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Cooperation in alternating interactions with memory constraints
Peter S Park1, Martin A Nowak1,2, Christian Hilbe3
1Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA.
Nature Communications
|February 9, 2022
Summary
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.
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.
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