Following the pattern of Exercise S4, analyze an
evolutionary version of the tennis point game Regard servers and receivers as
separate species, and construct a figure like What can you say about the ESS
and its dynamics?
U5. Recall from Exercise U1 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
(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.)