Previous studies have shown that non-human primates can generate highly stochastic choice behaviour, especially when this is required during a competitive interaction with another agent. To understand the neural mechanism of such dynamic choice behaviour, we propose a biologically plausible model of decision making endowed with synaptic plasticity that follows a reward-dependent stochastic Hebbian learning rule. This model constitutes a biophysical implementation of reinforcement learning, and it reproduces salient features of behavioural data from an experiment with monkeys playing a matching pennies game. Due to interaction with an opponent and learning dynamics, the model generates quasi-random behaviour robustly in spite of intrinsic biases. Furthermore, non-random choice behaviour can also emerge when the model plays against a noninteractive opponent, as observed in the monkey experiment. Finally, when combined with a meta-learning algorithm, our model accounts for the slow drift...