Exam 4: Game Theory: Games Between Three or More Players

You are at a sports memorabilia convention and you are the last of 100 people chosen to have your picture taken with either Joe Montana or Nolan Ryan. Your payoff depends on how quickly you can have your picture taken, as you have many other things you want to see at the convention. You have no preference with whom you have your picture taken, and since you were the last chosen you will be the last person in line to get your picture taken with the sports legend you select. Draw a graph that represents this 100 player game. Let the horizontal axis represent the number of people who choose to have their picture taken with Joe Montana.

Figure 4.2: -Refer to Figure 4.2. Use best-response analysis to answer the following question. If Ferris's choice placed us in the bowling alley, his best response, depending on the row and column Sloane and Cameron find themselves in, would include choosing all of the following cells except the one located at the ________ section of the appropriate payoff matrix.

Figure 4.2: -Refer to Figure 4.2. The dominant strategy for Ferris is to

Figure 4.1 : -Refer to Figure 4.1. The dominant strategy for Theodore is

Figure 4.5: You and your 9 classmates each have a chance to earn extra points on a test by selecting either the solid downsloping line or the dashed upsloping line, and the points awarded to each student will be based on the choices made by each member of the class. -Refer to Figure 4.5. In which of the following cases will you be rewarded with the most extra points?

Figure 4.1 : -Refer to Figure 4.1. Simon is the ________ player.

Figure 4.2: -Refer to Figure 4.2. Use best-response analysis to answer the following question. If Ferris's choice placed us in the movie theater, Cameron's best response, depending on the row he finds himself in, would include choosing all of the following cells except the one located at the ________ section of the appropriate payoff matrix.

In a multiplayer game of chicken, natural incentives tend to push the outcome toward the point where payoffs to the two strategies are identical.

Figure 4.1 : -Refer to Figure 4.1. Alvin's available strategies include

Figure 4.8: You and 100 of your closest friends all decide to spend the day playing Frisbee. There are two places in town that have enough space for all of you to play Frisbee: the local beach, or the local park which is across the street from the beach. The more people who play, the more fun everyone has, and your payoff depends on the number of people that show up to the same location as you. Specifically, you will receive 5 points for each person (besides yourself) at the same location as you. Assume that everyone else's payoff is determined in the same way. The payoffs for this game are shown in the above figure. -Refer to Figure 4.8. The game described in the payoff graph has the characteristics of a(n) ________ game.

Figure 4.8: You and 100 of your closest friends all decide to spend the day playing Frisbee. There are two places in town that have enough space for all of you to play Frisbee: the local beach, or the local park which is across the street from the beach. The more people who play, the more fun everyone has, and your payoff depends on the number of people that show up to the same location as you. Specifically, you will receive 5 points for each person (besides yourself) at the same location as you. Assume that everyone else's payoff is determined in the same way. The payoffs for this game are shown in the above figure. -Refer to Figure 4.8. If half of your friends go to the beach and half go to the park, and you decide to go to the park, then

Figure 4.8: You and 100 of your closest friends all decide to spend the day playing Frisbee. There are two places in town that have enough space for all of you to play Frisbee: the local beach, or the local park which is across the street from the beach. The more people who play, the more fun everyone has, and your payoff depends on the number of people that show up to the same location as you. Specifically, you will receive 5 points for each person (besides yourself) at the same location as you. Assume that everyone else's payoff is determined in the same way. The payoffs for this game are shown in the above figure. -Refer to Figure 4.8. If half of your friends go to the beach and half go to the park, you will receive a payoff of ________ if you go to the beach.

Assume there are two competing social network sites, Mugshot and Graybar, and each grow in value as more people use them. Mugshot has been around longer and has the most users, but people tend to agree that Graybar is a better site, so the equilibrium where everyone uses Graybar is preferred to the equilibrium where everyone uses Mugshot. This situation describes a multiplayer

In a three-player game, if a player's best choice depends on the choices made by the other two players, then the player does not have a dominant strategy.