1. Consider the following battle-of-sex game played by husband and wife. Both of them choose whether to watch a football game or a movie in the weekend. Choices are made independently and simultaneously. Payoffs are presented below. (30 points) Wife Football Movie Husband Football -u- Mom 59 (1) Find all pure strategy Nash equilibria. (2) Suppose Husband chooses Football with probability '? , Wife chooses Football with probability '2. Determine Husband's best response to any choice of 'P by Wife, and Wife's best response to any choice of ? by Husband. Find all mixed strategy Nash equilibrium. (3) Show these reaction functions and all of the equilibria on a graph. A monopolist is facing a threat of entry by another rm. First the entrant decides whether or not to enter, and then the incumbent decides whether or not to cut its price (ght) in response. If the entrant decides to stay out, it gets a payoff of 0 and the incumbent gets a payoff of 10 as a monopolist. If the entrant decides to enter the market, two rms' payoff depends on whether the incumbent ghts or not. If the incumbent ghts, then both rms end up with a negative payoff -5. If the incumbent decides not to fight, they divide the market prot and both get a payoff of 5. Draw the extensive form of the game and solve the backward induction outcome. (20 points) Consider the following public goods game. A group has 4 members. Each group member 1' is endowed with $10 and needs to allocate 3; xi (3': is an integer between 0 and 10) out of the $10 to a public account and $(10 x I.) to a private account. The total amount in the public account is the summation of the money allocated by all group members. Each dollar 'om the public account gives 50 cents as a return to each group member, and each