1. Leta*be an evolutionarily stable action. Doesa*necessarily weakly dominate every other action? Is it possible that some action weakly dominatesa*?
2. Suppose that * is a mixed ESS, and letabe an action to which * assigns positive probability. Show that if * assigns positive probability to an action different froma, then (a,a) is not a pure strategy Nash equilibrium, and henceais not an ESS.