This is a sequential game with two players A and B. In this game a dime...

This is a sequential game with two players A and B. In this game a dime is put on the table. A can take it or pass. If A takes a dime, the game ends; if A passes, then B can take 2 dimes or pass; if B takes 2 dimes, the game ends; if B passes, then A can take 3 dimes or pass; and so on until a choice of a dollar. This process is shown in the game tree below. The rollback equilibrium of this game is that B is sure to take the dollar at last round, so A should take 90¢ at the penultimate stage, and so on. Thus, A should take the first dime and end the game.

True

False

Expert Solution

Answer - True

Figure shows the tree for this game. Because of the appearence of the tree, this type of game is often called as Centipede game. Player B is sure to take the dollar at the last stage; so A should take the 99 cents at the penultimate stage, and so on. Thus, A should take the very first dime and end the game.

Note: A will get 99 cents at the penultimate stage, not 90 cents (mentioned in the question)

Rahul Sunny answered 2 years ago

This question is about the sequential moves Stag Hunt game. There are two players. Player 1...

This question is about the sequential moves Stag Hunt game. There are two players. Player 1 moves first, player 2 observes player 1’s move, and then player 2 moves. Players get 10 jollies each if they both choose Stag; 5 jollies if they choose Hare; and 0 jollies if they choose Stag but the other player does not. What is the set of (pure) strategies for player 1? What is the set of (pure) strategies for player 2? Explain why...

A sequential game with two-players 1 and 2, where player 1 has the first move advantage....

A sequential game with two-players 1 and 2, where player 1 has the first move advantage. Each player has two strategies, A and B. If both players choose A, each gets a payoff of 2. Both choose B, each gets a payoff of 3. For player 1 choose A and player 2 choose B, player 1 gets 4, and player 2 gets 1. If player 1 chooses B and player 2 choose A, player 1 gets a payoff of 1,...

Two players A and B play a game of dice . They roll a pair of...

Two players A and B play a game of dice . They roll a pair of dice alternately . The player who rolls 7 first wins . If A starts then find the probability of B winning the game ?

Consider this childhood game with two players, A and B. There are 11 lit candles. The...

Consider this childhood game with two players, A and B. There are 11 lit candles. The players take turns blowing out 1, 2, or 3 candles, with A going first. The player that blows out the last candle wins. It is possible to solve this game using backwards induction. The numbers below may help you to organize your thoughts. 1 2 3 4 5 6 7 8 9 10 11 a. In equilibrium, which player wins the game? b. On...

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...

Two players A and B play a dice game with a 6-face fair dice. Player A...

Two players A and B play a dice game with a 6-face fair dice. Player A is only allowed to roll the dice once. Player B is allowed to roll the dice maximally twice (that is, Player B can decide whether or not she or he would roll the dice again after seeing the value of the first roll). If the player with the larger final value of the dice wins, what is the maximal probability for Player B to...

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...

Two players (player A and player B) are playing a game against each other repeatedly until...

Two players (player A and player B) are playing a game against each other repeatedly until one is bankrupt. When a player wins a game they take $1 from the other player. All plays of the game are independent and identical. Suppose player A starts with $6 and player B starts with $6. If player A wins a game with probability 0.5, what is the probability the game ends (someone loses all their money) on exactly the 10th play of...

(10 marks) Two players (player A and player B) are playing a game against each other...

Two players (player A and player B) are playing a game against each other repeatedly until one is bankrupt. When a player wins a game they take $1 from the other player. All plays of the game are independent and identical. a) Suppose player A starts with $2 and player B starts with $1. If player A wins a game with probability p, what is the probability that player A wins all the money? b) Suppose player A starts with...

Consider the following game that has two players. Player A has three actions, and player B...

Consider the following game that has two players. Player A has three actions, and player B has three actions. Player A can either play Top, Middle or Bottom, whereas player B can play Left, Middle or Right. The payoffs are shown in the following matrix. Notice that a payoff to player A has been omitted (denoted by x). Player B Left Middle Right Top (-1,1) (0,3) (1,10) Middle (2,0) (-2,-2) (-1,-1) Bottom (x,-1) (1,2) (3,2) (player A) Both players...

Question