  The evolution of fairness in dyadic relationships has been studied using
ultimatum games. However, human fairness is not limited to two-person
situations and universal egalitarianism among group members is widely observed.
In this study, we investigated the evolution of favoritism and group fairness
in a three-person ultimatum game (TUG) under a co-evolutionary framework with
both strategy updating and partner switching dynamics. In the TUG, one proposer
makes an offer to two responders and the proposal is accepted at the group
level if at least one individual responder accepts the offer. Investigating
fairness beyond dyadic relationships allows the possibility of favoritism
because the proposer can secure acceptance at the group level by discriminating
in favor of one responder. Our simulation showed that the proposer favors one
responder with a similar type when the frequency of partner switching is low.
In contrast, group fairness is observed when the frequency of partner switching
is high. The correlation between strategy and neighborhood size suggested that
partner switching influences the strategy through the proposer's offer rather
than through the responder's acceptance threshold. In addition, the average
degree negatively impacts the emergence of fairness unless the frequency of
partner switching is high. Furthermore, a higher frequency of partner switching
can support the evolution of fairness when the maximum number of games in one
time step is restricted to smaller values.
