Game-Theoretic Robustness in Cooperation and Prejudice Reduction: A Graphic Measure

In Luis M. Rocha, Larry S. Yaeger, Mark A. Bedau, Dario Floreano & Robert L. Goldstine (eds.), Artificial Life X: Proceedings of the Tenth International Conference on the Simulation and Synthesis of Living Systems. MIT Press. pp. 445-451 (2006)
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Talk of ‘robustness’ remains vague, despite the fact that it is clearly an important parameter in evaluating models in general and game-theoretic results in particular. Here we want to make it a bit less vague by offering a graphic measure for a particular kind of robustness— ‘matrix robustness’— using a three dimensional display of the universe of 2 x 2 game theory. In a display of this form, familiar games such as the Prisoner’s Dilemma, Stag Hunt, Chicken and Deadlock appear as volumes, making comparison easy regarding the extent of different game-theoretic effects. We illustrate such a comparison in robustness between the triumph of Tit for Tat in a spatialized environment (Grim 1995, Grim, Mar, and St. Denis 1998) and a spatialized modeling of the Contact Hypothesis regarding prejudice reduction (Grim, et. al 2005a, 2005b). The geometrical representation of relative robustness also offers a possibility for links between geometrical theorems and results regarding robustness in game theory.
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