Consider a bankruptcy game with two risk neutral players where V =$800,000, C1= $300,000 and C2=$800,000 a) What is the Kalai-Smorodinsky bargaining solution?
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Consider a bankruptcy game with two risk neutral players where V =$800,000, C1= $300,000 and C2=$800,000
a) What is the Kalai-Smorodinsky bargaining solution?
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- Consider a bankruptcy game with two risk-neutral players where V = $600,000, C1 = $400,000, and C2 = $800,000. What is the Nash bargaining solution?Consider a bankruptcy game with two risk neutral players where V =$800,000, C1= $300,000 and C2=$800,000. a) What is the Nash bargaining solution?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?
- Suppose there are N identical firms in a market where the maximum total profit is 12. Assuming an infinite game, if the firms fully cooperate, each would get 12/N in profit. If one firm cheats, it gets the entire market profit for one period, followed by a profit of 1 in all future periods, The discount rate r is .33. How large can N be and still sustain cooperation? That is, how many firms can there be before cooperation breaks down?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."Using only numbers 0 and 1 for payoffs, construct a 4x4 game that has a solution through iterated dominance in themaximal possible number of steps.
- Economics Consider an infinitely repeated game played between two firms with the following payoffs (firm 1 is listed first): · (250, 290) if both firms deviate · (290, 330) if both firms cooperate · (230, 370) if only firm 2 deviates · (350, 270) if only firm 1 deviates a. What probability-adjusted discount factor would ensure that Firm 1 would cooperate in a Nash equilibrium if Firm 2 applied a trigger strategy in the event that Firm 1 deviated? b. What probability-adjusted discount factor would ensure that Firm 2 would cooperate in a Nash equilibrium if Firm 1 applied a trigger strategy in the event that Firm 2 deviated?10) Consider a repeated game in which the following one-shot game between two players is repeated "infinitely." Denote by "d" the discount factor. (Assume both players have the same discount factor.) Player 2 Cooperate Defect Player 1 Cooperate 5, 4 0, 5 Defect 6, 0 1, 1 The two players try to support cooperation by using "grim trigger strategy" as discussed in class. Answer YES or NO to each of the following three questions. (a) Can they support cooperation if the common discount factor, d, is equal to 0.23? (b) Can they support cooperation if the common discount factor, d, is equal to 0.4? (c) Can they support cooperation if the common discount factor, d, is equal to 0.15?A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3. Player B b1 b2 b3 a1 -40,30 70,20 -10,120 Player A a2 40,60 80,80 60,20 a3 -30,40 -50,110 150, -70 Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?
- Explain all will rate what is always true for a pure nash equilibrium of a two-person non zero-sum game A.No player can improve his payoff with a unilateral change of strategy B. it is a Pareto maximum of the payoff matrix C. No player can worsen the payoff of his opponent with a unilateral change of strategy D. It gives worse payoffs to both players than any berge equilibriumCompare the Cournot and Stackleberg games and explain the benefit of being the incumbent. Explain why such a benefit would not exist in a Bertrand game with a first mover.There are two oil producers, Saudi Arabia and Iran (these are countries which we are treating as players in this example). The market price will be $60/barrel if the total volume of sales is 9 million barrels daily, $50 if the total volume of sales is 11 million barrels daily, and $35 if the total volume of sales is 13 million barrels daily. Saudi Arabia has two strategies; either produce 8 million barrels daily or 6 million. Iran has two strategies; either produce 3 million barrels daily or 5 million. Assume for simplicity that marginal cost of production is zero for both countries. Here is the normal form representation of this game (where Saudi Arabia and Iran are players, they can choose strategies over what quantity to produce and they face payoffs in terms of profits). Note that the following paragraph is simply an explanation of this representation of the game. If you are already comfortable with the structure, feel free to skip to the questions below the horizontal line…