Consider a game with two players, each of whom has two types. The types of player...

Consider a game with two players, each of whom has two types. The types of player 1 are T1 = (a,b). The types of player 2 are T2 = (c,d). Suppose the beliefs of the types are p1(c/a) = p2(a/c) = 0.25 and p1(c/b) = p2(a/d) = 0.75. Is there a common prior? If yes, construct one; if no, prove why not.

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orchestra answered 2 years ago

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...

This game is meant for two or more players. In the game, each player starts out...

This game is meant for two or more players. In the game, each player starts out with 50 points, as each player takes a turn rolling the dice; the amount generated by the dice is subtracted from the player’s points. The first player with exactly one point remaining wins. If a player’s remaining points minus the amount generated by the dice results in a value less than one, then the amount should be added to the player’s points. (As an...

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...

There are two players in the game. Each player can pick any integer number between 1...

There are two players in the game. Each player can pick any integer number between 1 and n. If two numbers are the same then player 1 pays 1 dollar to player 2. If two numbers are different than nothing happens. (a) Prove that there are no equilibria in pure strategies; (b) Prove that in the equilibrium each strategy should be played with a positive probability. (c) Find all NE of the game.

Below is a game between player A and player B. Each player has two possible strategies:...

Below is a game between player A and player B. Each player has two possible strategies: 1 or 2. The payoffs for each combination of strategies between A and B are in the bracket. For example, if A plays 1 and B plays 1, the payoff for A is -3, and the payoff for B is -2. Player B Strategy 1 Strategy 2 Player A Strategy 1 (-3,-2) (10,0) Strategy 2 (0,8) (0,0) How many pure strategy Nash equilibria does...

Below is a game between player A and player B. Each player has two possible strategies:...

Below is a game between player A and player B. Each player has two possible strategies: 1 or 2. The payoffs for each combination of strategies between A and B are in the bracket. For example, if A plays 1 and B plays 1, the payoff for A is 1, and the payoff for B is 0. Player B Strategy 1 Strategy 2 Player A Strategy 1 (1,0) (0,1) Strategy 2 (0,1) (1,0) How many pure strategy Nash equilibria does...

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,...

Coin taking game This game is played between 2 players, player 1 and player 2. There...

Coin taking game This game is played between 2 players, player 1 and player 2. There are two piles of coins. The values of a coin can be any integer. Both players know the values of all coins in both piles. Player 1 makes the first move, and play alternates between the players. A move consists of taking a coin from the top of either of the piles (either player can take from either pile). The game ends when both...

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...

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Consider a game with two players, each of whom has two types. The types of player...

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