Consider a bargaining situation (S, d) for two individuals. The disagreement point is d = (0, O). The set of feasible utilities is S = {(u1, u2)} given %3D %3D 6u1? + 3uz? s 72 Determine the Nash bargaining solution fV (S, d). Note: This question is from game theory.
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- Consider the bargaining problem of splitting a pie of size 1 with utility u(x1) = x1 for player 1 and v(x2) = 2x2 − x22 for player 2, where x1 and x2 denote the share of the pie for player 1 and 2 respectively. What is the Nash bargaining solution if the disagreement outcome is any d1 and d2 in S (utility possibility frontier)?Consider a Common Value auction with two bidders who both receive a signal X that is uniformly distributed between 0 and 1. The (common) value V of the good the players are bidding for is the average of the two signals, i.e. V = (X1+X2)/2. Compute the symmetric Nash equilibrium bidding strategy for the second-price sealed-bid auction assuming that players are risk-neutral and have standard selfish preferences. Furthermore, you may assume that the other bidder is following a linear bidding strategy. Make sure to explain your notation and the steps you take to derive the result.Consider a Common Value auction with two bidders who both receive a signal X that is uniformly distributed between 0 and 1. The (common) value V of the good the players are bidding for is the average of the two signals, i.e. V = (X1+X2)/2. the symmetric Nash equilibrium bidding strategy for the second-price sealed-bid auction assuming that players are risk-neutral and have standard selfish preferences. Furthermore, you may assume that the other bidder is following a linear bidding strategy. Make sure to explain your notation and the steps you take to derive the result.
- Which of the following is FALSE for the grim trigger strategy and the infinite horizon repeated Prisoner's Dilemma game illustrated above? A. In the grim trigger strategy profile, if a player chooses D in a period, then both players chooses D forever after that period B. The threshold discount factor for sustaining cooperation under grim trigger strategy depends on the utility numbers in the stage game C. If all utility numbers remain the same but 3 is replaced by 5 in the stage game, then cooperation CANNOT be sustained in this game for all possible values of the discount factor.Consider the bargaining problem of splitting a pie of size 1 with utility u(x1) = x1 for player 1 and v(x2) = 2x2 − x22 for player 2, where x1 and x2 denote the share of the pie for player 1 and 2 respectively. a) Consider the bargaining problem of the two players. Find the utility possibility frontier S. b) What is the Nash bargaining solution for this problem (i.e., on which division of the pie (?₁,?₂) will players agree), if the disagreement outcome (the utilities players obtain in case of disagreement) is d1 = d2 = 0? c) What is the Nash bargaining solution if the disagreement outcome is any d1 and d2 in S?Consider the attached extensive-form game tree, where player 1 moves first, then player 2. The top payoff accrues to player 1, the bottom payoff to player 2. (a) Draw the strategic form for this extensive form game.(b) Find all of the Nash equilibria, including any mixed.(c) Which of these Nash equilibria do you think would be actually played? Why?
- Is the following statement true? "5 bidders with private values uniformly distributed between 0 and 1 enter a 1st price auction. Assuming that everyone is playing the symmetric equilibrium bidding strategy, the optimal bid for a bidder who makes a draw of 0.75 is 0.7."Given the stage game above/below. Suppose that the players play (C,C) in period t = 1; 3; 5; ::: and plays (D,D) in period t = 2; 4; 6; ::. Compute the discounted payoff of each player.Consider a modified Traveler’s Dilemma. In terms of strategy options that the players have and the dollars they earn, it is like the standard Traveler’s Dilemma, but the players do not have endless appetite for money. Up to 100 dollars, each dollar feels like a dollar. But any moneybeyond 100 is psychologically like 100 dollars. Assuming that players are maximizers of ‘psychological’ dollars instead of real dollars, describe all the Nash equilibria of this modified Traveler’s Dilemma.
- Suppose that 5 risk neutral competitors participate in a rent seeking game with a fixed prize of $100. Each player may invest as much as he wishes in the political contest, although those investments have an opportunity cost equal 1. The probability of winning is directly proportional to the candidate’s share of the total rent-seeking investment. What is the profit-maximizing investment by player 1 as a function of the investment by all the others? What is a Nash equilibrium investment by each player in a symmetric game?Consider the “trust game” discussed in class. The first player starts with a $100 endowment and chooses how much to give to the second player. The gift triples in value (i.e. if $20 is given, the second player receives $60). The second player then chooses how much to give back. The first player receives exactly how much is returned (i.e. if $40 is returned, the first player receives $40). The Nash equilibrium of the game is: Group of answer choices: -First player gives $100, second player returns nothing. -First player gives $50, second player returns $50. -First player gives $100, second player returns $300. -There is no Nash equilibrium of this game. -First player gives nothing, second player returns nothing.lease find herewith a payoff matrix. In each cell you find the payoffs of the players associated with a particular strategy combination: The first entry is the payoff of player 1, the second entry is the payoff of player2. Player 2 t1 t2 t3 Player 1 S1 3, 4 1, 0 5, 3 S2 0, 12 8, 12 4, 20 S3 2, 0 2, 11 1, 0 Suppose both players select their strategies (S1, S2 or S3 for player 1 and t1, t2 or t3 for player 2) simultaneously and that the game is played once. In your explanation to the questions below, please do refer to the figures in the matrix. Does player 2 have a dominant strategy? If so, which one? Does player 1 have a dominant strategy? If so, which one? No explanation required. Is there one or more Nash equilibria in the game? If so, which one(s)?