Open AccessGame-theory models of binary collective behavior
Author(s) -
Vladimir V. Breer,
Vladimir V. Breer
Publication year - 2020
Publication title -
matematičeskaâ teoriâ igr i eë priloženiâ
Language(s) - English
Resource type - Journals
ISSN - 2074-9872
DOI - 10.17076/mgta_2020_2_13
Subject(s) - nash equilibrium , mathematical economics , binary number , normal form game , best response , mathematics , game theory , group (periodic table) , conformal map , algebraic number , repeated game , mathematical analysis , physics , arithmetic , quantum mechanics
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.