Stochastic Evolutionary Dynamics: A Graphical Reformulation Of Evolutionarily Stable Strategy (ESS) Analysis
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionElectrical Engineering Program
Date
2018-06-25Online Publication Date
2018-06-25Print Publication Date
2019-01Permanent link to this record
http://hdl.handle.net/10754/630439
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We propose a novel graph-based reformulation for the concept of evolutionarily stable strategies. Evolutionarily stable strategy (ESS) analysis cannot always explain the long-term behavior of a natural selection-mutation process. Stochastic stability is a more general analysis tool as compared to ESS analysis because it can precisely characterize long-term stochastic behavior. However, one of the reasons why ESS analysis is still widely popular is its computational simplicity. Our objective is to provide a balance between the convenience of ESS analysis and the generality of stochastic stability. The fundamental object in our development is the transitive stability (TS) graph of an evolutionary process. From the TS-graph, we show that we can efficiently compute the smallest set of strategies that always contains the stochastically stable strategies (SSS) for a particular class of evolutionary processes. In particular, we prove that each terminal class of the TS-graph is potentially a stochastically stable group of strategies. In case there is a unique terminal class, then it corresponds exactly to the set of SSS. In case there are multiple terminal classes, then these contain the set of possible SSS, and we show that a unique determination is impossible without higher order analysis.Citation
Touri B, Jaleel H, Shamma JS (2019) Stochastic Evolutionary Dynamics: A Graphical Reformulation of Evolutionarily Stable Strategy (ESS) Analysis. IEEE Control Systems Letters 3: 55–60. Available: http://dx.doi.org/10.1109/lcsys.2018.2850375.Sponsors
This work was supported by KAUST.Journal
IEEE Control Systems LettersAdditional Links
https://ieeexplore.ieee.org/document/8395356/ae974a485f413a2113503eed53cd6c53
10.1109/lcsys.2018.2850375