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Dynamic aspiration based on Win-Stay-Lose-Learn rule in spatial prisoner's dilemma game
Zhenyu Shi1,2,3,4, Wei Wei1,2,3,4, Xiangnan Feng1,2,3,4
1School of Mathematical Sciences, Beihang University, Beijing, China.
This study introduces a dynamic aspiration model for the spatial prisoner's dilemma game, showing how changing aspirations influence cooperation. Dynamic aspiration offers a better explanation of evolutionary game dynamics than fixed models.
Area of Science:
- Evolutionary Game Theory
- Computational Social Science
- Agent-Based Modeling
Background:
- The Prisoner's Dilemma is a key model for studying competition among self-interested individuals.
- The Win-Stay-Lose-Learn (WSLL) strategy, based on aspiration, effectively promotes cooperation in spatial Prisoner's Dilemma games.
- Aspiration levels are crucial for understanding cooperation dynamics in evolutionary games.
Purpose of the Study:
- To propose and analyze a dynamic aspiration model for the spatial Prisoner's Dilemma game, integrating Expected Value Theory and Achievement Motivation Theory.
- To investigate the impact of dynamic aspiration on cooperation and defection dynamics.
- To identify key network structures and temporal patterns driving evolutionary outcomes.
Main Methods:
- Developed a dynamic aspiration model where individual aspiration is payoff-dependent, based on the WSLL rule.
- Simulated the spatial Prisoner's Dilemma game with varying initial aspiration levels.
- Analyzed network structures and introduced END- and EXP-periods to examine temporal evolution and network reciprocity.
Main Results:
- Dynamic aspiration significantly impacts the evolutionary process, leading to distinct outcomes: Stable Coexistence (Low Aspiration), Dependent Coexistence (Moderate Aspiration), and Defection Explosion (High Aspiration).
- Identified specific network structures and node types (Infectors, Infected nodes, High-risk cooperators) responsible for defector re-expansion.
- Demonstrated the role of network reciprocity through END- and EXP-periods in explaining temporal dynamics.
Conclusions:
- Dynamic aspiration provides a more nuanced and satisfactory explanation of population evolution laws in spatial games compared to fixed aspiration models.
- The proposed model enhances the understanding of the underlying mechanisms of the Prisoner's Dilemma.
- This research highlights the importance of adaptive aspiration levels in fostering cooperation in evolutionary systems.
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