Discrete-valued neural networks have attracted increasing attention because they require less memory and lower computational cost than conventional floating-point neural networks. While discrete weights are often obtained by quantizing pretrained continuous-valued networks, such approaches are not applicable to reinforcement learning tasks that cannot be trained by gradient-based methods. This paper investigates the training of multilayer perceptrons (MLPs) with ternary connection weights {−1,0,1} using Genetic Algorithm (GA) for the Atari Space Invaders reinforcement learning task. The performance of ternary-weight networks is compared with that of binary-weight networks {−1,1} under identical network topologies and GA configurations. Experimental results show that GA configuration employing a smaller population size and a larger number of generations significantly outperforms a configuration with a larger population size and fewer generations when the total number of fitness evaluations is fixed. Furthermore, no statistically significant difference is observed between ternary and binary weight representations in terms of game performance. Although ternary weights exhibit slightly better median and worst-case performance, binary weights occasionally achieve higher best scores while requiring less memory. These findings suggest that binary-weight neural networks provide an attractive trade-off between performance and memory efficiency, making them an attractive representation for evolutionary reinforcement learning.