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Games 2018, 9(3), 46; https://doi.org/10.3390/g9030046

Computation of Sparse and Dense Equilibrium Strategies of Evolutionary Games

and
†,*
Department of Mathematics, Iowa State University, Ames, IA 50011, USA
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 8 May 2018 / Revised: 1 July 2018 / Accepted: 4 July 2018 / Published: 7 July 2018
(This article belongs to the Special Issue Mathematical Biology and Game Theory)
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Abstract

The evolution of social or biological species can be modeled as an evolutionary game with the equilibrium strategies of the game as prediction for the ultimate distributions of species in population, when some species may survive with positive proportions, while others become extinct. We say a strategy is dense if it contains a large and diverse number of positive species, and is sparse if it has only a few dominant ones. Sparse equilibrium strategies can be found relatively easily, while dense ones are more computationally costly. Here we show that by formulating a “complementary” problem for the computation of equilibrium strategies, we are able to reduce the cost for computing dense equilibrium strategies much more efficiently. We describe the primary and complementary algorithms for computing dense as well as sparse equilibrium strategies, and present test results on randomly generated games as well as a more biologically related one. In particular, we demonstrate that the complementary algorithm is about an order of magnitude faster than the primary algorithm to obtain the dense equilibrium strategies for all our test cases. View Full-Text
Keywords: evolutionary games; Nash equilibrium; Shapley-Snow algorithm; dense vs. sparse strategies; biodiversity evolutionary games; Nash equilibrium; Shapley-Snow algorithm; dense vs. sparse strategies; biodiversity
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Hao, Y.; Wu, Z. Computation of Sparse and Dense Equilibrium Strategies of Evolutionary Games. Games 2018, 9, 46.

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