According to Herrnstein's famous matching law of repeated choice behavior, the probability of choosing an alternative is proportional to the reward derived from that alternative. Although this empirical law of behavior has been studied extensively by psychologists, economists, and neuroscientists, the question of its neural
basis has received little attention.
 

Here we show that a classic neural model of decision making, when combined with Hebbian synaptic plasticity, reproduces matching behavior. Choices between alternatives are mediated by lateral inhibition between decision neurons, while stochasticity is generated by fluctuations in the activity of input neurons. For exponentially distributed inputs, the choice probabilities are proportional to the strengths of the synapses from the input neurons to the decision neurons. Therefore, plasticity of these synapses leads to changes in choice probabilities over time. In particular, we demonstrate equivalence between neural and behavioral models, by showing that two forms of Hebbian plasticity cause our neural model to reproduce two well-known reinforcement learning models that lead to matching behavior. These two models can be distinguished behaviorally by their dependence of speed of convergence on the overall reward rate, and by the way they learn to play games. In both models, the mean activity of an input neuron, conditioned on choice of the corresponding alternative, is a decreasing function of that alternative's choice probability. The two models can be distinguished physiologically by measuring how the mean activity of a decision neuron, conditioned on choice of the corresponding alternative, depends on the reward rates of other alternatives.