GAME THEORY : Hawk - Dove Game

We use the Hawk-Dove game to explore animal territoriality and certain aspects of our sense of rights. Specifically, when considering animal territorial behavior, we question why conflicts over mates, territory, or food are often symbolic, with one animal typically yielding after a brief encounter. This animal is usually the one that arrived at the resource second. In humans, there's a clear parallel in our sense of rights: we believe those who "possess, find, or create an item" have a 'right' to it, and we're willing to argue or fight to defend these rights, for instance, when someone takes something that belongs to us. However, unlike animals, we typically don't simply take things that aren't rightfully ours.

In the simplest version of the game, two players are contesting a resource worth v > 0. Each can be a dove (passive) or a hawk (aggressive). If one is aggressive and the other passive, the aggressive opponent gets the resource. If both are passive, each obtains the resource with equal likelihood. If both are aggressive, both players incur cost c, and each obtains the resource with equal likelihood. We assume c is large relative to the value of the good, c > v/2.

a. Fill in the blanks in the following payoff matrix. Write the payoffs each player gets from each strategy profile. The top number in each quadrant goes to the Player 1. (5 points)

Player 1 Player 2 Hawk Dove Hawk Doveb. Find and explain the Nash equilibrium of this game. (5 points) c. What is the significance of Nash equilibrium in understanding strategic interactions? How does this game apply to real-life scenarios like territorial disputes among insects and human conflicts over resources? (4 Points)