design. Empirical regularities — identifiable-victim effects, deservingness, anonymity — directly inform fundraising. The "single identifiable victim" frame consistently beats statistical-victim appeals because it triggers the same channels that raise giving in the lab.
• Online platforms and reputation. Image effects in the dictator game predict why public ratings, badges and donor walls work. Removing observability tanks contribution in both lab and field.
• Tax policy and redistribution. Voter preferences over redistribution map onto the empirical β distribution: a majority with moderate inequality aversion produces moderate redistributive policy, with both tails (β ≈ 0 and β ≈ 1) systematically over-represented at the political extremes.
• Salary negotiations and offers. Hiring-manager allocations to job candidates inherit dictator-game-style fairness patterns, especially when the candidate's outside option is opaque.
• Inheritance and bequest splits. Family allocation decisions echo the dictator distribution: a bimodal pattern of equal-share splits and disproportionate "to one favoured child" splits, with the relative weight predicted by familial closeness measures.

Common pitfalls

• Conflating "what the dictator gives" with "what the dictator wants to give". Anonymity and audience effects mean that observed transfers are a noisy signal of underlying preferences. The double-blind transfer is closer to the "preference" measure; the public-information transfer is closer to the "willingness to perform".
• Treating the mean as the typical subject. The empirical distribution is bimodal. Saying "the average dictator gives 28 percent" is technically correct but conceptually misleading — no large group of subjects actually picks 28.
• Forgetting endowment effects. Whether the X was given or earned changes the result by 10 – 20 percentage points. Studies that don't standardise the endowment-acquisition step are not comparable.
• Reading dictator giving as "altruism" full stop. Pure altruism, warm glow, inequity aversion and image management all predict positive transfers. Dictator results constrain the population to have some non-selfish preference but do not on their own identify which one.
• Generalising lab numbers to real economic stakes. Mean dictator giving at $10 stakes does not necessarily extrapolate to $10,000 stakes or to anonymous real-world charity decisions. The mechanism is real, but the magnitude is context-dependent.