Ultimatum Game

A two-stage bargaining game highlighting the gap between rational prediction and observed fairness.

Ask the Game theory assistant 1 min read · Updated September 9, 2026

Definition

Proposer offers a split $(x,1-x)$ of a pie; responder accepts (payoffs $(x,1-x)$ ) or rejects (payoffs $(0,0)$ ).

Subgame-perfect equilibrium: proposer offers $x\to 1$ , responder accepts any $x<1$ .

Self-interested rationality predicts a near-zero offer accepted; experiments show offers of $40$ - $50$ % and rejection of small offers.

Fairness, reciprocity, and spite enter the empirical picture.

In the classical G\"uth-Schmittberger-Schwarze (1982) experiment, modal offers are $50/50$ and offers below $20$ % are routinely rejected.

Dictator-game variants remove responder power to isolate pure altruism.

SPE predictions fail empirically — led to behavioral economics models such as inequity aversion (Fehr-Schmidt) and reciprocity (Rabin).

Evolutionary models with reputational tracking recover near-fair offers.

Behavioral economics, experimental game theory, and cross-cultural anthropology (Henrich et al.).

Foundational data point for bounded rationality research.

Assembled from the ReLU.chat curated knowledge base. These explanations are concise on purpose; check the sources for anything important.