We consider here a set of agents, each of them having her own argumentation. Arguments and conflicts between them are subjective. The aim of each agent is to enrich her argumentation by taking into account the arguments and conflicts of the other agents. We adopt here an individual-based approach where the cross-fertilization of argumentations emerge from the interactions between the agents. For this purpose, we formalize a multi-party argumentation game using Event Calculus. At the end of the game, each agent extends its argumentation by using the arguments exchanged and the conflicts shared. As we show formally, such an expansion is consensual. By adopting an individual-based approach, our model is explanatory since it highlights the conflicts between the agents.