Prejudice, privilege, and power: Conflicts and cooperation between recognizable groups

Jeremy Bingham; Pietro Landi; Cang Hui; Jeremy Bingham; Pietro Landi; Cang Hui

doi:10.3934/mbe.2019203

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 4092-4106. doi: 10.3934/mbe.2019203

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Research article Special Issues

Prejudice, privilege, and power: Conflicts and cooperation between recognizable groups

1.
Department of Mathematical Sciences, Stellenbosch University, Matieland 7602, South Africa
2.
African Institute for Mathematical Sciences, Cape Town 7945, South Africa

Received: 31 December 2018 Accepted: 16 April 2019 Published: 09 May 2019

The problem of cooperation remains one of the fundamental questions in the fields of biology, sociology, and economics. The emergence and maintenance of cooperation are naturally affected by group dynamics, since individuals are likely to behave differently based on shared group membership. We here formulate a model of socio-economic power between two prejudiced groups, and explore the conditions for their cooperative coexistence under two social scenarios in a well-mixed environment. Each scenario corresponds to an asymmetrical increase in the payoffs for mutual cooperation in either cross-group or within-group interactions. In the 'inter-dependence' scenario payoffs of cross-group cooperation are enhanced, while in the 'group-cohesion' scenario payoffs of within-group cooperation are enhanced. We find that stable cooperative coexistence is possible only in the inter-dependence scenario. The conditions for such coexistence are highly sensitive to prejudice, defined as the reduction in probability for cross-group cooperation, and less sensitive to privilege, defined as the enhancements to payoffs of cross-group cooperation.
- evolutionary game theory; prisoner’s dilemma,
- stag hunt,
- tags,
- mathematical sociology,
- de-segregation
Citation: Jeremy Bingham, Pietro Landi, Cang Hui. Prejudice, privilege, and power: Conflicts and cooperation between recognizable groups[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 4092-4106. doi: 10.3934/mbe.2019203

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Abstract

The problem of cooperation remains one of the fundamental questions in the fields of biology, sociology, and economics. The emergence and maintenance of cooperation are naturally affected by group dynamics, since individuals are likely to behave differently based on shared group membership. We here formulate a model of socio-economic power between two prejudiced groups, and explore the conditions for their cooperative coexistence under two social scenarios in a well-mixed environment. Each scenario corresponds to an asymmetrical increase in the payoffs for mutual cooperation in either cross-group or within-group interactions. In the 'inter-dependence' scenario payoffs of cross-group cooperation are enhanced, while in the 'group-cohesion' scenario payoffs of within-group cooperation are enhanced. We find that stable cooperative coexistence is possible only in the inter-dependence scenario. The conditions for such coexistence are highly sensitive to prejudice, defined as the reduction in probability for cross-group cooperation, and less sensitive to privilege, defined as the enhancements to payoffs of cross-group cooperation.

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