  The Robinson-Goforth topology of swaps in adjoining payoffs elegantly
arranges 2x2 ordinal games in accordance with important properties including
symmetry, number of dominant strategies and Nash Equilibria, and alignment of
interests. Adding payoff families based on Nash Equilibria illustrates an
additional aspect of this order and aids visualization of the topology. Making
ties through half-swaps not only creates simpler games within the topology,
but, in reverse, breaking ties shows the evolution of preferences, yielding a
natural ordering for the topology of 2x2 games with ties. An ordinal game not
only represents an equivalence class of games with real values, but also a
discrete equivalent of the normalized version of those games. The topology
provides coordinates which could be used to identify related games in a
semantic web ontology and facilitate comparative analysis of agent-based
simulations and other research in game theory, as well as charting
relationships and potential moves between games as a tool for institutional
analysis and design.
