Question

In: Statistics and Probability

Consider the following game: 3 players can contribute or not to a public good. For the...

  1. Consider the following game: 3 players can contribute or not to a public good. For the public good to be successfully created, 2 contributions are necessary (a third contribution would not add anything to the public good).
    These are the payoffs each of the three players assign to all possible outcomes:

    3: I didn't contribute but the public good was created anyway 2: I did contribute and the public good was created
    1: I didn't contribute and the public good was not created
    0: I did contribute and the public good was not created

    The decisions are made sequentially: player 1 moves, then player 2, then player 3.

    (a) Find the set of pure strategy Nash equilibria of this game if it is played as a simultaneous move game.

    (b) Find the set of subgame perfect Nash equilibria of this game when it is played sequentially.

Solutions

Expert Solution


Related Solutions

1. Consider the following game. There are two piles of matches and two players. The game...
1. Consider the following game. There are two piles of matches and two players. The game starts with Player 1 and thereafter the players take turns. When it is a player's turn, she can remove any number of matches from either pile. Each player is required to remove some number of matches if either pile has matches remaining, and can only remove matches from one pile at a time. Whichever player removes the last match wins the game. Winning gives...
Consider a following zero-sum game of two players a) Reduce the initial game to a 2x2...
Consider a following zero-sum game of two players a) Reduce the initial game to a 2x2 game. Eliminate only strictly dominated strategies. In the obtained 2x2 game name Player 1’s (Row player’s) strategies “Up” and “Down” and Player 2’s (Column player’s) strategies “Left” and “Right”. b) Find all Nash equilibria of the 2x2 game (both in pure and mixed strategies) ALL ANSWERS MUST BE EXPLAINED. 2 0 1 -1 1 0 1 2 3 1 2 0
Consider a following zero-sum game of two players a) Reduce the initial game to a 2x2...
Consider a following zero-sum game of two players a) Reduce the initial game to a 2x2 game. Eliminate only strictly dominated strategies. In the obtained 2x2 game name Player 1’s (Row player’s) strategies “Up” and “Down” and Player 2’s (Column player’s) strategies “Left” and “Right”. b) Find all Nash equilibria of the 2x2 game (both in pure and mixed strategies) ALL ANSWERS MUST BE EXPLAINED. 2          0          1          -1 1          0          1          2 3...
•Suppose two consumers can choose to contribute or free-ride on a public good that can clean...
•Suppose two consumers can choose to contribute or free-ride on a public good that can clean up the air. •To monetarize the benefit, if a consumer contributes to the public good, it generates 50% of the amount the consumer pay. •For example, if $100 is contributed, the consumer can get back a benefit of $150. •As the public good is non-exclusive, the benefit is evenly share between the two consumers. •Form a game matrix and determine the Nash.
Question 4: Jar Game Consider the following game: Players: 2 - We designate player #1 to...
Question 4: Jar Game Consider the following game: Players: 2 - We designate player #1 to be the one that starts with the jar. Actions: - Each round at the same time both players deposit between 1 to 4 pennies into the jar. - Then both players are able to count the pennies in the jar. - If there are 21 or more pennies, the person with the jar is the winner. - If there are 20 or less pennies,...
Consider a game between a parent and a child. The child can choose to be good...
Consider a game between a parent and a child. The child can choose to be good (G) or bad (B); the parent can punish the child (P) or not (N). The child get enjoyment worth a 1 from bad behavior, but hurt worth -2 from punishment. Thus, a child who behaves badly and is punished gets 1 - 2 = -1; and so on. The parents gets -2 from the child's bad behavior and -1 from inflicting punishment. (a) Set...
Consider the Stage Game below, and consider the repeated game where players play twice (T =...
Consider the Stage Game below, and consider the repeated game where players play twice (T = 2). Payoffs for each agent are simply period one plus period two payoffs. L C R T 6,6 0,7 1,2 M 7,0 1,1 2,0 B 2,1 0,1 3,3 (a) Do any strategies dominate any other? (b) What are the two NE of the Stage Game? What is the difference between the two? (c) Call the TL strategy profile (1 plays T, 2 plays L)...
5. Consider the following games played between two players, A and B.   Game 1: A and...
5. Consider the following games played between two players, A and B.   Game 1: A and B have reached a verbal agreement: A would deliver a case of beer to B, and B would deliver a bag of beer nuts to A. Now, each player needs to take an action: keep the promise (to deliver the goods), break the promise. If both keep their promises, then each player gets a payoff of 5; if both break their promises, then each...
Consider the following game, which might model the “Split-or-Steal” game show. Two players simultaneously choose whether...
Consider the following game, which might model the “Split-or-Steal” game show. Two players simultaneously choose whether to split or steal. If they each choose to split, they each get $50. If one chooses steal and the other chooses split, then the stealer gets $100 and the splitter gets $0. If both choose steal, they each get $0. (a) Assume the players care both about their own monetary earnings and the amount of inequality between their earnings: for a pair of...
Question 3 Consider a team of eleven (11) soccer players, all of whom are equally good...
Question 3 Consider a team of eleven (11) soccer players, all of whom are equally good players and can play any position. (a) Suppose that the team has just finished regulation time for a play-off game and the score is tied with the other team. The coach has to select five players for penalty kicks to decide which team wins the game. Since each player takes penalty kicks differently, the order in which the players are arranged for the penalty...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT