A graphic measure for game-theoretic robustness

Abstract

Robustness has long been recognized as an important parameter for evaluating game-theoretic results, but talk of ‘robustness’ generally remains vague. What we offer here is a graphic measure for a particular kind of robustness (‘matrix robustness’), using a three-dimensional display of the universe of 2×2 game theory. In such a measure specific games appear as specific volumes (Prisoner’s Dilemma, Stag Hunt, etc.), allowing a graphic image of the extent of particular game-theoretic effects in terms of those games. The measure also allows for an easy comparison between different effects in terms of matrix robustness. Here we use the measure to compare the robustness of Tit for Tat’s well-known success in spatialized games (Axelrod, R. (1984). The evolution of cooperation. New York: Basic Books; Grim, P. et al. (1998). The philosophical computer: Exploratory essays in philosophical computer modeling. Cambridge, Mass: MIT Press) with the robustness of a recent game-theoretic model of the contact hypothesis regarding prejudice reduction (Grim et al. 2005. Public Affairs Quarterly, 19, 95–125).