Homework 10. Due at the beginning of you tutorial on week 12 1. Stag hunt. Two guys go hunting for food, and each can choose to hunt stag or hunt hares. Only if both players hunt stag will they succeed; if only one player hunts stag, he will fail. On the other hand, the players are able to successfully hunt hares on their own—but hares are much smaller, and so have a smaller payoff than catching (and sharing) a stag. The payoff matrix therefore looks like the following: if both go for Stag – the payoff of each is 8; if Player 1 goes for Stag, Player 2 for Hare – payoffs are 0 and 2, if Player 1 goes for Hare, Player 2 for Stag – payoffs are 2 and 0, if both go for Hares – 2 and 2. Draw the game as a table. What are the Nash equilibria of this game? How does this game differ from a prisoner’s dilemma, and how can participants achieve the optimal (both hunt Stag) outcome? 2. Chicken. In the movies about the 60th in USA the following scene sometimes occurs. Two young lads position their cars on the narrow road facing each other and remove the brakes. Then they start racing towards each other. The crowd of the equally young friends cheers. At some point the players simultaneously either have to keep on going or swerve into the ditch. Model and draw this is a game of simultaneous actions. The payoffs that you choose should reflect the following rankings of outcomes. If both lads go straight they both die which is the worst for each. If one of the players swerves (no matter what the other does) the outcome for him is public humiliation which is bad but not as bad as death. If player 1 goes straight and his opponent swerves this is the best outcome for player 1. If the roles of the players are reversed the payoffs are reversed. What are the Nash equilibria of this game? 3. Another Chicken. Suppose before racing player 1 can publicly remove his steering wheel and throw it away. If he does not remove the wheel the game continues as the simultaneous actions games of chicken…