2. Cindy and Andy are both workers on a team. At the same time both workers can choose to work on the risky project (R) or the safe project (S). If both choose to work on the R project the payoffs are 5 to Cindy and 4 to Andy. If both work on the S project the payoffs are 4 to Cindy and 5 to Andy. If Cindy works on R and Andy on S, the payoffs are (8, 10) to Cindy and Andy respectively. Finally, if Cindy plays S and Andy plays R, the payoffs are (10, 7). a. What are the Nash equilibria of the game? Interpret your equilibria in terms of a firm using teams. b. Now assume that Cindy can move first and choose which project to work on. Andy observes Cindy's choice before making his choice of either R or S. What are the subgame perfect equilibria of the game? Interpret this sequential game in terms of

2. Cindy and Andy are both workers on a team. At the same time both workers can choose to work on the risky project (R) or the safe project (S). If both choose to work on the R project the payoffs are 5 to Cindy and 4 to Andy. If both work on the S project the payoffs are 4 to Cindy and 5 to Andy. If Cindy works on R and Andy on S, the payoffs are (8, 10) to Cindy and Andy respectively. Finally, if Cindy plays S and Andy plays R, the payoffs are (10, 7). a. What are the Nash equilibria of the game? Interpret your equilibria in terms of a firm using teams. b. Now assume that Cindy can move first and choose which project to work on. Andy observes Cindy's choice before making his choice of either R or S. What are the subgame perfect equilibria of the game? Interpret this sequential game in terms of

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. Consider two workers 1 and 2 who simultaneously must choose between working on two projects, labelled A and B. The payoffs are as follows. If both 1 and 2 choose project A each worker gets 0. Similarly, if both workers choose B each gets 0. If worker 1 chooses B and worker 2 chooses A, each gets 10 and 3 (for worker 1 and 2) respectively. Finally, if 1 opts for A and worker 2 opts for B the payoffs to worker 1 and 2 are 8 and 7, respectively. a. What are the Nash equilibria of the game? Is this game a realistic one for an organisation? Explain your answer. What might an organisation do if it found itself in a situation similar to the one represented by this game.
(a) Stan and Ollie are two students who share a flat. Both of them prefer to live in a clean flat. However, neither is too fond of housecleaning. Each of them receives a payoff of 12 if they both clean the flat. If neither person cleans the flat, they receive a payoff of 6 each. If one person cleans the flat but the other person does not, then the payoff for the person who does the cleaning is 5 and the payoff for the person who doesn't do any cleaning is 15. (i) Write down the payoff matrix of this game. Derive the dominant strategy equilibrium. Is this also a Nash equilibrium? (ii) Expiain your reasoning. Consider a game with N players. Each player chooses Black or White. If a player (b) chooses Black, she gets 100 if everyone else also chooses Black, and she gets 0 if any of the other players does not choose Black. If a player chooses White, she always gets 50. Show that everyone choosing Black and everyone choosing White are both Nash equilibria of this game.
Question 5 ave Answer Player 1 has two options: L and R. If Player 1 chooses L, then Player 2 has two options; she can choose A or B. If Player 2 chooses A payoffs are (2; 1) and if she chooses B payoffs are (1; 2). If Player 1 chooses R, then Player 2 has two options; she can choose Y or N. If Player 2 shows Y payoffs are (0; 3) and if she chooses N payoffs are (1; 2). Which of the following statements is true? O A. (L; B,Y ) is a subgame perfect equilibrium of this game O B. (R; B,N ) is a subgame perfect equilibrium of this game O C.(L; A,Y) is a subgame perfect equilibrium of this game O D. (R; B,Y ) is a subgame perfect equilibrium of this game
Player 1 Cooperate (C) Defect (D) Cooperate (C) 3,3 8,0 Player 2 Defect (D) 0,8 1,1 In general, a combination of strategies is a Nash equilibrium if ... Every player is choosing a best response against the other players' strategies. Every player has a positive payoff. The players maximize the sum of their payoffs. The players choose identical strategies. If the game is repeated, which cooperative actions could benefit both players? O Both players choose C. Player 1 chooses C, Player 2 chooses D. O Player 1 chooses D, Player 2 chooses C. Both players choose D.
