Investigating the social boundaries of fairness by modeling Ultimatum Game responders' decisions with multinomial processing tree models

Fairness in competitive games such as the Ultimatum Game is often defined theoretically. According to some of the literature, in which fairness is determined only based on resource allocation, a proposal splitting resources evenly (i.e., 5:5) is generally assumed as fair, and minimal deviation (i.e., 4:6) is considered enough to classify the proposal as unfair. Relying on multinomial processing tree models (MPTs), we investigated where the boundaries of fairness are located in the eye of responders, and pit fairness against relative and absolute gain maximization principles. The MPT models we developed and validated allowed us to separate three individual processes driving responses in the standard and Third-Party Ultimatum Game. The results show that, from the responder's perspective, the boundaries of fairness encompass proposals splitting resources in a perfectly even way and include uneven proposals with minimal deviance (4:6 and 6:4). Moreover, the results show that, in the context of Third-Party Ultimatum Games, the responder must not be indifferent between favoring the proposer and the receiver, demonstrating a boundary condition of the developed model. If the responder is perfectly indifferent, absolute and relative gain maximization are theoretically unidentifiable. This theoretical and practical constraint limits the scope of our theory, which does not apply in the case of a perfectly indifferent decision-maker.