Ultimatum game: regret or fairness?

In the ultimatum game, the challenge is to explain why responders reject non-zero offers thereby defying classical rationality. Fairness and related notions have been the main explanations so far. We explain this rejection behavior via the following principle: if the responder regrets less about losing the offer than the proposer regrets not offering the best option, the offer is rejected. This principle qualifies as a rational punishing behavior and it replaces the experimentally falsified classical rationality (the subgame perfect Nash equilibrium) that leads to accepting any non-zero offer. The principle 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 via rational punishment; e.g. the comparison between "fair" and "superfair", the behavior under raising the stakes etc. Hence we also propose experiments that can distinguish these two scenarios (fairness versus regret-based punishment). 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 of the game.Comment: 13 pages, 2 figure

Alternative equilibria in two-period ultimatum bargaining with envy

A two-period ultimatum bargaining game is developed in which parties experience an envy-type externality coming from the surplus captured by their counterparts. Our assumptions on envy levels and outside opportunities allow us to characterize a richer set of bargaining outcomes than that identified by the prior literature, which includes a novel agreement equilibrium which we label Type I agreement. As this novel agreement solution is delivered by a negotiation resembling a one-shot ultimatum game, only characteristics of the second-moving player shape the sources of bargaining power. This property contrasts with that of Type II agreement—an agreement solution previously reported by related literature—in which characteristics of both players influence negotiating strengths. Numerical simulations are performed to illustrate the interplay between envy, impatience rates and outside opportunities as well as the degree of inequity generated by each agreement type