  Changes in payoffs can transform Prisoner's Dilemma and other social dilemmas
into harmonious win-win games. Using the Robinson-Goforth topology of 2x2
games, this paper analyzes how payoff swaps turn Prisoner's Dilemma into other
games, compares Prisoner's Dilemmas with other families of games, traces paths
that affect the difficulty of transforming Prisoner's Dilemma and other social
dilemmas into win-win games, and shows how ties connect simpler and more
complex games. Charts illustrate the relationships between the 144 strict
ordinal 2x2 games, the 38 symmetric 2x2 ordinal games with and without ties,
and the complete set of 1,413 2x2 ordinal games. Payoffs from the symmetric
ordinal 2x2 games combine to form asymmetric games, generating coordinates for
a simple labeling scheme to uniquely identify and locate all asymmetric ordinal
2x2 games. The expanded topology elegantly maps relationships between 2x2 games
with and without ties, enables a systematic understanding of the potential for
transformations in social dilemmas and other strategic interactions, offers a
tool for institutional analysis and design, and locates a variety of
interesting games for further research.
