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Dynamics of a Quantum Common-Pool Resource Game with Homogeneous Players' Expectations.

Juan Grau-Climent1, Luis García-Pérez1, Ramon Alonso-Sanz1

  • 1Complex Systems Group, Universidad Politécnica de Madrid, 28040 Madrid, Spain.

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|December 23, 2023
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Summary

This study introduces a quantum model for common-pool resource games with boundedly rational players. It analyzes resource exploitation and stability, offering insights into avoiding overexploitation in such economic games.

Keywords:
bifurcation and chaoscommon-pool resource gameentanglementhomogeneous playerslocal stability analysisquantum games

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Area of Science:

  • Game Theory
  • Quantum Economics
  • Resource Management

Background:

  • Common-pool resource games are crucial for understanding resource allocation.
  • Previous models often lack consideration for quantum entanglement and bounded rationality.
  • Homogeneous player expectations in these games are underexplored.

Purpose of the Study:

  • To introduce and analyze a novel quantum model for common-pool resource games.
  • To investigate the impact of player strategies and resource capacity on game dynamics.
  • To identify conditions leading to resource overexploitation and explore mitigation strategies.

Main Methods:

  • Utilizing a Cournot-type payoff function within a quantum framework.
  • Analyzing fixed points, Nash equilibrium, and system stability with varying parameters.
  • Employing analytical methods and bifurcation diagrams to visualize game dynamics.

Main Results:

  • The study details how game parameters influence fixed points and system stability.
  • It identifies scenarios where resource overexploitation is likely.
  • The research provides insights into adjusting parameters to prevent overexploitation.

Conclusions:

  • The quantum model offers a new perspective on boundedly rational common-pool resource games.
  • Understanding parameter effects is key to sustainable resource management.
  • This framework can inform policy for preventing resource depletion.