Transmuting Social Dilemmas into Win-win Games: Payoff Families in the Topology of 2x2 Ordinal Games

Abstract

"The Robinson-Goforth topology of 2x2 ordinal games offers a useful tool for understanding the potential to transform social dilemmas into win-win games. The topology maps how 2x2 ordinal games are linked by swaps in adjoining payoff ranks, including intensively-studied symmetric games, such as Prisoner’s Dilemma, Chicken, Battles of the Sexes, and Stag Hunts, and the less-studied but much more numerous asymmetric games. Transmutations between ordinal games could result from new information, unilateral action, or deliberate redesign of governance institutions. The topology can be used in analyzing the robustness or instability of game outcomes, and the relative ease or difficulty of realigning incentives to improve outcomes. To help apply the topology for institutional analysis and design, this paper identifies additional families of games, based on Nash Equilibrium payoffs, including Second Best, Biased, and Unfair games, and subfamilies of Tragic, Samaritan, Self-serving, and Harmonious games. Visualization methods are used to display payoff families in a modified version of the periodic table of the strict ordinal 2x2 games."