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Solving multispecies population games in continuous space and time.

Emil F Frølich1, Uffe H Thygesen1

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Game theory now models complex ecosystems by analyzing populations in continuous space. This approach reveals how bounded rationality influences spatial distributions, aligning with real-world observations.

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Area of Science:

  • Ecology
  • Evolutionary Game Theory
  • Mathematical Biology

Background:

  • Game theory is crucial for understanding interacting populations, but traditional methods struggle with complex, continuous systems.
  • Existing models often simplify habitats into discrete patches and assume perfect information, limiting real-world applicability.
  • Modeling population dynamics in continuous space is essential for realistic ecological insights.

Purpose of the Study:

  • To develop a novel method for studying population dynamics in continuous space using game theory.
  • To incorporate bounded rationality into ecological models for more realistic predictions.
  • To enable the analysis of complex ecosystems with interacting populations.

Main Methods:

  • Reformulated instantaneous multiplayer games for continuous spatial settings.
  • Applied advanced discretization techniques and modern optimization software.
  • Utilized numerical methods to solve complex game-theoretic problems in continuous space.

Main Results:

  • Developed a generalizable method applicable to complex ecosystems.
  • Modeled the vertical distribution and seasonal migration of forage fish, separating light and population density effects.
  • Demonstrated that bounded rationality leads to realistic spatial distributions, while population dynamics remain equivalent to complete rationality.

Conclusions:

  • The new game-theoretic approach effectively models population dynamics in continuous space, incorporating bounded rationality.
  • The method offers a significant advancement for studying complex ecological interactions and distributions.
  • Findings align with empirical observations, highlighting the importance of continuous space and bounded rationality in ecological modeling.