Ultimatum game belongs to the classical economic experiments, frequently used to study altruism and pro-social behavior. The objective of the research is to understand relations between the personality and the ultimatum game from the responder´s perspective. Participants (N=224, females 62%) filled the web-based questionnaires on Hexaco-PI and hypothetic minimal acceptable sum as respondents in the ultimatum game. Data was analyzed by means of the structural equation model and the binominal regression model, using the narrow traits as input variables. Interestingly, the most frequented value of minimal acceptable amount was a fair offer (50 % of the total sum). A fair offer was expected by 50 % of females and 42 % of males; what erodes the traditional thesis of economic rationality, according to which any offer higher than 0 should be accepted. Hence, people have natural tendency to expect and require a fair deal. Results from the logit model show that the minimal acceptable sum in the ultimatum game is predicted, firstly, by liveliness and sociability (wider trait extraversion) and secondly, by sentimentality and dependence (wider trait emotionality). In other words, tendency to expect and require fair offer manifests at optimistic and joyful people able to create strong emotional connections. Logit model´s results were reconfirmed by the structural equation models, where wider traits extraversion and emotionality were found statistically significant. Findings have interesting implications as regards the understanding of underlying psychological processes in the frame of altruistic decision-making.