Get Solutions for: Imagine that two players are competing over a valuable resource.

a. Oops! The payoffs are missing. You??ll have to fill them in. Remember, if there??s a fight, there is a 50% chance of winning 60 but also a 50% of losing the fight, which has payoff ??100. What??s the expected outcome? If both animals choose Dove, assume that they peacefully split the resource. If one is a Hawk and the other is the Dove, the Hawk gets the resource, and the Dove receives nothing . . .
b. Explain why (Hawk, Dove) and (Dove, Hawk) are both Nash equilibriums.
c. The Hawk-Dove game is often used to discuss international relations. Can you explain why a country might like to be perceived as a Hawk? What are the dangers of being a Hawk? What are the dangers of being a Dove?
d. Biologists also use game theory to understand animal behavior, but they interpret the strategies a little differently. Instead of allowing an animal to choose a strategy, they assume that x percent of animals in a population will always play Hawk and 100 ?? x percent of animals in a population will always play Dove, and they also assume that animals will meet randomly.
Biologists argue that if Hawk has an expected higher payoff than Dove, then Hawks will outcompete Doves so that over time, evolution will increase the percentage of animals playing Hawk. Similarly, if Dove has a higher payoff, then over time, evolution will increase the percentage of animals playing Dove.
Can you find a strategy that is evolutionarily stable; that is, can you find a strategy where the percentages of animals playing Hawk and Dove are stable over time?
Here are two hints: Let x be the percentage of animals playing Hawk. If 0% of animals play Hawk (x = 0%) and thus all play Dove, is that evolutionarily stable? If all animals play Hawk (x = 100%), is that evolutionarily stable?