Ultimatum game: Regret or fairness?

Abstract

In the ultimatum game, the challenge is to explain why responders reject non-zero offers thereby defying classical rationality. Fairness and related concepts have been among the main explanations so far. Here, the ultimatum game is reformulated based on probabilistic lotteries, enabling modern decision-making tools to be applied to this problem. We explain the rejection behavior via the following principle: if the responder regrets less about losing the offer than the proposer regrets not offering a better option, the offer is rejected. This principle qualifies as a rational conflict behavior. Similar concepts were applied in the economy of wars. The principle replaces the experimentally falsified classical rationality (the subgame perfect Nash equilibrium) that leads to accepting any non-zero offer. It is implemented via the transitive regret theory for probabilistic lotteries. The expected utility implementation is a limiting case of this. We show that several experimental results normally prescribed to fairness and intent-recognition can be given an alternative explanation; e.g. the comparison between “fair” and “superfair”, the behavior under raising the stakes, the influence of the initial wealth, etc. Hence we also propose experiments that can distinguish these two scenarios (fairness versus regret). They assume different utilities for the proposer and responder. We focus on the mini-ultimatum version of the game and also show how it can emerge from a more general setup.