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- Consider the extensive form game portrayed below. The top number at aterminal node is player 1’s payoff, the middle number is player 2’s payoff,and the bottom number is player 3’s payoff.a. Derive the strategy set for each player. (Note: If you do not want to listall of the strategies, you can provide a general description of a player’sstrategy, give an example, and state how many strategies are in thestrategy set.)b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it isnot a SPNE.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.(a) Assuming that each fishery chooses fi ∈ (0,F), to maximize its payoff function, derive the players’ best response functions and find a Nash equilibrium. (b) Is the equilibrium you found in (a) unique or not? What are equilibrium payoffs? (c) Suppose that a benevolent social planner wants maximize the util- ity of both fisheries. In other words, the social planner solves the following problem: max w(f1, f2) = u1(f1, f2) + u2(f1, f2) (f1 ,f2 )= 2ln(f1)+2ln(f2)+2ln(F −f1 −f2). Find the social planner’s solution. (d) What are the fisheries’ payoffs if the quantities of fish they catch are solutions to the social planner’s problem? What can you say about the Nash equilibrium quantities of fish being caught as compared to the social planner’s solution? (e) If fishery j decides to follow the recommendation of the social planner, how much fish will firm i catch?
- In a situation where you have a strong neighbor, as a country, do conventional weapons offer an effective deterrence? Explain through different models available within the game theory. Establish the rules of the game and find the equlibrium through the game theory models.A occurs if all players in a game play their best strategies given what their competitors do.Are the following true or false (justify answer: just T or F will not suffice): A) In a sequential game, the leader always receives a higher payoff due to his/her knowledge of the rationality of the second player. B) Games of complete information are a sub-type of games of perfect information. C) If a game with a more than one unique Nash Equilibrium is played finitely many times, the only type of sub-game perfect equilibriums is some sequence of Nash equilibriums played at every stage.
- Q) Let x and y be real numbers and consider the game in Table 1. Using the concepts of dominance, best response and rationalizability, for which values of x and y is this game dominance solvable? Make sure to clearly explain the concepts used, and your reasoning. Hint: There are two possible cases which do not involve the same NE. i attached image. solve it early i upvote definetlyIndustrial Organziation game - Business Strategy & Game theory Consider a game with competitive for market-share in a large region (a country or city). Firm 1 initially makes a decision to either compete in the Eastern (E) or Western (W) part of a region, or to opt out entirely (O). Once this decision has been made, Firm 1 and Firm 2 (who is already present in the region) simultaneously make a decision to be aggressive (A) or passive (P) in the region. Denote actions in the Eastern region without a prime (i.e. A and P) and those in the Western region with a prime (i.e. A` and P`). We'll make the following assumptions about these firms - If Firm 1 opts out, its payoff is 8 and the payoff for Firm 2 is 12 If Firm 1 ENTERS the Eastern region both firms receive 9 if both are AGGRESSIVE both firms receive 6 if both are PASSIVE if one plays AGGRESSIVE and the other plays PASSIVE, the aggresive firm gets 5 and the passive firm gets 2 If Firm 1 ENTERS the Western region…Paramter y = 0 What is the highest payoff any player can receive in any subgame perfect Nashequilibrium of the repeated game?
- 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?Answer all questions, show all working. Consider the following game in strategic or normal form. A2 B2 C2 A1 1,0 1,2 -2,1 B1 6,2 0,3 2,3 C1 2,2 -2,1 2,3 Use the iterative elimination of strictly dominated strategies to reduce the game as much as possible. What is the set of rationalizable strategies for each player? What is/are Nash equilibrium(s) in this game? Explain the differences between cooperative and non- cooperative games. What are the fundamental hypotheses about the behavior of the persons in Game theory?Cooperation in a Finite Game We have seen that if we play the Prisoners' dilemma with finite repetition, there will be no cooperation in the subgame-perfect equilibrium. There are other games, however, when cooperation can be enforced for at least some time in a finite repetition as well. Give an example with explanation.