  We are concerned about action selection in the basal ganglia (BG). We
quantitatively analyze functions of direct pathway (DP) and indirect pathway
(IP) for action selection in a spiking neural network with 3 competing
channels. For such quantitative analysis, in each channel, we obtain the
competition degree ${\cal C}_d$, given by the ratio of strength of DP (${\cal
S}_{DP}$) to strength of IP (${\cal S}_{IP}$) (i.e., ${\cal C}_d = {\cal
S}_{DP} / {\cal S}_{IP}$). Then, a desired action is selected in the channel
with the largest ${\cal C}_d$. Desired action selection is made mainly due to
strong focused inhibitory projection to the output nucleus, SNr (substantia
nigra pars reticulata) via the DP in the corresponding channel. Unlike the case
of DP, there are two types of IPs; intra-channel IP and inter-channel IP, due
to widespread diffusive excitation from the STN (subthalamic nucleus). The
intra-channel IP serves a function of brake to suppress the desired action
selection. In contrast, the inter-channel IP to the SNr in the neighboring
channels suppresses competing actions, leading to highlight the desired action
selection. In this way, function of the inter-channel IP is opposite to that of
the intra-channel IP. However, to the best of our knowledge, no quantitative
analysis for such functions of the DP and the two IPs was made. Here, through
direct calculations of the DP and the intra- and the inter-channel IP
presynaptic currents into the SNr in each channel, we obtain the competition
degree of each channel to determine a desired action, and then functions of the
DP and the intra- and inter-channel IPs are quantitatively made clear.
