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Evolutionary stability in continuous nonlinear public goods games.

Chai Molina1, David J D Earn2

  • 1Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4K1, Canada. chai.molina@gmail.com.

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|June 15, 2016
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Summary
This summary is machine-generated.

This study explores continuous contributions in public goods games, finding conditions for cooperative strategies to evolve and persist. The research shows these strategies remain stable even with significant population changes.

Keywords:
Adaptive dynamicsCooperationEvolutionary game theorySnowdrift game

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Area of Science:

  • Evolutionary Game Theory
  • Behavioral Economics
  • Mathematical Biology

Background:

  • Public goods games model scenarios where individuals contribute to a common resource at personal cost.
  • Real-world contributions are often continuous, unlike discrete models typically studied.
  • Nonlinear production functions (synergy, diminishing returns) are common in public goods scenarios.

Purpose of the Study:

  • To analyze n-player snowdrift games with continuously varying contributions.
  • To determine conditions under which cooperative strategies can evolve and persist.
  • To extend existing stability analyses of cooperative strategies.

Main Methods:

  • Static evolutionary game theory applied to n-player snowdrift games.
  • Analysis of strategy stability under continuous contribution scenarios.
  • Investigation of stability against large population perturbations.

Main Results:

  • Identified conditions for the global evolutionary stability of an "equally cooperative" strategy.
  • Demonstrated local stability of this strategy against significant population perturbations.
  • Extended previous findings on evolutionary stability in snowdrift games.

Conclusions:

  • Cooperative strategies can be evolutionarily stable in public goods games with continuous contributions.
  • The "equally cooperative" strategy shows robustness to substantial population fluctuations.
  • Results have implications for understanding cooperation in diverse real-world contexts.