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New Variations for Strategy Set-shifting in the Rat
09:45

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Published on: January 23, 2017

Mixed strategy under generalized public goods games.

Yanling Zhang1, Te Wu, Xiaojie Chen

  • 1Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China. yanlzhang@pku.edu.cn

Journal of Theoretical Biology
|May 25, 2013
PubMed
Summary

Nonlinear public goods games show that cooperation fails when group and population sizes are similar. Otherwise, nonlinear functions can lead to stable strategies or repellers, but not evolutionary branching.

Keywords:
Adaptive dynamicsFinite populationsNonlinear production function

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Area of Science:

  • Evolutionary game theory
  • Mathematical biology
  • Behavioral economics

Background:

  • Public goods games model cooperation and resource allocation.
  • Nonlinear relationships between contributions and public goods are common but understudied in evolutionary contexts.
  • Understanding mixed strategy evolution is key to explaining cooperation dynamics.

Purpose of the Study:

  • To investigate the impact of nonlinear production functions on the evolution of mixed strategies in finite populations.
  • To analyze conditions leading to stable or unstable evolutionary outcomes.
  • To explore the role of hysteresis in generalized public goods games.

Main Methods:

  • Mathematical modeling of evolutionary game dynamics.
  • Analysis of finite population models with nonlinear production functions.
  • Identification of evolutionary stable strategies (ESS) and bifurcations.

Main Results:

  • Cooperation is eliminated when group and population sizes are comparable.
  • Nonlinear functions can lead to a convergent evolutionary stable strategy (CESS) or a repeller, but not evolutionary branching.
  • Hysteresis effects were observed across three families of production functions.
  • Specific nonlinear functions (concave, convex, sigmoidal) yielded unique CESS or repellers, or coexistence of strategies depending on group size.

Conclusions:

  • Nonlinear production functions significantly alter mixed strategy evolution in public goods games.
  • The study reveals novel evolutionary outcomes, including hysteresis and bifurcations, not seen in simpler models.
  • Findings provide insights into the complex dynamics of cooperation under varying contribution-production relationships.