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War of attrition with implicit time cost
Anders Eriksson1, Kristian Lindgren, T Torbjörn Lundh
1Department of Physical Resource Theory, Chalmers University of Technology, SE-41296 Göteborg, Sweden. frtae@fy.chalmers.se
Journal of Theoretical Biology
|August 11, 2004
Summary
This study models the war of attrition game with implicit time costs, revealing that strategy stability depends on the winner-to-loser score ratio. High ratios lead to unstable distributions and limit cycles, while low ratios ensure stability.
Area of Science:
- Game Theory
- Evolutionary Biology
- Mathematical Modeling
Background:
- Traditional war of attrition models feature explicit time costs.
- Implicit time costs, dependent on population strategies, are less explored.
- Understanding these implicit costs is crucial for evolutionary game dynamics.
Purpose of the Study:
- To construct and analyze a game-theoretic model of the war of attrition with implicit time costs.
- To identify the mechanisms driving these implicit costs.
- To investigate the stability and dynamics of strategy distributions.
Main Methods:
- Developed a novel game-theoretic model incorporating implicit time costs.
- Analyzed player strategies, game frequency, and accumulated scores.
- Utilized replicator dynamics to derive stationary strategy distributions.
- Assessed evolutionary and dynamical stability.
Main Results:
- The stability of strategy distributions is contingent on the winner's to loser's score ratio.
- High score ratios result in unstable distributions and convergence to limit cycles.
- Low score ratios lead to stable stationary distributions.
- Intermediate ratios yield dynamically stable but evolutionarily unstable distributions.
Conclusions:
- The implicit time cost mechanism significantly alters war of attrition dynamics.
- Score ratios are critical determinants of evolutionary stability and population strategy.
- Findings offer new insights into evolutionary game theory and contest models.