Use the generalized Nash bargaining solution to show that an individual's share increase with his power, but deceases with the power of his rival.
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Bargaining lecture slides
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- Does each individual in a prisoners dilemma benefit more from cooperation or from pursuing self-interest? Explain briefly.parameter z= 1 In the unique subgame perfect Nash equilibrium, what is the sum of the payoffs tothe two players?Game theory: Consider a collective action game with thirty individuals (N = 30). When the number of participants in the joint project is n, each individual, including shirkers, receives a benefit of B(n) = 18n and each participant incurs a cost of C(n) = 32 − 2n. 1. Find all of the Nash equilibria, both stable and unstable ones. 2. Find the socially optimal outcome. 3. Check if any of the Nash equilibria is socially optimal. Explain your answer.
- Consider a game where each player picks a number from 0 to 60. The guess that is closest to half of the average of the chosen numbers wins a prize. If several people are equally close, then they share the prize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30;(C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization.Q:1 Jhon have server and many clients or bidders bidders who are bidding with their resources (datasize,bandwidth) and price they want to sell their resources. Jhon is using first price sealed bid auction here. Jhon need to select winners. Please apply Nash equilibrium strategy for clients to maximize the expected profit and expected utility theory to give guidance to the aggregator to obtain the expected resources from clients. Note: related material is attached in pictures.In the attached table determine, for each player, whether any action is strictly or weakly dominated. Justify youranswer. Find the Nash equilibria of the game and determine whether any equilibrium is strict.
- on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.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.TRADE. Consider a bilateral trade model with two-sided asymmetric information. The buyer's value is private information to the buyer, vB and the seller's value vs is private information to the seller. (a)Derive the linear Bayes Nash Equilibrium in a double auction. (b)Assume that the seller can credibly disclose their valuae. What is your intuition, would he want to commit to such transparency?
- Jacob wants to rent out car from James. Jacob has a big passion for cars and enjoys speeding, so much that he often gets fined. Jacob receives £400 in utility from being able to speed on the road whereas James would like to avoid getting fined. If Jacob spreads don the road, it will cost James £700. Thus, James is considering charging Jacob a fine deposit of £700. a) Draw the extensive form of this principal-agent problem and use backward induction to solve for the Nash Equilibrium. b) Explain why this situation could be considered a principal-agent problemMicro Nash game theory Show that if in a game G, the sets of actions (A i) i in N are compact, and the payment functions (u i) i in N are continuous, then for all i in N, the application of Best response has a closed graph. Conclude that the application of best response has a closed graph.Please no written by hand and no image (Bertrand's duopoly game with discrete prices) Consider the variant of the example of Bertrand's duopoly game in this section in which each firm is restricted to choose a price that is an integral number of cents. Take the monetary unit to be a cent, and assume that c is an integer and a>c+!. Is (c,c) a nash equilibrium of this game? Is there any other nash equilibrium?
