Self-induced class stratification in competitive societies of agents: Nash stability in the presence of envy

Gros, Claudius

doi:10.1098/rsos.200411

Cited by 4 publications

(15 citation statements)

References 40 publications

(46 reference statements)

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“…The agent-to-agent interaction is mediated in the shopping trouble model by two averaging fields,

and

, as discussed further above. It can be shown [ 26 ] that this property allows to derive analytic expressions for the rewards of the lower and of the upper class, respectively,

and

Remarkably, the above expressions are not explicitly dependent on the basic utility

. The only free parameter in ( 7 ) and ( 8 ) is the fraction

of agents in the lower class, which can be determined numerically.…”

Section: Resultsmentioning

confidence: 99%

“…The agent-to-agent interaction is mediated in the shopping trouble model by two averaging fields,R andp i , as discussed further above. It can be shown [26] that this property allows to derive analytic expressions for the rewards of the lower and of the upper class, respectively, R L and R U ,…”

Section: Analytic Properties Of the Class-stratified Statementioning

confidence: 99%

“…The effect is that agents with high/low rewards tend to pursue pure/mixed strategies. Equation ( 3 ) is called the “shopping trouble model”, as it can be applied, besides the general social context, to the case that agents need to optimize their shopping list [ 26 ]. Note that that agents have only a single goal within the shopping trouble game—reward maximisation—in contrast to most status-seeking games [ 27 , 28 ], for which both status and utility are separately important [ 29 , 30 ].…”

Section: Shopping Trouble Modelmentioning

confidence: 99%

“…The situation is illustrated for two players in Figure 3 . By avoiding each other, agents seemingly cooperate, a state called “forced cooperation” [ 26 ].…”

Section: Shopping Trouble Modelmentioning

confidence: 99%

“…The fraction of pure strategies drops for all

, until only one or two upper-class members remain, the monarchy state. Adapted from [ 26 ].…”

Section: Figurementioning

confidence: 99%

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Collective Strategy Condensation: When Envy Splits Societies

Gros

2021

Entropy

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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.

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“…The agent-to-agent interaction is mediated in the shopping trouble model by two averaging fields,

and

, as discussed further above. It can be shown [ 26 ] that this property allows to derive analytic expressions for the rewards of the lower and of the upper class, respectively,

and

Remarkably, the above expressions are not explicitly dependent on the basic utility

. The only free parameter in ( 7 ) and ( 8 ) is the fraction

of agents in the lower class, which can be determined numerically.…”

Section: Resultsmentioning

confidence: 99%

Section: Analytic Properties Of the Class-stratified Statementioning

confidence: 99%

Section: Shopping Trouble Modelmentioning

confidence: 99%

“…The situation is illustrated for two players in Figure 3 . By avoiding each other, agents seemingly cooperate, a state called “forced cooperation” [ 26 ].…”

Section: Shopping Trouble Modelmentioning

confidence: 99%

“…The fraction of pure strategies drops for all

, until only one or two upper-class members remain, the monarchy state. Adapted from [ 26 ].…”

Section: Figurementioning

confidence: 99%

See 3 more Smart Citations

Collective Strategy Condensation: When Envy Splits Societies

Gros

2021

Entropy

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Collective strategy condensation towards class-separated societies

Gros

2022

Eur. Phys. J. B

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In physics, the wavefunctions of bosonic particles collapse when the system undergoes a Bose–Einstein condensation. In game theory, the strategy of an agent describes the probability to engage in a certain course of action. Strategies are expected to differ in competitive situations, namely when there is a penalty to do the same as somebody else. We study what happens when agents are interested how they fare not only in absolute terms, but also relative to others. This preference, denoted envy, is shown to induce the emergence of distinct social classes via a collective strategy condensation transition. Members of the lower class pursue identical strategies, in analogy to the Bose–Einstein condensation, with the upper class remaining individualistic. Graphical abstract

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Collective strategy condensation: When envy splits societies

Gros

2021

Preprint

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Human societies are characterized, besides others, by three constituent features. (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 with others. (C) People care 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. 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.

show abstract

Self-induced class stratification in competitive societies of agents: Nash stability in the presence of envy

Cited by 4 publications

References 40 publications

Collective Strategy Condensation: When Envy Splits Societies

Collective Strategy Condensation: When Envy Splits Societies

Collective strategy condensation towards class-separated societies

Collective strategy condensation: When envy splits societies

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