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    Stochastic Evolutionary Dynamics: A Graphical Reformulation Of Evolutionarily Stable Strategy (ESS) Analysis

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    Type
    Article
    Authors
    Touri, Behrouz
    Jaleel, Hassan
    Shamma, Jeff S. cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Electrical Engineering Program
    Date
    2018-06-25
    Online Publication Date
    2018-06-25
    Print Publication Date
    2019-01
    Permanent link to this record
    http://hdl.handle.net/10754/630439
    
    Metadata
    Show full item record
    Abstract
    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.
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Journal
    IEEE Control Systems Letters
    DOI
    10.1109/lcsys.2018.2850375
    Additional Links
    https://ieeexplore.ieee.org/document/8395356/
    ae974a485f413a2113503eed53cd6c53
    10.1109/lcsys.2018.2850375
    Scopus Count
    Collections
    Articles; Electrical Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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