Decision-making in negotiation with incomplete i nformation, having an irrational part, is a complex problem. Inspired from research works aiming to analyze human behavior and those o n social negotiation psychology, the integration of personality aspects, with the essential time parameter, is becoming necessary. For this purpose, first, one to one bargaining process, in which a buyer agent and a seller agent negotiate over single issue (price), is developed , where the basic behaviors based on time (Faratin et al. , 1998) and personality aspects (conciliatory, neutral, and aggressive) are suggested . Second, a cognitive approach, based on the five -factor model in personality (Fiske, 1949; Tupes and Christal, 1961; Norman, 1963), is suggested to control the resulting time -personality behaviors with incomplete information. In fact, the five factors are the extraversion, the agreeableness, the conscientiousness, the neuroticism, and the openness to experience. Afterwards, experimental environments and measures, allowing a set of experiments are detailed. Results, concerning time - personality behaviors, demonstrate that more increasing conciliatory aspects lead to increased agreement point (price) and decreased agreement time, and more increasing aggressive aspects lead to decreased agreement point and increased agreement time. Finally, from a study case, of three different personalities corresponding to three different cognitive orientations, experimental results illustrate the promising way of the suggested cognitive approach in the control of the time-personality behaviors.