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Names for Games: Locating 2 × 2 Games

Author

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  • Bryan Randolph Bruns

    (Consulting Sociologist, 208 Old Germantown Road, P.O. Box 176, Warm Springs, VA 24484, USA)

Abstract

Prisoner’s Dilemma, Chicken, Stag Hunts, and other two-person two-move (2 × 2) models of strategic situations have played a central role in the development of game theory. The Robinson–Goforth topology of payoff swaps reveals a natural order in the payoff space of 2 × 2 games, visualized in their four-layer “periodic table” format that elegantly organizes the diversity of 2 × 2 games, showing relationships and potential transformations between neighboring games. This article presents additional visualizations of the topology, and a naming system for locating all 2 × 2 games as combinations of game payoff patterns from the symmetric ordinal 2 × 2 games. The symmetric ordinal games act as coordinates locating games in maps of the payoff space of 2 × 2 games, including not only asymmetric ordinal games and the complete set of games with ties, but also ordinal and normalized equivalents of all games with ratio or real-value payoffs. An efficient nomenclature can contribute to a systematic understanding of the diversity of elementary social situations; clarify relationships between social dilemmas and other joint preference structures; identify interesting games; show potential solutions available through transforming incentives; catalog the variety of models of 2 × 2 strategic situations available for experimentation, simulation, and analysis; and facilitate cumulative and comparative research in game theory.

Suggested Citation

  • Bryan Randolph Bruns, 2015. "Names for Games: Locating 2 × 2 Games," Games, MDPI, vol. 6(4), pages 1-26, October.
    • Handle: RePEc:gam:jgames:v:6:y:2015:i:4:p:495-520:d:57623
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Rusch, Hannes, 2019. "The evolution of collaboration in symmetric 2×2-games with imperfect recognition of types," Games and Economic Behavior, Elsevier, vol. 114(C), pages 118-127.
    2. Brams, Steven & Kilgour, Marc, 2017. "Stabilizing unstable outcomes in prediction games," MPRA Paper 77655, University Library of Munich, Germany.
    3. 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.
    4. Brams, Steven J. & Ismail, Mehmet S., 2019. "Farsightedness in Games: Stabilizing Cooperation in International Conflict," MPRA Paper 91370, University Library of Munich, Germany.
    5. Hannes Rusch, 2017. "The Evolution of Collaboration in Symmetric 2x2-Games with Imperfect Recognition of Types," MAGKS Papers on Economics 201739, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
    6. Brams, Steven J. & Ismail, Mehmet S., 2018. "Stabilizing Cooperative Outcomes in Two-Person Games: Theory and Cases," MPRA Paper 86295, University Library of Munich, Germany.

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