In Los Angeles there are times when young people are arrested for playing Rebel without A Cause a.k.a The Game of Chicken. The game consists of driving cars towards each other on a street. Before impact, drivers must simultaneously choose whether to swerve the car, or continue head-on. Suppose two youngsters: Amy and Bob, borrowed their parents' cars and played a variant of this game. If both swerve (S), they are chicken, and both get no respect from peers, but suffer no losses, thus both get a payoff of 0. If one drives head-on (H) and the other plays S, then the former gains all the respect, which is a payoff of w, and the chicken gets no respect, which gives payoff of 0. In this case they suffer no additional losses. Finally, if both play H, they "split" the respect (since respect is considered to be relative...), but an accident is bound to happen and their parents will impose upon them a personal loss of k, so the payoff to each kid is w/2 k. a) Represent this game in Normal Form for k = 0. What are the Nash equilibria in this game? b) Suppose the punishment, k, depends on the type of parents they have. For each kid, parents can be either strict or lenient with equal probability, and the draws are independent. If they are strict, they ground their children for a month and we denote this by the cost being k = G. If they are lenient, then they lecture about why this behavior is unacceptable, and we denote this by the cost being k = L. Each kid knows the type of his parents, but does not know the type of the opponent's parents. The distribution of types is common knowledge. Draw the tree that represents this game in extensive form; be careful when labeling and repre- senting information sets. What are the pure strategies for each player? Draw the matrix that represents the normal form of this game of incomplete information. Now assume that w = 8, G = 16, and L = 0. Find all Nash equilibria and solve for the Bayesian Nash equilibria of this game. If all parents were strict, the children would be better off. Is this right? (Your answer should be supported with an equilibrium argument).