Peer review is the cornerstone of modern scientific publication system. Not only do scientists submit papers to be published in journals, they also evaluate others' submission on a voluntary basis. Open peer review, i.e., the full transparency in the identity of authors in the evaluation process may have the peer review system be exposed to reviewers' opportunistic behaviour. We developed an agent-based model of the peer review system and ran computer simulations of an open peer review system. Results suggest that the transparent identity of authors may induce scientists to develop strategies of direct reciprocation of benefits, which could be highly detrimental for the overall outcome of the scientific publication system. The research has been made within the EU-COST Action "PEERE: New frontiers of peer review"