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Names for Games: Locating 2 × 2 Games

Consulting Sociologist, 208 Old Germantown Road, P.O. Box 176, Warm Springs, VA 24484, USA
An earlier version of this paper was presented at the International Conference on Game Theory, Stony Brook, NY, USA, 7–11 July 2014 [1].
Academic Editor: Ulrich Berger
Games 2015, 6(4), 495-520; https://doi.org/10.3390/g6040495
Received: 2 August 2015 / Revised: 24 September 2015 / Accepted: 14 October 2015 / Published: 22 October 2015
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. View Full-Text
Keywords: taxonomy of 2 × 2 games; transforming strategic situations; strict and non-strict ordinal games; social dilemmas; collective action problems taxonomy of 2 × 2 games; transforming strategic situations; strict and non-strict ordinal games; social dilemmas; collective action problems
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Bruns, B.R. Names for Games: Locating 2 × 2 Games. Games 2015, 6, 495-520.

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