In nature, individuals often show a different consistent behavioural tendency from each other, called “personality differences”. Various hypotheses have been proposed in order to explain what causes such personality differences, but the evolutionary causes have not been sufficiently understood yet. In this study, we considered a simple theoretical model in which individuals repeatedly play a two-player two-option simultaneous game. The payoff matrix of the game can vary depending on an environmental value, and individuals can estimate the environmental value before each interaction and change their behaviour. Then the strategy of each individual can be represented by a reaction norm against the estimated environment. By using individual based simulations, we found that when (i) the estimation of environment is imperfect and (ii) interaction occurs inside of the local sub-population, the optimal reaction norm becomes the “threshold response” (i.e., switching from one option to the other at a threshold environmental value), where the thresholds are continuously distributed in population-scale. In other words, the uncertainty of environment and the social interaction with local individuals can drive the emergence of variation in the consistent behaviour. This is a novel hypothesis explaining the personality differences in various social traits, e.g., agreeableness, aggressiveness or boldness.