Application of Game Theory to Neuronal Networks

The paper is a theoretical investigation into the potential application of game theoretic concepts to neural networks (natural and artificial). The paper relies on basic models but the findings are more general in nature and therefore should apply to more complex environments. A major outcome of the paper is a learning algorithm based on game theory for a paired neuron system. 1. Introduction Individual neurons are the building blocks for more complex neural circuits. In natural systems these more complex neural circuits interact with other components in a manifold of ways thereby generating the compellingly sensual world of behavior around us. Although tireless and tedious efforts in various disciplines culminated in fundamental insights in the field, there are still many unknowns about individual neurons and the processes in which individual neurons interact and organize themselves in neural circuits (e.g., [1]). Recently, game theory has obtained some attention in the field of neuroscience. The field of neuroeconomics, for instance, combines the two fields in experiments with human and nonhuman players in order to better understand human decision-making (e.g., [2]). This paper has a different motivation and proposes a neural network model under a concept of game theory where individual neurons are assumed to optimally behave with a given payoff matrix. The paper theoretically analyzes a paired neuron system and critically specifies that the value game theory may have as an organizing principle for such a system (in the sense of a guiding principle or mechanism involved in neural communication, organization, and synchronization). The paper also specifies a learning algorithm based on game theory for a paired neuron system, which is a major contribution in this text. In the remainder of this text, Section 2 summarizes the motivation for this paper and validates an intuitively appealing (though not unproblematic) relationship between game theory and biological/artificial neurons. Sections 3 and 4 investigate this relationship, the theory, and the major concepts and challenges involved in more detail, concentrating, among other things, on static and dynamic games of complete/perfect information. Section 5 applies game theoretic constructs to artificial neural networks and presents a learning algorithm based on game theory for network learning. The discussion in Section 6 revolves around related work and Section 7 ends the paper with a summary. 2. Game Theory, Biological Neurons, and Artificial Neural Networks Our previous work in various areas (e.g.,