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The two-sex problem with persistent unions: a generalization of the birth matrix-mating rule model
1Department of Economics, University of Pennsylvania.
Theoretical Population Biology
|October 1, 1987
Summary
The birth matrix-mating rule persistent unions (BMMRPU) model extends stable population theory by allowing unions to persist beyond a single period. This advancement establishes equilibrium existence through a supplemented fixed-point argument, enhancing demographic modeling.
Area of Science:
- Demography
- Mathematical Biology
- Population Dynamics
Background:
- Classical stable population theory faces challenges in modeling the two-sex problem.
- The existing birth matrix-mating rule (BMMR) model simplifies this by assuming single-period unions.
- This simplification limits the model's applicability to more realistic scenarios.
Purpose of the Study:
- To introduce the BMMRPU (BMMR persistent unions) model, which relaxes the single-period union assumption.
- To demonstrate the existence of equilibrium within this new BMMRPU model.
- To enhance demographic models by incorporating persistent unions.
Main Methods:
- Extending the BMMR model to allow for persistent unions.
- Supplementing the original BMMR existence proof.
- Employing a fixed-point argument to establish equilibrium existence in the BMMRPU model.
Main Results:
- The BMMRPU model is presented, accommodating unions of multiple periods.
- The existence of equilibrium in the BMMRPU model is proven.
- A novel fixed-point argument is utilized to support the existence proof.
Conclusions:
- The BMMRPU model offers a more realistic approach to stable population dynamics.
- The inclusion of persistent unions improves the theoretical framework for demographic analysis.
- This work provides a foundation for further research into multi-period union dynamics in population models.