A Game Theoretic Approach to Decision Making in Neuronal Networks

We formulate as a game, the dynamic interaction scenario among three populations of neurons with different functions and capabilities. Specifically, we consider two populations of excitatory neurons where each population is responsible for a direction of movement, say, right and left. Both the excitatory neuron populations are connected to an inhibitory neurons population. Each excitatory population wants to take control of the movement. We formulate a game theoretic view of this competition. Specifically, we assume that the activity level of each neuronal population is quantized in to two levels. We transform the dynamical system model that exists in the literature, see for example [1], for this problem to create the game utilities. We characterize, through the replicator dynamics of the evolutionary game, the evolutionary stable strategies and find conditions under which they hold. Finally, we use the phase portrait to show the evolution of the evolutionary stable strategies from different initial conditions. We find that mixed strategies cannot be a part of the game solution. In addition, we find that the case of no or low activity is the worst case and there are no initial conditions or neurons coordination that can overcome it.