Computation of Sparse and Dense Equilibrium Strategies of Evolutionary Games

• Main Authors: Yiping Hao, Zhijun Wu
• Format: Article
• Language: English
• Published: MDPI AG 2018-07-01
• Series: Games
• Subjects: evolutionary games; Nash equilibrium; Shapley-Snow algorithm; dense vs. sparse strategies; biodiversity
• Online Access: http://www.mdpi.com/2073-4336/9/3/46

The evolution of social or biological species can be modeled as an evolutionary gamewith the equilibrium strategies of the game as prediction for the ultimate distributions of speciesin population, when some species may survive with positive proportions, while others becomeextinct. We say a strategy is dense if it contains a large and diverse number of positive species, and issparse if it has only a few dominant ones. Sparse equilibrium strategies can be found relativelyeasily, 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 thecost for computing dense equilibrium strategies much more efficiently. We describe the primary andcomplementary algorithms for computing dense as well as sparse equilibrium strategies, and presenttest 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 theprimary algorithm to obtain the dense equilibrium strategies for all our test cases.