Game-theory models of binary collective behavior

Abstract

Game-theoretic models were investigated not from the point of view of the maxima of the players' utility functions, as is usually done, but by solving algebraic equations that characterize the Nash equilibrium. This characterization is obtained for models of binary collective behavior, in which players choose one of two possible strategies. Based on the results for the general model, game-theoretic models of conformal threshold Binary Collective Behavior (BCB) are studied, provided the collective is divided into L groups. The conditions for the existence of Nash equilibria is proved. For each Nash equilibrium, its structure is defined. The results obtained are illustrated by two examples of conformal threshold BCB when the group coincides with the whole team and when the latter is divided into two groups. It is shown that the Nash equilibria in the first and second examples are analogues of the equilibria in the dynamic models of M. Granovetter and T. Schelling, respectively.