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Article

Dynamics of Strategy Distributions in a One-Dimensional Continuous Trait Space for Games with a Quadratic Payoff Function

National Center for Biotechnology Information, National Institutes of Health, Bldg. 38A, 8600 Rockville Pike, Bethesda, MD 20894, USA
Games 2020, 11(1), 14; https://doi.org/10.3390/g11010014
Received: 9 January 2020 / Revised: 5 February 2020 / Accepted: 12 February 2020 / Published: 2 March 2020
(This article belongs to the Special Issue Non-Imitative Dynamics in Evolutionary Game Theory)
Evolution of distribution of strategies in game theory is an interesting question that has been studied only for specific cases. Here I develop a general method to extend analysis of the evolution of continuous strategy distributions given a quadratic payoff function for any initial distribution in order to answer the following question—given the initial distribution of strategies in a game, how will it evolve over time? I look at several specific examples, including normal distribution on the entire line, normal truncated distribution, as well as exponential and uniform distributions. I show that in the case of a negative quadratic term of the payoff function, regardless of the initial distribution, the current distribution of strategies becomes normal, full or truncated, and it tends to a distribution concentrated in a single point so that the limit state of the population is monomorphic. In the case of a positive quadratic term, the limit state of the population may be dimorphic. The developed method can now be applied to a broad class of questions pertaining to evolution of strategies in games with different payoff functions and different initial distributions. View Full-Text
Keywords: continuous strategy space; quadratic payoff function; evolution of distribution; HKV method continuous strategy space; quadratic payoff function; evolution of distribution; HKV method
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MDPI and ACS Style

Karev, G. Dynamics of Strategy Distributions in a One-Dimensional Continuous Trait Space for Games with a Quadratic Payoff Function. Games 2020, 11, 14. https://doi.org/10.3390/g11010014

AMA Style

Karev G. Dynamics of Strategy Distributions in a One-Dimensional Continuous Trait Space for Games with a Quadratic Payoff Function. Games. 2020; 11(1):14. https://doi.org/10.3390/g11010014

Chicago/Turabian Style

Karev, Georgiy. 2020. "Dynamics of Strategy Distributions in a One-Dimensional Continuous Trait Space for Games with a Quadratic Payoff Function" Games 11, no. 1: 14. https://doi.org/10.3390/g11010014

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