Recall from Exercise Ul the population of animals fighting over a food source worth 200 calories. Assume that, as in part (b) of that exercise, the cost of a fight is 150 calories per fighter. Assume also that a third phenotype exists in the population. That phenotype is a mixer; it plays a mixed strategy, sometimes fighting and sometimes sharing.
(a) Use your knowledge of mixed strategies in rationally played games to posit a reasonable mixture for the mixer phenotype to use in this game.
(b) Draw the three-by-three payoff table for this game when the mixer type uses the mixed strategy that you found in part (a).
(c) Determine whether the mixer phenotype is an ESS of this game. (Hint: Test whether a mixer population can be invaded successfully by either the fighting type or the sharing type.)