Game Theory III

A signed network is a network with positive and negative signs on the edges. Balance theory [1] explains the forces behind the structure of social systems commonly modeled as static undirected signed networks. A signed graph (network) is balanced if its set of vertices can be partitioned into two subsets such that each negative edge joins vertices belonging to different subsets and each positive edge joins vertices belonging to the same subset [1].

We model a system of autonomous and collaborative decision-making agents who self-organize themselves in groups in order to solve complex tasks. Previous literature argues that such groups should be static, in terms of not periodically adapting to the environment by replacing its members, since it is detrimental to the groups’ performances [1]. In contrast, other lines of research suggest that static group structures do not necessarily bring a better performance than dynamic group structures [2].

The Langevin equation is a stochastic differential equation for the velocity of a Brownian particle. In this sense, it can be considered as a physically improved counterpart of the Wiener process, the velocity of which can only be defined as a stochastic distribution. On the contrary, the velocity of the Langevin model is a function valued stochastic process, what allows to calculate the kinetic energy of the Brownian particle. In fact, this calculation has been employed as a benchmark in the history of the classical Itô vs Stratonovich dilemma.

The analogy of a market as a computational process that churns out prices and quantities is a recurring theme in economics [1]. For the most part this is a conceptual analogy without precise definitions of the micro-economic processes that are doing the computational work or what the relationship is to computational complexity, the field in which the theoretical limits of computation are studied. Without this connection these analogies lack sufficient substance to provide a useful foundation for a computational economics that makes use of simulations.