 One might expect it to be possible to predict the strategies that will prevail in EPDs meeting various conditions, and to justify such predictions by formal proofs. Until recently, however, mathematical analyses of the EPD have been plagued by conceptual confusions about “evolutionary stability,” the condition under which, as Nowak and Sigmund say, “evolution stops”. Axelrod and Axelrod &amp; Hamilton claim to show that TFT is evolutionarily stable. Selten 1983, includes an example of a game with no evolutionarily stable strategy, and Selten's argument that there is no such strategy clearly applies to the EPD and other evolutionary games. Boyd and Lorberbaum and Farrell and Ware present still different proofs demonstrating that no strategies for the EPD are evolutionarily stable. Unsurprisingly, the paradox is resolved by observing that the three groups of authors each employ slightly different conceptions of evolutionary stability. The conceptual tangle is unraveled in a series of papers by Bendor and Swistak. Two central stability concepts are described and applied to the EPD below. Readers who wish to compare these with some others that appear in the literature may consult the following brief guide: