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The Robinson-Goforth topology of swaps in adjoining payoffs elegantlyarranges 2x2 ordinal games in accordance with important properties includingsymmetry, number of dominant strategies and Nash Equilibria, and alignment ofinterests. Adding payoff families based on Nash Equilibria illustrates anadditional aspect of this order and aids visualization of the topology. Makingties through half-swaps not only creates simpler games within the topology,but, in reverse, breaking ties shows the evolution of preferences, yielding anatural ordering for the topology of 2x2 games with ties. An ordinal game notonly represents an equivalence class of games with real values, but also adiscrete equivalent of the normalized version of those games. The topologyprovides coordinates which could be used to identify related games in asemantic web ontology and facilitate comparative analysis of agent-basedsimulations and other research in game theory, as well as chartingrelationships and potential moves between games as a tool for institutionalanalysis and design.

Navigating the Topology of 2x2 Games: An Introductory Note on Payoff Families, Normalization, and Natural Order