Problem 1. Ultimatum Game with Inequality Aversion Players 1 and 2 are in an ultimatum game and will divide a part...
Problem 1. Ultimatum Game with Inequality Aversion Players 1 and 2 are in an ultimatum game and will divide a particular good. 1-1. . Playe r l offers a division ( r, y) with ® and y nonnegative and If Player 2 accepts this offer then Player 1 will receive the fraction r of the good and Player 2 will receive the fraction y . If Player 2 rejects the offer, then both players receive zero. . The value a...
Consider the following bargaining game in which two players are trying to share a cake of size 1. Player 1 offers ri e [o, 1jand player 2 either accepts (Y) of rejects (N): If player 2 accepts player 1 receives a payoff of ri and player 2 receives 1-1. If player 2 rejects, then player 2 moves again to offer 72 [0, 1] to which player 1 responds by either accepting (Y) or rejecting (N): If player 1 accepts player...
13. Consider the following n-player game. Simultaneously and independently, the players each select either X, Y, or Z. The payoffs are defined as follows. Each player who selects X obtains a payoff equal to y, where y is the num- ber of players who select Z. Each player who selects Y obtains a payoff of 2a, where a is the number of players who select X. Each player who selects Z obtains a payoff of 3B, where ß is the...
You play the following bargaining game. Player A moves first and makes Player B an offer for the division of $1000. (For example, Player A could suggest that she take $600 and Player B take $400.) Player B can accept or reject the offer. If he rejects it, the amount of money available drops to $900, and he then makes an offer for the division of this amount. If Player A rejects this offer, the amount of money drops...
Suppose that two players are playing the following game. Player 1 can choose either top or bottom, and Player 2 can choose either left of right. The payoffs are given in the following table Player 2 Left Right top 9,4 2,3 Player 1 Bottom 1,0 3,1 where the number on the left is the payoff to Player 1 and the number on the right is the payoff to player 2. 1) Determine the nash equilibrium of the game. 2) If...
QUESTION 8 Consider a game with two players, players and player 2. Player 1's strategies are up and down, and player 2's strategies are left and right. Suppose that player 1's payoff function is such that for any combination of the players chosen strategies, player 1 always receives a payoff equal to 0. Suppose further that player 2's payoff function is such that no two combinations of the players' chosen strategies ever give player 2 the same payoff Choose the...
1. Suppose we played the following game in the lab. There are two players who have 10 dollars to divide. There are two stages. In stage 1, player A proposes an offer to divide the $10 between herself and player B. Player B can accept or reject the offer. If player B accepts, the offer is implemented. If player B rejects the game moves to stage 2. In stage 2, there is only $8 to divide. Player A proposes a...
Consider a bargaining problem with two agents 1 and 2. There is a prize of $1 to be divided. Each agent has a common discount factor 0 < δ < 1. There are two periods, i.e., t ∈ {0,1}. This is a two period but random symmetric bargaining model. At any date t ∈ {0,1} we toss a fair coin. If it comes out “Head” ( with probability p = 21 ) player 1 is selected. If it comes out...
3. (15 points) Consider a sequential game with two players with three-moves, in which player 1 moves twice: Player 1 chooses Enter or Erit, and if she chooses Exit the game ends with payoffs of 2 to player 2 and 0 to player 1. • Player 2 observes player l's choice and will have a choice between Fight or Help if player 1 chose Enter. Choosing Help ends the game with payoffs of 1 to both players. • Finally, player...
Consider the following extensive-form game with two players, 1 and 2. a). Find the pure-strategy Nash equilibria of the game. [8 Marks] b). Find the pure-strategy subgame-perfect equilibria of the game. [6 Marks] c). Derive the mixed strategy Nash equilibrium of the subgame. If players play this mixed Nash equilibrium in the subgame, would 1 player In or Out at the initial mode? [6 Marks] [Hint: Write down the normal-form of the subgame and derive the mixed Nash equilibrium of...