This paper investigates the neural mechanism that underlies the effect of group identity on hold-up problems. The behavioral results indicated that the investment rate among members of the in-group was significantly higher than that of the out-group. In comparison to the NoChat treatment, the Chat treatment resulted in significantly lower offers for both in-group and out-group members. The event-related potentials (ERP) results demonstrated the presence of a distinct N2 component in the frontal midline of the brain when investment decisions were made for both in-group and out-group members. During the offer decision-making stage, the P3 peak amplitude was significantly larger when interacting with in-group members compared to the out-group members. The event-related potentials oscillations (ERO) results indicated that when investment decisions were made for in-group members in the NoChat treatment, the beta band (18-28 Hz, 250-350 ms) power was more pronounced than when decisions were made for out-group members. In the NoChat treatment, offer decisions for in-group members yielded a more pronounced difference in beta band (15-20 Hz, 200-300 ms) power when compared to out-group members. Evidence from this study suggests that group identity can reduce the hold-up problem and corroborates the neural basis of group identity.

The Hold-up problem is very common in transactions with specific investment in incomplete contractual relationships, which is affected by human trusting, cooperative, altruistic behavior. Recent neuroscience studies have shown that TPJ plays an important role in social cognition and prosocial decision-making. However, most of the studies have focused on RTPJ in the right hemisphere, while few studies have focused on LTPJ in the left hemisphere. The purpose of this study is to modulate the excitability of LTPJ through transcranial direct current stimulation (tDCS) and to explore the effects of LTPJ on the investment and offer behavior of participants in the repeated hold-up game. Our results showed that cathodal stimulation significantly improved the investment rate of participants in the repeated hold-up game compared with sham stimulation. One possible explanation is that the change of LTPJ activity caused by cathodal stimulation may reduce the participants\' inference ability of the others\' intention, thus reducing the participants\' betrayal aversion behavior, so that the participants will not reduce their investment behavior in the repeated game.

Hold-up problem is very common in non-contractible relation-specific investment transactions. And this problem can affect by trust, cooperation and altruism behavior of human beings. Recent neuroscience researches had explored a network of right temporo-parietal junction (rTPJ) involved in human cooperation and altruism behavior. The purpose of this study is to modulate the activation of rTPJ through transcranial direct current stimulation (tDCS), and to study the influence of rTPJ on investment and offer behavior in hold-up game. The results of our study showed that the anodal stimulation significantly increased participants\' offer compared with the cathodal and sham stimulation. A possible explanation is that changes in rTPJ activity induced by anodal stimulation improve the accuracy of agents\' mental reasoning and promote cooperation by influencing agents\' offer behavior.