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The ESS for evolutionary matrix games under time constraints and its relationship with the asymptotically stable rest point of the replicator dynamics

  • Tamás VargaEmail author
  • Tamás F. Móri
  • József Garay
Article
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Abstract

Recently we interpreted the notion of ESS for matrix games under time constraints and investigated the corresponding state in the polymorphic situation. Now we give two further static (monomorphic) characterizations which are the appropriate analogues of those known for classical evolutionary matrix games. Namely, it is verified that an ESS can be described as a neighbourhood invader strategy independently of the dimension of the strategy space in our non-linear situation too, that is, a strategy is an ESS if and only if it is able to invade and completely replace any monomorphic population which totally consists of individuals following a strategy close to the ESS. With the neighbourhood invader property at hand, we establish a dynamic characterization under the replicator dynamics in two dimensions which corresponds to the strong stability concept for classical evolutionary matrix games. Besides, in some special cases, we also prove the stability of the corresponding rest point in higher dimensions.

Keywords

Evolutionary stability Matrix game Time constraint Monomorphic Polymorphic Population game Replicator dynamics 

Mathematics Subject Classification

37N25 91A05 91A22 91A40 92D15 

Notes

Acknowledgements

This research was supported by the EU-funded Hungarian Grant EFOP-3.6.1-16-2016-00008 (to T. Varga). The project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 690817 (to J. Garay and T. Varga). T. F. Móri was supported by the Hungarian National Research, Development and Innovation Office NKFIH—Grant No. K125569. J. Garay was supported by the Hungarian National Research, Development and Innovation Office NKFIH (GINOP 2.3.2-15-2016-00057).

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Bolyai InstituteUniversity of SzegedSzegedHungary
  2. 2.Department of Probability Theory and StatisticsEötvös Loránd UniversityBudapestHungary
  3. 3.Alfréd Rényi Institute of MathematicsBudapestHungary
  4. 4.MTA-ELTE Theoretical Biology and Evolutionary Ecology Research GroupEötvös Loránd UniversityBudapestHungary
  5. 5.Department of Plant Systematics, Ecology and Theoretical BiologyEötvös Loránd UniversityBudapestHungary
  6. 6.Evolutionary Systems Research GroupMTA Centre for Ecological ResearchTihanyHungary

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