In the ultimatum game, responders routinely reject positive offers below roughly 20-30% of the stake, forgoing free money to punish a proposer perceived as unfair. This refutes the prediction that self-interested players accept any positive amount, showing that people will pay a personal cost to retaliate against inequitable treatment.
People's utility depends not only on their own payoff but on the distribution of payoffs across players, including aversion to inequity and concern for others' outcomes. Modeling this as additional terms in the utility function (rather than abandoning optimization) lets standard game theory accommodate altruism, spite, and fairness without discarding its machinery.
Players can be modeled as doing a limited number of iterated steps of reasoning: level-0 players act randomly, level-1 best-respond to level-0, level-2 best-respond to level-1, and so on, with most people stopping after one or two steps. Average reasoning depth typically clusters around 1.5 steps, explaining why observed play falls short of full equilibrium.
Nash equilibrium behavior, when it appears, often emerges gradually through repeated play and feedback rather than from immediate introspective calculation. Adaptive learning models (reinforcement and belief-based) track how choices converge over rounds, so equilibrium is better treated as a possible endpoint of a process than as a starting assumption.
When players pick a number from 0 to 100 and the winner is closest to two-thirds of the group's average, the equilibrium answer is zero, yet real players typically choose numbers around 20-35. The pattern reveals finite levels of reasoning: people anticipate others' limited reasoning rather than iterating all the way down.
Classical game theory's assumptions (self-interest, unlimited reasoning, instant equilibrium) should be treated as empirical hypotheses measurable in controlled laboratory experiments rather than as axioms. Reading strategic theory through this experimental lens turns normative predictions into testable claims that can be revised when behavior systematically deviates.