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Updated: Jan 28, 2026

The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm
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Best reply structure and equilibrium convergence in generic games.

Marco Pangallo1,2, Torsten Heinrich1,2,3, J Doyne Farmer1,2,4,5

  • 1Institute for New Economic Thinking at the Oxford Martin School, University of Oxford, Oxford OX2 6ED, UK.

Science Advances
|February 26, 2019
PubMed
Summary
This summary is machine-generated.

Game theory models interacting systems. Best reply cycles in complex games predict learning dynamics will not converge to equilibrium, necessitating explicit modeling of these oscillations.

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Area of Science:

  • Evolutionary Game Theory
  • Computational Social Science
  • Theoretical Ecology

Background:

  • Game theory models interactions in biological and social systems.
  • Systems can converge to equilibrium (e.g., Nash equilibrium) or exhibit endogenous oscillations.
  • Predicting convergence versus oscillation is crucial for understanding system dynamics.

Purpose of the Study:

  • To determine whether systems are more likely to converge to equilibrium or oscillate.
  • To identify factors predicting nonconvergence in game dynamics.
  • To evaluate the applicability of equilibrium assumptions in complex games.

Main Methods:

  • Generating random payoff matrices with constraints reflecting real-world game properties.
  • Employing an approach from theoretical ecology for ecosystem stability analysis.
  • Analyzing the predictive power of best reply cycles on learning algorithm convergence.

Main Results:

  • Best reply cycles were identified as key topological structures in games.
  • These cycles predict the nonconvergence of six common learning algorithms used in biology and human experiments.
  • Best reply cycles are prevalent in complicated and competitive games.

Conclusions:

  • Equilibrium is often an unrealistic assumption in complex and competitive games.
  • The presence of best reply cycles indicates a tendency towards endogenous oscillations rather than convergence.
  • Explicit modeling of learning dynamics is necessary when best reply cycles dominate.