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Game theory has been at the heart of modern analysis of the scientific basis for human judgment and decision making. This work proposes game theoretic modelling as a solution to persistent road traffic problems in Nigeria, Africa and indeed many parts of the world. It is expected that readers of this work will get a thorough insight into game theory and one of its important applications: solutions to road traffic problems. The game theoretic analysis done in this work has actually given an insight into scientific reasons for persistent traffic problems in Nigeria, Africa and many parts of the world. These problems have impacted negatively on the socio-economic situation in the affected countries and regions. Armed with the analytical tools used in this work, traffic problems could be controlled by employing appropriate control mechanisms and problem solutions recommended in this work. The analysis done in this work will be very useful to game theorists, engineers, economists, management scientists, psychologists and sociologists who are actively involved in the science of decision making and its consequences on the society.