Typed plzzz And AsapThanks 12 W X y a 5,1 1,2 1,1 b 3,4 4,3 0,1 C 8,4 8,2 9,3 Is player 1's strategy x dominated? If yes, provide a strategy that dominatesx. If provide a belief that makes x a best response.no,that makes x a best response.is player 1's strategy x dominated? If yes, provide a strategy that dominates x. If no, provide a beliefy1,10,19,33X1,24,38,2cShow Transcribed TextW5,13,48,4Tab2

1\2 A B C W 5, 1 3, 4 8, 4 X 1, 2 4, 3 8, 2 Y 1, 1 0, 1 9, 3

12 WX y a 5,1 1,2 1,1 b 3,4 4,3 0,1 C 8,4 8,2 9,3 Is player 1's strategy x dominated? If yes, provide a strategy that dominates provide a belief that makes x a best response. x. If no, that makes x a best response is player 1's strategy x dominated? If yes, provide a strategy t 1,1 0,1 9,3 3 1,2 4,3 8,2 C M 5,1 3,4 8,4 a b

12 WX y a 5,1 1,2 1,1 b 3,4 4,3 0,1 C 8,4 8,2 9,3 Is player 1's strategy x dominated? If yes, provide a strategy that dominates provide a belief that makes x a best response. x. If no, that makes x a best response is player 1's strategy x dominated? If yes, provide a strategy t 1,1 0,1 9,3 3 1,2 4,3 8,2 C M 5,1 3,4 8,4 a b

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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4 Consider an extensive game where player 1 starts with choosing of two actions, A or B. Player 2 observes player 1’s move and makes her move; if the move by player 1 is A, then player 2 can take three actions, X, Y or Z, if the move by player 1 is B, then player 2 can take of of two actions, U or V. Write down all teminal histories, proper subhistories, the player function and strategies of players in this game.
Two bidders compete in a second price auction (i.e., the winning bidder pays the losing bidder’s bid, and the losing bidder does not pay anything). They submit sealed bids, and the one with the highest bid wins the contract and pays the other bidder’s bid. Each bidder i’s private valuation is vi and is distributed independently and uniformly between 0 and 50. 1. For any given bidder, prove that he has a dominant strategy bid and show what it is. 2. Assuming each bidder bids his dominant strategy noted above, if a bidder with vi = 40 wins, what price does he expect to pay?
You and a rival are engaged in a game in which there are three possible outcomes: you win, your rival wins (you lose), or the two of you tie. You get a payoff of 50 if you win, a payoff of 20 if you tie, and a payoff of 0 if you lose. What is your expected payoff in each of the following situations? (a) There is a 50% chance that the game ends in a tie, but only a 10% chance that you win. (There is thus a 40% chance that you lose.) (b) There is a 50–50 chance that you win or lose. There are no ties. (c) There is an 80% chance that you lose, a 10% chance that you win, and a 10% chance that you tie.
Mohamed and Kate each pick an integer number between 1 and 3 (inclusive). They make their choices sequentially.Mohamed is the first player and Kate the second player. If they pick the same number each receives a payoff equal to the number they named. If they pick a different number, they get nothing. What is the SPE of the game? a. Mohamed chooses 3 and Kate is indifferent between 1, 2 and 3. b. Mohamed chooses 3 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2, and 3 if Mohamed chooses 3. c. Mohamed chooses 1 and Kate chooses 1 if Mohamed chooses 1, 2 if Mohamed chooses 2 and 3 if Mohamed chooses 3. d. Mohamed chooses 3 and Kate chooses 3.
Normal Form: Which one of the following descriptions below is CORRECT according to this Normal Form shown? 1.) If Player 2 believes that Player 1 randomly choose H or L with same probability, then Player 2's expected for choosing HC is 2. 2.) If Player 1 has 20% chance to play H and 80% chance to play L, Player 2 has 40% chance to play HD and 60% chance to play LC; then Player 1's expected payoff is 2. 3.) If Player 2 randomly play one of its 4 strategies without any preference, then Player 1's expected payoff for playing L is 2.5. 4.) If Player 2 believes that Player 1 has no probability to play L, then Player 2 would prefer to choose HC or HD.
Q56 A Nash equilibrium is an outcome... a. Achieved by cooperation between players in the game. b. That is achieved by collusion where no party has an incentive to change their behaviour. c. Where each player's strategy depends on the behaviour of its opponents. d. That is achieved when players in the game have jointly maximized profits and divided those profits according to market share of each player. e. Where each player's best strategy is to maintain its present behaviour given the present behaviour of the other players.
Consider a situation of after-match penalty shoot-out. The striker can target either East or West side of the goal. If he targets West, with 80% chance he shoots on target. If he shoots East, he is accurate with 75%. The goalkeeper has to choose the corner to jump to. If he does not guess the corner correctly and the shot is on target, then the striker scores. If the striker shoots West, the shot is on target and the goalkeeperjumps West, then with 75% chance he saves the goal. If the striker shoots East, the shot is on target and the goalkeeper jumps East, then with chance of 2/3 he saves the goal. Suppose, that it is a zero-sum game and if the striker scores his payoﬀ is 1, otherwise it is 0.1. Formulate this situation as a strategic game and Find all Nash equilibria of the game.
Consider the following game 1\2 Y Z A 10,3 3,9 B 8,5 6,1 Suppose Player 2 holds the following belief about Player 1: θ1 (A,B) = (9/10,1/10) What is the expected payoff from playing ‘Y’ ? What is the expected payoff from playing ‘Z’ ? Based on these beliefs, player 2 should respond by playing _____
Q17. What the information sets in the above game denote? Player 2 does not observe the action of player 1, so he does not know in which decision node he/she is playing at. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and b, or one between c and d. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played one between a and c, or one between b and d. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and d, or one between b and c.
Q17. What the information sets in the above game denote? Player 2 does not observe the action of player 1, so he does not know in which decision node he/she is playing at. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and b, or one between c and d. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played one between a and c, or one between b and d. Player 2 does not observe the precise action of player 1, but he does know that player 1 has played either one between a and d, or one between b and c. Q18. If we want to describe the above game with a strategic form representation, what would the strategy sets for the three players? Player 1={a, b, c, d} ; Player 2={x, y} Player 1={a, b, c, d} ; Player 2={xx, xy, yx, yy}
Consider the following variation to the Rock (R), Paper (P), Scissors (S) game:• Suppose that the Player 1 (row player) has a single type, Normal.• Player 2 (column player) has two types Normal and Simple.• A player of Normal type plays this zero-sum game as we studied in class whereas a player of type Simple always play P.• Player 2 knows whether he is Normal or Simple, but player 1does not.a) Suppose player 2 is of type Normal with probability 1/3 and of type Simple with probability (2/3). Find all pure strategy Bayesian Nash Equilibria.b) Suppose player 2 is of type Normal with probability 2/3 and of type Simple with probability (1/3). Find all pure strategy Bayesian Nash Equilibria.
Each of the two players independently (and simultaneously with the other) decides whether to go to a play or a concert. Each would rather go with the other to a concert than with them to a play, but prefers this to not being together, in which case they don't care where they go alone. Additionally, each is indifferent between attending the play together and participating in a lottery where both go to the concert with a probability of ¾ and to different events with a probability of ¼. Describe the game in matrix form and find all its equilibria under the assumption that the players have von Neumann-Morgenstern preferences.