This paper elaborates on the effect of predictive memory on cognitive agents that are acting in selfish routing games. Selfish routing describes a situation, where agents are moving in a network with defined latency functions, and act in a strictly selfish manner. Under certain situations – i.e. specific definition of the network, associated latency functions, and agents acting strictly selfish – the Braess Paradox occurs. The Braess Paradox contradicts human intuition by the fact that adding a new low-latency edge to a given network does not reduce overall latency. By incorporating cognitive agents in the game theoretical approach, agents could overcome their strictly selfish behaviour, which in turn reduces overall latency. By incorporating a kind of predictive memory, each agent can learn from a number of personal experiences and alter their present behaviour accordingly, which can reduce overall latency.