Names for Games: Locating 2 × 2 Games

Bryan Randolph Bruns
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Bryan Randolph Bruns: Consulting Sociologist, 208 Old Germantown Road, P.O. Box 176, Warm Springs, VA 24484, USA

Games, 2015, vol. 6, issue 4, 1-26

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.

Keywords: taxonomy of 2 × 2 games; transforming strategic situations; strict and non-strict ordinal games; social dilemmas; collective action problems (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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