Y A BA B (PERFECT-INFO GAME) Consider the game shown at the right. -1 a. What is the number of pure strategies of Player 1? Player 2? 2 -2 4 b. How many subgames are in this game? c. Find all subgame perfect equilibria (SPE)? -2 d. Find all other NE which is not SPE. -3
Player 2 Left Center 30, 40 6, 20 20, 20 Right 21, 24 32, 35 10, 5 Up Middle 5, 5 40, 11 Player 1 Down 38, 42 Use the information in the game matrix above to answer questions #3 and # 4. 3. If both Players move simultaneously, then a. Player 1 has a dominant strategy, and Player 2 does not. b. Player 2 has a dominant strategy, and Player 1 does not. c. There is more than one pure strategy Nash Equilibrium. d. Both players have a dominant strategy. e. There are no Nash Equilibria in pure strategies. 4. If Player 1 moves first, then is the subgame perfect equilibrium. a. (Up, Left) b. (Middle, Center) c. (Middle, Right) d. (Down, Left) e. (Down, Center)
Problem 10-03 (algo) Use the following payoff matrix for a simultaneous-move one-shot game to answer the accompanying questions. с 9, 8 23, 13 a. What is player 1's optimal strategy? Strategy A B Player 1 O Strategy A O Player 1 does not have an optimal strategy. O Strategy B b. Determine player 1's equilibrium payoff. Player 2 D 14, 14 10, 18 E 18, 25 14, 26 F 12, 19 19, 21
6. Two players each pick a positive integer between 1 and 100. If the numbers are identical, noone wins. If the numbers differ by 1, the one with the lower number pays 1 to the opponent. If the difference is at least 2, the one with the higher number pays 2 to the opponent. What is the NE? Hint: Draw a sketch of the game matrix (while you can't consider all 100 strategies, at least consider the lowest 5-6 numbers) and think about dominated strategies.
(Demand Game) Two players can divide ten dollars. Find the Nash equilibria of the following two games. (a) The players simultaneously submit demands, numbers in {0, 1, ... ,10}. If the sum of the demands is at most 10, each player gets what she demands. Otherwise both get 0. (b) As in the previous part, except that if the sum of the demands exceeds 10, then (i) if the demands differ then the player who demands less gets her demand and the other player gets the rest, and (ii) if the demands are the same then each player gets 5. (Hint- write the best response functions).
Two workers are on a production line. They each have two actions: exert effort, E, or shirk, S. Effort costs a worker e > 0 and shirking costs them nothing. If two workers do action E a lot of output is produced and the workers earn £3 each. If only one worker chooses action E less output is produced and they both earn £1. The workers earn nothing if they both shirk. (i) Describe this situation as a strategic form game (assuming the workers do not observe each other's effort choice when making their own decision). (ii) For what values of e does this game have strictly dominant strategies? (iii) Describe the Nash equilibria of this game for e = 0,1, 2, 3. (iv) The workers now are re-arranged into a production line. First worker 1 moves and then worker 2 moves. Worker 2 can now see worker l's effort level before they choose their effort. Draw this extensive form game. (v) Find the subgame perfect equilibria of the production-line game for c = 1/2 and c = 3/2.
UI. In American football, the offense can either run the ball or pass the ball, whereas the defense can either anticipate (and prepare for) a run or anticipate (and prepare for) a pass. Assume that the expected payoffs (in yards) for the two teams on any given down are as follows: (a) (b) (c) (d) OFFENSE Run Pass Anticipate Run 1,-1 DEFENSE 9,-9 Anticipate Pass 5,-5 3, -3 Show that this game has no pure-strategy Nash equilibrium. Find the unique mixed-strategy Nash equilibrium of this game. Explain why the mixture used by the offense is different from the mixture used by the defense. How many yards is the offense expected to gain per down in equilibrium?
Question 1 Using your knowledge of the "method of elimination.of dominated strategy". solve for the equilibrium solution(s) to the following pay-off matrix for two players. Player A Player B Strategyl Strategy 2 Strategy 3 Strategy 4 Strategy 5 Strategy1 (40, 200) Strategy 2 (60, 25) Strategy 3 (88, 55) (55,102) (45, 142) (109) 42) K09. 120) (50, 100) (99, 155)70 la. (80. 100) K104, 55) (44,90) (100,50) C403)165)(17 190 (60, 160) (155,115) (95.120) (50, 90) (84, 100) Strategy 4 Strätegy 5 172) 140) (85, 145) (48, 200) 123)125) (100, 145) Is your solution in "a above unique? Why? b. Present the following extended form of pay-off matrix in a normal form pay-off matrix for the player Extended Form of Pay-»ff Matrix Player B Strategy 1 (40, 20) (30,25) Strategy 2 (90, 300) (85.55) 30 25 Player A Strategy 1 Strategy 2 20