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(Darwin's theory of the sex ratio) A population of males and females mate pairwise to produce offspring. Suppose that each offspring is male with probability p and female with probability 1 - p. Then there is a steady state in which the fraction p of the population is male and the fraction 1 - p is female. If p ∗= 1 then males and females have different numbers of offspring (on average). Is such an equilibrium evolutionarily stable? Denote the number of children born to each female by n, so that the number of children born to each male is (p/(1 - p))n. Suppose a mutation occurs that produces boys and girls each with probability 1 .
Assume for simplicity that the mutant trait is dominant: if one partner in a couple has it, then all the offspring of the couple have it. Assume also that the number of children produced by a female with the trait is n, the same as for "normal" members of the population. Since both normal and mutant females produce the same number of children, it might seem that the ?tness of a mutant is the same as that of a normal organism. But compare the number of grand children of mutants and normal organisms. How many female offspring does a normal organism produce? How many male offspring? Use your answers to ?nd the number of grandchildren born to each mutant and to each normal organism. Does the mutant invade the population? Which value (values?) of p is evolutionarily stable?
Assume that the relationship between the growth of a fish population and the population size can be expressed as g = 2P - 0.1P, where g is the growth in tons and P is the size of the population (in thousands of tons).
Assume that the companies in an oligopolistic market engage in a price war and, as a result, all companies earn lower profits. Game theory would describe this as what?
Kodak & Fuji develop photographic film. Assume that there are no other significant manufactures, so that Kodak and Fuji constitute a duopoly
Find the Nash revision strategies for Ann and Bob which form a SGPNE with the δ identified in part (a) - Verify that the strategies found in part (b) do form a SGPNE
What is the payoff of a person whose number is the highest of the three? Can she increase this payoff by announcing a different number?
A hat contains three coins - one gold, one silver and one copper. You will select coins one at a time without replacement until you choose the gold coin. The outcome of interest is the sequence of coins that are selected during this process.
A famous hypnotist performs to a crowd of 350 students and 180 non-students. The hypnotist knows from previous experience that one half of the students and two third on the non-students are hypnotizable.
A telemarketing firm in a certain city uses a device that dials residential telephone numbers in that city at random. Of the first 100 numbers dialed, 51% are unlisted. This is not surprising because 48% of all residential phone numbers in this ci..
Player 1 has the following set of strategies {A1;A2;A3;A4}; player 2’s set of strategies are {B1;B2;B3;B4}. Use the best-response approach to find all Nash equilibria.
write a program in c that takes n number finite players using gambit format and output is to be all pure strategy nash
Consider the two-period repeated game in which this stage game is played twice and the repeated-game payos are simply the sum of the payos in each of the two periods.
Write down an expression (in terms of w) for the wheel monopolist's profit. Show that for any w> 0, the total profits of the skate and wheel monopolists is lower than the integrated monopolist's profit.
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