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Evolutionary game dynamics in finite populations with strong selection and weak mutation
Drew Fudenberg1, Martin A Nowak, Christine Taylor
1Department of Economics, Harvard University, Cambridge, MA 02138, USA. dfudenberg@harvard.edu
Theoretical Population Biology
|September 22, 2006
Summary
We analyzed stochastic game dynamics in finite populations using an extended Moran process. Our findings reveal that finite population size significantly alters evolutionary game dynamics, even in large populations, impacting strategy selection.
Area of Science:
- Evolutionary Game Theory
- Population Dynamics
- Mathematical Biology
Background:
- Classical evolutionary game theory often assumes infinite populations.
- The Moran process models genetic drift and selection in finite populations.
- Frequency-dependent selection and mutation are crucial factors in evolutionary dynamics.
Purpose of the Study:
- To extend the Moran process for frequency-dependent selection and mutation in finite populations.
- To analyze long-run behavior and strategy selection in 2x2 and 3x3 games.
- To compare model dynamics with standard replicator dynamics.
Main Methods:
- Extension of the classical Moran process.
- Mathematical analysis of stochastic game dynamics.
- Application to selective language dynamics.
Main Results:
- Complete analysis of long-run behavior for 2x2 games with small mutation rates.
- A simple rule for strategy selection in 3x3 coordination games.
- Demonstration of qualitative differences between finite and infinite population dynamics.
Conclusions:
- Finite population size, even when large, can lead to behaviors distinct from standard replicator dynamics.
- The extended Moran process provides insights into strategy evolution in finite populations.
- Selective language dynamics in large finite populations can be predicted with intuitive results.
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