Game theory homework
Using the results of the following runs and additional runs required for questions 5
to 9, answer the following questions on your own paper, identifying your
responses by number. The simulation runs on this handout are a guide to help
you answer the following questions. Turn in your results stapled to the back of
your answers to help explain your answers to these questions. You will be graded
only on what you put for these 9 questions.
1. What were the differences in the success of hawks and doves when hawk began as a
rare gene, when dove began as a rare gene, and when they were initiated at equal
frequencies?
2. What were general differences between the stochastic and analytic runs? Why do they
differ? Is one more representative of natural circumstances, or do they each have their
advantages and disadvantages? Justify your answer. What would you do to the
stochastic simulation to make it more like the analytic?
3. Discuss the runs with the bourgeois gene and how they differed from the runs that only
had hawk and dove. If bourgeois goes extinct what is the ESS for hawk and dove?
4. What is more important, relative costs and benefits or absolute costs and benefits?
Why?
Returning to the program, vary RV CI and CD and run simulations and look
at predicted ESS to answer the following questions.
5. Under what circumstances is hawk an ESS?
6. Under what circumstances is dove more common than hawk?
7. Why is it unlikely that dove will ever drive the hawk allele to extinction?
8. How does the simulation change when bourgeois is added?
9. Does bourgeois benefit hawk or dove under equal circumstances and does the
to this question depend on RV CI and CD?
answer
Game Theory Simulations
This homework will require the use of the game theory program written by Keith
Goodnight that is on the fileserver at in the BioSciences computer lab. A guide to the
program is at the end of this assignment. Run the simulations below. The following
abbreviations will be used:
RV = resource value
CI = cost of injury
CD = cost of display
ESS = evolutionarily stable strategy
Following the example in Krebs and Davies, set RV at 50, CI at 100, and CD at 10.
Let the population consist of all doves. Add between 10 and 20 hawks.
What is the ESS?________________________________________________
Run the program for 200 generations.
Run 1. What is the highest and lowest gene frequency ever taken by hawk and dove?
Hawk, highest__________, lowest _____________
Dove, highest___________, lowest _____________
What is the maximum difference between the analytical and the stochastic frequency of
the
gene for hawk?___________________________________________________________
About what generation did it occur in (not including the first 30 generations)?
__________
Was the gene for dove
hawk?___________________
ever
more
common
than
the
gene
for
How many times was it more common?________________________________________
What were the maximum and minimum # of generations for which dove was more
common? _______________________________________________________________
Was hawk or dove more common overall in the stochastic run after the first 30
generations?
Run this program again 2 more times and answer the same questions below.
Run 2. What is the highest and lowest gene frequency ever taken by hawk and dove?
Hawk, highest__________, lowest _____________
Dove, highest___________, lowest ____________
What is the maximum difference between the analytical and the stochastic frequency of
the
gene for hawk?___________________________________________________________
About what generation did it occur in (not including the first 30 generations)?
__________
Was the gene for dove
hawk?___________________
ever
more
common
than
the
gene
for
How many times was it more common?________________________________________
What were the maximum and minimum # of generations for which dove was more
common? _______________________________________________________________
Was hawk or dove more common overall in the stochastic run after the first 30
generations?
Run 3. What is the highest and lowest gene frequency ever taken by hawk and dove?
Hawk, highest__________, lowest _____________
Dove, highest___________, lowest _____________
What is the maximum difference between the analytical and the stochastic frequency of
the
gene for hawk?___________________________________________________________
About what generation did it occur in (not including the first 30 generations)?
__________
Was the gene for dove
hawk?___________________
ever
more
common
than
the
gene
for
How many times was it more common?________________________________________
What were the maximum and minimum # of generations for which dove was more
common? _______________________________________________________________
Was hawk or dove more common overall in the stochastic run after the first 30
generations?
Leaving the values for RV, CI and CD constant, create a population of equal
numbers of hawks and doves. Run the simulation once and answer the questions
below.
Run 4. What is the ESS?________________Hawk, highest__________, lowest
_________
Dove, highest___________, lowest _____________
What is the maximum difference between the analytical and the stochastic frequency of
the
gene for hawk?___________________________________________________________
About what generation did it occur in (not including the first 30 generations)?
__________
Was the gene for dove
hawk?___________________
ever
more
common
than
the
gene
for
How many times was it more common?________________________________________
What were the maximum and minimum # of generations for which dove was more
common? _______________________________________________________________
Was hawk or dove more common overall in the stochastic run after the first 30
generations?
Leaving the values for RV, CI and CD constant, create a population of all hawks.
Add 1 to 10 doves and run the simulation once and answer the questions below.
Run 5. What is the ESS?__________________________________
Hawk, highest__________, lowest _____________
Dove, highest___________, lowest _____________
What is the maximum difference between the analytical and the stochastic frequency of
the
gene for hawk?___________________________________________________________
About what generation did it occur in (not including the first 30 generations)?
