Males of a certain species frequently come into conict with other males over the
ID: 1126764 • Letter: M
Question
Males of a certain species frequently come into conict with other males over the opportunity to mate with females. If a male runs into a situation of conict, he has two alternative “strategies.” A male can play “Hawk” in which case he will ght the other male until he either wins or is badly hurt. Or he can play “Dove,” in which case he makes a display of bravery but retreats if his opponent starts to ght. If an animal plays Hawk and meets another male who is playing Hawk, they both are seriously injured in battle. If he is playing Hawk and meets an animal who is playing Dove, the Hawk gets to mate with the female and the Dove slinks o to celibate contemplation. If an animal is playing Dove and meets another Dove, they both strut around for a while. Eventually the female either chooses one of them or gets bored and wanders o. The expected payos to each of two males in a single encounter depend on which strategy each adopts. These payos are depicted in the box below.
Game info
Players Animal A, Animal B
Srats: Hawk, Dove for each
Payoffs: HH -5,-5 HD 10,0 DH 0,10 DD 4,4
(a) Now while wandering through the forest, a male will encounter many conict situations of this type. Suppose that he cannot tell in advance whether another animal that he meets will behave like a Hawk or like a Dove. The payo to adopting either strategy oneself depends on the proportion of the other guys that is Hawks and the proportion that is Doves. For example, suppose all of the other males in the forest act like Doves. What is the payoff of a Hawk? A Dove?
(b) If strategies that are more protable tend to be chosen over strategies that are less protable, explain why there cannot be an equilibrium in which all males act like Doves.
(c) If all the other males acted like Hawks, then what is the payoff of a male who adopted the Hawk strategy?
(d) If instead, this male adopted the Dove strategy, then what is his payoff?
(e) Explain why there could not be an equilibrium where all of the animals acted like Hawks.
(f) Suppose that the fraction of a large male population that chooses the Hawk strategy is p. Then if one acts like a Hawk, the fraction of one’s encounters in which he meets another Hawk is about p and the fraction of one’s encounters in which he meets a Dove is about 1p. Therefore the average payo to being a Hawk when the fraction of Hawks in the population is p, must be ?
(g) Similarly, if one acts like a Dove, the probability of meeting a Hawk is about p and the probability of meeting another Dove is about (1 p). Therefore the average payo to being a Dove when the proportion of Hawks in the population is p will be?
(h) Write an equation that states that when the proportion of the population that acts like Hawks is p, the payo to Hawks is the same as the payos to Doves.
(i) Solve this equation for the value of p such that at this value Hawks do exactly as well as Doves.
(j) On a graph, use blue ink to graph the average payo to the strategy Dove when the proportion of the male population who are Hawks is p. Use red ink to graph the average payo to the strategy, Hawk, when the proportion of the male population who are Hawks is p. Label the equilibrium proportion in your diagram by E.
(k) If the proportion of Hawks is slightly greater than E, which strategy does better?
(l) If the proportion of Hawks is slightly less than E, which strategy does better?
(m) If the more protable strategy tends to be adopted more frequently in future plays, then if the strategy proportions are out of equilibrium, will changes tend to move the proportions back toward equilibrium or further away from equilibrium?
Explanation / Answer
(a) Now while wandering through the forest, a male will encounter many conict situations of this type. Suppose that he cannot tell in advance whether another animal that he meets will behave like a Hawk or like a Dove. The payo to adopting either strategy oneself depends on the proportion of the other guys that is Hawks and the proportion that is Doves. For example, suppose all of the other males in the forest act like Doves. What is the payoff of a Hawk? A Dove?
Ans:- i) suppose all of the other males in the forest act like Doves, If a male behave like Hawk then he find his rivalry always chnage his mind and would therefore enjoy payoff 10 in every encounter. and If a male behave like a Dove then other males also behave like dove so avergare payoff is 4
(b) If strategies that are more protable tend to be chosen over strategies that are less protable, explain why there cannot be an equilibrium in which all males act like Doves.
Ans:- If a person know that he is meeting a Dove then definitely it pays to Hawk . Thatswhy there can not be an equilibrium in which all males act like doves.
(c) If all the other males acted like Hawks, then what is the payoff of a male who adopted the Hawk strategy?
Ans:- He definitely sure to encounter another Hawk and get payoff of -5
(d) If instead, this male adopted the Dove strategy, then what is his payoff?
Ans:- If this male adopted dove stratgey then again he sure to encounter a Hawk and payoff will be 0
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.