3. Player 1 and Player 2 are going to play the following stage game twice: Top Bottom Left 4,3 0,0 Player 2 Middle 0,0 2,1 Right 1,4 0,0 Player 1 There is no discounting in this problem and so a player's payoff in this repeated game is the sum of her payoffs in the two plays of the stage game. (a) Find the Nash equilibria of the stage game. Is (Top, Left) a Nash of the stage game? (b) Find a subgame perfect Nash equilibrium of the repeated game where the first time they play the stage game Player 1 chooses Top and Player 2 chooses Left.

38. Consider the following game. There are ten churches in town: nine are Catholic and one is Eastern Orthodox. All churches conduct their divine services at 10am on Sunday morning. You and your friend, without communication, agree to meet at a church service. If you fail to meet at the same church, then you are sad and become a Doomer. What is this game's focal point? Remember that you cannot communicate about this. (A) You meet at any of the Catholic churches. (B) You meet at any of the churches – denomination does not matter. We're all the same bro. (C) You meet at the Orthodox church. (D) There is no focal point. 39. Consider a fractional-reserve banking system in which an initial deposit of $1,000 can generate up to $4,000 in money. What is the reserve ratio? (A) 4 percent. (B) 5 percent. (C) 25 percent. (D) 75 percent.

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7. Solving for dominant strategies and the Nash equilibrium Suppose Carlos and Deborah are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 5 and Deborah will receive a payoff of 1. Carlos Deborah Left Left 4,4 Right 2,4 Right 6,7 5,1 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses and Deborah chooses

For the game in FIGURE 7.6, derive players’ best-reply functions, plot them as shown in Figure 7.5, and find the Nash equilibrium.

9. For the payoff matrix below, consider a sequential version of the game in which Player 2 moves first and then Player 1 moves second. Which of the following is not a correct statement? Player 1 Top Center Bottom Left 1,2 5,1 6,0 Player 2 Middle 7,1 11,2 -4,3 Right 10,4 1,0 8,5 The subgame perfect payoffs coincide with those of a Nash equilibrium b. Depending on Player 2's move, Player 1 will sometimes optimally choose Bottom c. Player 2 will choose Right in the subgame perfect equilibrium d. Player 2 would be willing to pay a positive $ amount to move first rather than second e. Player 1 would be willing to pay a larger $ amount than Player 2 to move first

Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.

QUESTION 3 Up Down In the game above, what is/are the sub-game perfect Nash equilibrium? Ⓒ (up,up) (up,down) Player 1 (down, up) (down, down) No equilibrium exists Up Down Up Down Player 2 P1 gets $25 P2 gets $25 P1 gets $7 P2 gets $30 P1 gets $13 P2 gets $9 P1 gets $8 P2 gets $6

2. For the following payoff matrix find all of the mixed strategy Nash equilibria (check for dominated strategies to eliminate). Player 1 X Y Z A 1,3 4,1 2,3 Player 2 B 2,4 3,1 0,0 C 2,3 5,0 4,2