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Article

Collective Strategy Condensation: When Envy Splits Societies

Institute for Theoretical Physics, Goethe University Frankfurt, 60323 Frankfurt, Germany
Entropy 2021, 23(2), 157; https://doi.org/10.3390/e23020157
Received: 29 December 2020 / Revised: 22 January 2021 / Accepted: 25 January 2021 / Published: 27 January 2021
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. View Full-Text
Keywords: self-organization; sociophysics; game theory; strategy condensation; nash equilibrium; phase transition; envy; social classes; complex systems self-organization; sociophysics; game theory; strategy condensation; nash equilibrium; phase transition; envy; social classes; complex systems
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MDPI and ACS Style

Gros, C. Collective Strategy Condensation: When Envy Splits Societies. Entropy 2021, 23, 157. https://doi.org/10.3390/e23020157

AMA Style

Gros C. Collective Strategy Condensation: When Envy Splits Societies. Entropy. 2021; 23(2):157. https://doi.org/10.3390/e23020157

Chicago/Turabian Style

Gros, Claudius. 2021. "Collective Strategy Condensation: When Envy Splits Societies" Entropy 23, no. 2: 157. https://doi.org/10.3390/e23020157

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