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Cooperation can emerge in alternating games where players take turns, even with memory-one strategies. However, these strategies differ from simultaneous games and are not evolutionarily stable in noisy environments.

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Area of Science:

  • Evolutionary game theory
  • Behavioral economics
  • Social dynamics

Background:

  • Reciprocity is key to cooperation in repeated social interactions.
  • Existing models often assume synchronized decision-making, which is unrealistic for many natural scenarios.
  • Asynchronous interactions, where help is exchanged alternately, are common in nature.

Purpose of the Study:

  • To investigate the emergence of cooperation and reciprocity in asynchronous, alternating games.
  • To mathematically analyze Nash equilibria in memory-one strategies for alternating games.
  • To explore the impact of game discounting, irregular alternation, and memory on cooperation.

Main Methods:

  • Mathematical characterization of Nash equilibria for memory-one strategies.
  • Evolutionary simulations to model game dynamics.
  • Analysis of discounted games, irregular alternation patterns, and higher memory effects.

Main Results:

  • Mutual cooperation evolves in alternating games across a broad parameter range.
  • Cooperation in alternating games requires different strategies than in simultaneous games, especially in noisy environments.
  • None of the analyzed strategies for alternating games are evolutionarily stable.

Conclusions:

  • Alternating games can support cooperation, but necessitate distinct strategies compared to simultaneous games.
  • The evolutionarily stable strategies differ between simultaneous and alternating interaction structures.
  • Understanding asynchronous reciprocity is crucial for explaining cooperation in natural systems.