Question: Let a* be an evolutionarily stable action. Does a* necessarily weakly dominate every other action? Is it possible that some action weakly dominates a* ?

  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.

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