Following the pattern of Exercise S4, analyze an evolutionary version of the tennis point game…

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?

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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
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.)

 

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