Altruists and envious people who meet in contests are symbionts. They do better than a population of narrowly rational individuals. If there are only altruists and envious individuals, a particular mixture of altruists and envious individuals is evolutionarily stable.

Fixed points of the (most) refined best reply correspondence, introduced in Balkenborg, Hofbauer, and Kuzmics (2013), in the agent normal form of extensive form games with perfect recall have a remarkable property. They induce fixed points of the same correspondence in the agent normal form of...