__________
Was the gene for dove
hawk?___________________
ever
more
common
than
the
gene
for
How many times was it more common?________________________________________
What were the maximum and minimum # of generations for which dove was more
common? _______________________________________________________________
Was hawk or dove more common overall in the stochastic run after the first 30
generations?
Leaving the values for RV, CI and CD constant, create a population of equal
numbers of hawks, doves and bourgeois. Run the simulation and answer the
questions below.
Run 6. What is the ESS?__________________________________________________
What is the highest and lowest gene frequency ever taken by hawk, dove and bourgeois?
Hawk, highest__________, lowest _____________
Dove, highest___________, lowest _____________
Bourgeois, highest___________, lowest _____________
What is the maximum difference between the analytical and the stochastic frequency of
the
gene for bourgeois?_______________________________________________________
About
what
generation
did
_________________________________________
Was the gene for dove
bourgeois?_______________
ever
more
it
common
occur
than
the
in?
gene
for
If so, how many times, when and for how many generations?______________________
________________________________________________________________________
Was the gene for hawk
bourgeois?_______________
ever
more
common
than
the
gene
for
If so, how many times, when and for how many generations?______________________
________________________________________________________________________
Did
any
of
the
genes
when?__________________
go
extinct?__________
Which
one
and
Which
strategy
is
more
run?_______________________
common
overall
in
the
stochastic
Leaving the values for RV, CI and CD constant, create a population of equal
numbers of hawks, doves and bourgeois as above. Run the simulation again and
answer the questions below.
Run 7. What is the ESS?__________________________________________________
What is the highest and lowest gene frequency ever taken by hawk, dove and bourgeois?
Hawk, highest__________, lowest _____________
Dove, highest___________, lowest _____________
Bourgeois, highest___________, lowest _____________
What is the maximum difference between the analytical and the stochastic frequency of
the
gene for bourgeois?_______________________________________________________
About
what
generation
did
_________________________________________
Was the gene for dove
bourgeois?_______________
ever
more
it
common
occur
than
the
in?
gene
for
If so, how many times, when and for how many generations?______________________
________________________________________________________________________
Was the gene for hawk
bourgeois?_______________
ever
more
common
than
the
gene
for
If so, how many times, when and for how many generations?______________________
________________________________________________________________________
Did
any
of
the
genes
when?__________________
Which
strategy
is
more
run?_______________________
go
extinct?__________
common
overall
Which
in
the
one
and
stochastic
Leaving the values for RV, CI and CD constant, create a population of equal
numbers of hawks, doves and bourgeois as above. Run the simulation again and
answer the questions below.
Run 8. What is the ESS?__________________________________________________
What is the highest and lowest gene frequency ever taken by hawk, dove and bourgeois?
Hawk, highest__________, lowest _____________
Dove, highest___________, lowest _____________
Bourgeois, highest___________, lowest _____________
What is the maximum difference between the analytical and the stochastic frequency of
the
gene for bourgeois?_______________________________________________________
About
what
generation
did
_________________________________________
Was the gene for dove
bourgeois?_______________
ever
more
it
common
occur
than
the
in?
gene
for
If so, how many times, when and for how many generations?______________________
________________________________________________________________________
Was the gene for hawk
bourgeois?_______________
ever
more
common
than
the
gene
for
If so, how many times, when and for how many generations?______________________
________________________________________________________________________
Did
any
of
the
genes
when?__________________
Which
strategy
is
more
run?_______________________
go
extinct?__________
common
overall
Which
in
the
one
and
stochastic
Set RV at 25 CI at 50 and CD at 5. Let the population consist of equal numbers of
hawks and doves. Run the simulation.
Run 9. What is the ESS?__________________________________
What is the highest and lowest gene frequency ever taken by hawk and dove?
Hawk, highest__________, lowest _____________
Dove, highest___________, lowest _____________
What is the maximum difference between the analytical and the stochastic frequency of
the
gene for hawk?___________________________________________________________
About
what
generation
did
_________________________________________
Was the gene for dove
hawk?___________________
ever
more
it
common
occur
than
the
in?
gene
for
If so, how many times, when and for how many generations?______________________
Which
strategy
is
more
run?_______________________
common
overall
in
the
stochastic
Set RV at 25 CI at 50 and CD at 5. Let the population consist of equal numbers of
hawks and doves. Run the simulation.
Run 10. What is the ESS?__________________________________
What is the highest and lowest gene frequency ever taken by hawk and dove?
Hawk, highest__________, lowest _____________
Dove, highest___________, lowest _____________
What is the maximum difference between the analytical and the stochastic frequency of
the
gene for hawk?___________________________________________________________
About
what
generation
did
_________________________________________
Was the gene for dove
hawk?___________________
ever
more
it
common
occur
than
the
in?
gene
for
If so, how many times, when and for how many generations?______________________
________________________________________________________________________
Which
strategy
is
more
run?_______________________
common
overall
in
the
stochastic