Mr. and Mrs. Ward typically vote oppositely In elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote.

- Individuals 1 and 2 are forming a company. The value of their relationship depends on the effort that each expends. Suppose that individual i's utility from the relationship is x² + x; − xixj, where x¿ is individual i 's effort and x ; is the effort of the other person (i = 1, 2). Assume x1, x2 ≥ 0. Which statement is true? There is a Nash equilibrium in which each player chooses effort level k > 0. This equilibrium is Pareto efficient. There is no mixed-strategy Nash equilibrium. There is a unique Nash equilibrium in which each player chooses no effort x¿ = x; = 0. The set of Nash equilibria in this game is finite. There is a Nash equilibrium in which xi = 0 and x ; = 1| =

To Vote or Not to Vote Mr. and Mrs. Ward typically vote oppositely in elections and so their votes “cancel each other out.” They each gain two units of utility from a vote for their positions (and lose two units of utility from a vote against their positions). However, the bother of actually voting costs each one unit of utility. Diagram a game in which they choose whether to vote or not to vote. Mrs. Ward vote. don't vote Mr. Ward Vote. -1, -1. 1, -2 don't vote. -2, 1. 0,0?

Consider two players, designated by i = 1,2, involved in a dynamic bargaining over a perfectly divisible surplus of size 1. At the beginning of the interaction (at timet 1), player 1 chooses x1 in [0, 1]. Player 2 observes this offer and decides whether or not to accept it. If player 2 accepts this offer, the game ends and the utilities of player 1 and 2 equal x1 and 1- x1, respectively. If player 2 does not accept this offer, the game goes into the second round with a probability of \pi = 2|1/2-x11, while with probability 1 -\ pi the game ends and both players get a payoff of 0. If the game reaches the second round, t = 2, player 2 makes a counter-offer x2 in [0, 1] observing the whole past. Player 1 sees this offer and decides whether or not to accept it. If player 1 accepts x2, then the game ends and player 1 gets a payoff of x2 and player 2 a utility of 1 - x2. Both players get a payoff of zero when player 1 rejects player 2's offer x2 and the game ends. We assume that the game is…