# Classification by decomposition: a novel approach to classification of symmetric $$2\times 2$$ 2 × 2 games

Mikael Böörs, Tobias Wängberg (), Tom Everitt and Marcus Hutter
Mikael Böörs: University of Gothenburg
Tobias Wängberg: Stockholm University

Theory and Decision, 2022, vol. 93, issue 3, No 4, 463-508

Abstract: Abstract In this paper, we provide a detailed review of previous classifications of $$2\times 2$$ 2 × 2 games and suggest a mathematically simple way to classify the symmetric $$2\times 2$$ 2 × 2 games based on a decomposition of the payoff matrix into a cooperative and a zero-sum part. We argue that differences in the interaction between the parts is what makes games interesting in different ways. Our claim is supported by evolutionary computer experiments and findings in previous literature. In addition, we provide a method for using a stereographic projection to create a compact 2-d representation of the game space.

Keywords: Classification; Symmetric games; $$2\times 2$$ 2 × 2 Games; Decomposition; Cooperation and conflict; Simplicity (search for similar items in EconPapers)
Date: 2022
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