**:** ..
**:** - . 1

**:** 99
**:**
**:** 2022
**:** .. - . 1 // . 99. .: , 2022. .6-35. DOI: https://doi.org/10.25728/ubs.2022.99.1

** :** , , , , - , , ,

** (.):** binary collective behavior, social interaction, Granovetter model, Schelling model, game-theoretic model, Nash equilibrium, indicator behavior, operator fixed point

**:** - , . , (), . , , . , , , (). , - . . ( ) . ( ) , , . ( ) , . - . .

** (.):** The article deals with game-theoretic models of threshold binary collective behavior that characterize social interaction between agents. For binary models, the function that characterizes the preferences of the players, equivalent to the utility function (UF) is the choice indicator. The sign of the choice indicator, and not the maximization of the UF, here characterizes the rational behavior of the agent. Using the choice indicator, we introduce a rational behavior operator that is an automorphism on the set of situations, and we prove the assertion that its fixed point is a Nash equilibrium (NE). It is also proved that any binary game-theoretic model is equivalent to some threshold model. Examples from the works of T. Schelling (two groups of agents) and M. Granovetter (one group of agents) are generalized to a collective consisting of an arbitrary number of groups, and for this model, statements about finding the NE through the agent threshold distribution function are proved. The existence conditions and the number (as well as the maximum possible number) of NE, as well as their structure, are investigated. Pareto-effective equilibria are found. Models of indicator behavior are studied and the convergence of its recurrent procedure to one of the NEs is proved.

PDF
: 692, : 142, : 10.