The role of unconventional oil is increasing in global energy markets. Although conventional oil is being depleted, unconventional oil might manage or eliminate supply constraints in meeting the demand for oil without large positive step changes in the prices. In this study, we use the ACEGES model, which is agent-based, to explore the potential impact of unconventional oil on the evolution of the oil markets, focusing on four important oil-producing countries. We also use quantile sheets to summarize the simulation results. Given the estimated potential of conventional and unconventional resources, the results suggest that the production profiles will change tremendously. Although countries rich in conventional oil, such as Saudi Arabia and Iran, will still occupy the global oil markets for approximately the first half of this century, oil production in countries with rich unconventional resources, such as Canada and Venezuela, will be higher in production than Saudi Arabia and Iran from 2050 to 2060. This change in production means that the market power in the global oil markets will shift from Middle Eastern countries to Canada and Venezuela in this century.