Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/257433 
Authors: 
Year of Publication: 
2020
Citation: 
[Journal:] Games [ISSN:] 2073-4336 [Volume:] 11 [Issue:] 1 [Article No.:] 14 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-12
Publisher: 
MDPI, Basel
Abstract: 
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
Subjects: 
continuous strategy space
evolution of distribution
HKV method
quadratic payoff function
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Creative Commons License: 
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Document Type: 
Article
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