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

Author

Listed:
  • Mikael Böörs

    (University of Gothenburg)

  • Tobias Wängberg

    (Stockholm University)

  • Tom Everitt

    (Google DeepMind
    Australian National University)

  • Marcus Hutter

    (Google DeepMind
    Australian National University)

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.

Suggested Citation

  • Mikael Böörs & Tobias Wängberg & Tom Everitt & Marcus Hutter, 2022. "Classification by decomposition: a novel approach to classification of symmetric $$2\times 2$$ 2 × 2 games," Theory and Decision, Springer, vol. 93(3), pages 463-508, October.
    • Handle: RePEc:kap:theord:v:93:y:2022:i:3:d:10.1007_s11238-021-09850-z
    DOI: 10.1007/s11238-021-09850-z
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    References listed on IDEAS

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    1. Adam Kalai & Ehud Kalai, 2013. "Cooperation in Strategic Games Revisited," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 917-966.
    2. Andreoni, James A & Miller, John H, 1993. "Rational Cooperation in the Finitely Repeated Prisoner's Dilemma: Experimental Evidence," Economic Journal, Royal Economic Society, vol. 103(418), pages 570-585, May.
    3. Ozan Candogan & Ishai Menache & Asuman Ozdaglar & Pablo A. Parrilo, 2011. "Flows and Decompositions of Games: Harmonic and Potential Games," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 474-503, August.
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    Cited by:

    1. Luke Marris & Ian Gemp & Georgios Piliouras, 2023. "Equilibrium-Invariant Embedding, Metric Space, and Fundamental Set of $2\times2$ Normal-Form Games," Papers 2304.09978, arXiv.org.
    2. Valeria Maggian & Ludovica Spinola, 2024. "Spillover effects of cooperative behaviour when switching tasks: the role of gender," Working Papers 2024: 09, Department of Economics, University of Venice "Ca' Foscari".

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