Consider the following two-person zero-sum game: 3-2 5-1 1 4 42 5 11 3 If the row player uses the mixed strategy (3,2,0), determine an optimal pure counter-strategy for the column player.
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- This is a two-player, simultaneous one-move game represented as a game table (normal form). What is the pure strategy Nash equilibrium outcome if there is one? Is this a socially optimal outcome? If not, which outcome is preferred?33. When neither player has a dominant strategy, A) game theory will not provide information.B) no Nash-Equilibrium exists.C) at least one Nash-Equilibrium exists.D) the game cannot be analyzed.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?
- 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?Solve the matrix game. -2 3 1 1 -1 -2 -3 -3 2 The optimal strategy for the row player is P*=______ (Type an integer or simplified fraction for each matrix element.) The optimal strategy for the column player is Q*=_______ (Type an integer or simplified fraction for each matrix element.) The value for the game is v=__________ (Type an integer or a simplified fraction.)Which one of the following statements is incorrect? A. A finite static game with complete information may not have a pure strategy Nash equilibrium. B. For dynamic games with complete information, not all subgame perfect Nash equilibrium points can be found by backward induction. C. A finite static game with complete information cannot have an extensive form representation. D. A finite dynamic game with complete information may also have a normal form representation.
- A game in which the players will not negotiate is a O A. zero-sum game. • B. non-cooperative game. C. cooperative game. • D. negative-sum game.This activity has 4 theorical and practical exercises for which you will have to describe the representation of each proposed game and its solutions.1. Consider the following game in strategic or normal form.A2 B2 C2A1 1,0 1,2 -2,1B1 6,2 0,3 2,3C1 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? Microeconomics (code ECO2023)Actividades 2© MIU City University Miami ▸ 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?2. Two hunters may choose, individually and simultaneously, to go deer hunting, as the deer can provide abundant and appetizing food, or to go hare hunting, also appetizing, but scarce. Deer hunting represents a challenge and requires mutual coordination. Hunting a…Provide a potential solution to the social dilemma in relation to game theory of prisoners dilemma, public goods game and nash equilibrium
- Which of the following best describes a dominant strategy? Question 4Answer a. The strategy that a player chooses depends on what the other player does b. The strategy that a player chooses minimizes the other player's payoff c. The strategy that a player chooses is independent of what the other player does d. The strategy that a player chooses maximizes joint payoffs for both players10) 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?Two takeaway restaurants, ChipAhoy and FishDish, compete for business in a small seaside town. The manager of ChipAhoy has engaged you to advise on the pricing of its main offering, a fish & chips supper. Your intention is to analyse the situation as a twoplayer competitive game. After making background investigations, you have decided to adopt the following assumptions in your analysis. A1 The cost of the producing and serving a portion of fish & chips is the same for both restaurants: £3.50.A2 In a typical week, holidaymakers buy a total of 1500 portions of fish & chips, and local residents buy 1000 portions.A3 Local residents always choose the restaurant with the lower price. If prices are the same at the two restaurants, their custom is divided equally between the two. A4 Holidaymakers divide their custom 50:50 between the two restaurants, irrespective of the prices. Derive the Nash equilibrium/equilibria for the game