Reference no: EM132400840
SUST3000: Environmental Decision Making Dalhousie University, Canada
Assignment : Game Theory (Part 1) - Cost and Benefit for Evolutionary Ecology
Question: Assume that two alternative strategies make up the mixed ESS at frequencies of 0.8 for strategy ‘A’, and 0.2 for stategy ‘B’. Assume that all individuals practice both A and B strategies. Describe each individual’s behavior.
Explain the difference between a pure strategy and a pure ESS.
Explain the difference between a mixed strategy and a mixed ESS.
What is the frequency of strategy B?
What is the frequency of A vs. A interactions?
What is the frequency of B vs. B interactions where the payoff is to A?
What is the frequency of B vs. A interactions where the payoff is to B?
Will the proportion of the total number of payoffs to A when vs. B be any different than the proportion of the total number of payoffs to B when vs. A?
What is the expression for determining whether or not strategy B is a Pure ESS against A?
Using the expression for B vs. A that you just wrote, explain whether or not B is stable against invasion by A.
What if neither strategy is a Pure ESS? If there are only two strategies, then there must be a mixed ESS.
What does this mean?
We also need to make explicit how we arrive at each payoff. Write the general form of the equations:
Calculate the payoff for aggressor vs. aggressor:
Calculation of the payoff to Aggressor when vs. Non-Aggressor:
Calculation of the payoff to non-aggressor when vs. Aggressor:
Does our example meet the criteria for a Pure ESS, why or why not?
What happens at the equilibrium point? What if you add individuals of either strategy?
Question: What does the addition of more aggressors do?
Question: How does the aggressor strategy do when in high frequency compared to when it’s rare? What does this mean?
Question: Is the non-aggressive strategy stable? Why or why not?
What assumptions would you have to make to turn this into a Pure ESS?
What can we generally say about the evolutionary strategy of the two Sable Island horse populations?
Attachment:- Assignment- Game Theory.rar
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