An Equilibrium Theorem of Strategies in Non-Linear Population Matrix Models

Mark Burgess

Working Paper Article Version 3 This version is not peer-reviewed

Version 1 : Received: 31 March 2017 / Approved: 31 March 2017 / Online: 31 March 2017 (11:29:09 CEST)
Version 2 : Received: 18 May 2017 / Approved: 18 May 2017 / Online: 18 May 2017 (03:34:39 CEST)
Version 3 : Received: 22 June 2021 / Approved: 24 June 2021 / Online: 24 June 2021 (08:38:13 CEST)

An evolutionary game is introduced which considers game-theoretic strategies in the context of non-linear population matrix models. This game considers the states and actions of the organisms of the evolving population, and a notion of dynamic equilibrium between strategies is described. The game’s formalism is expounded and a proof about equilibrium is given; specifically that any stable equilibrium can be described by proportions of pure strategies; particularly when population matrices are not defective.

evolutionary stable strategies (ESS); Markov decision evolutionary games (MDEG); Hawk-Dove game; evolutionary dynamics; evolutionary game theory

Computer Science and Mathematics, Algebra and Number Theory

Comment 1

Received: 24 June 2021
Commenter: Mark Burgess
Commenter's Conflict of Interests: Author

Comment: large cleanup, minimisation of proofs, restructuring

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An Equilibrium Theorem of Strategies in Non-Linear Population Matrix Models

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