TY  - JOUR
A1  - Gros, Claudius
T1  - Collective strategy condensation: when envy splits societies
T2  - Entropy
N2  - Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait –the propensity to compare one’s own success with that of others– expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.
KW  - self-organization
KW  - sociophysics
KW  - game theory
KW  - strategy condensation
KW  - nash equilibrium
KW  - phase transition
KW  - envy
KW  - social classes
KW  - complex systems
Y1  - 2021
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/57448
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-574481
SN  - 1099-4300
VL  - 23
IS  - Article 157
PB  - MDPI
CY  - Basel
ER  -