Rock paper scissors is a two-player game, in which each player simultaneously forms one of three shapes with an outstretched hand. These shapes are "rock", "paper", and "scissors". A player playing rock will beat another player playing chosen scissors, but will lose to one playing paper, a play of paper will lose to a play of scissors. If both players choose the same shape, the game is tied. Suppose the winner receives a payoff of 1 and the loser receives the payoff of -1. Both players receive zero payoff under a tie. In this game, is (rock, paper) a Nash equilibrium?

Rock paper scissors is a two-player game, in which each player simultaneously forms one of three shapes with an outstretched hand. These shapes are "rock", "paper", and "scissors". A player playing rock will beat another player playing chosen scissors, but will lose to one playing paper, a play of paper will lose to a play of scissors. If both players choose the same shape, the game is tied. Suppose the winner receives a payoff of 1 and the loser receives the payoff of -1. Both players receive zero payoff under a tie. In this game, is (rock, paper) a Nash equilibrium?

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 9MC

See similar textbooks

Similar questions

Samiyah and DeAndre decide to play the following game. They take turns choosing either 1, 2, or 3. As each number is chosen, it is added to the previously chosen numbers. The winner is the player who chooses a number that brings the cumulative number to 10. For example, if Samiyah chooses and DeAndre chooses 2 (so the cumulative number is 5) and Samiyah chooses 2 and DeAndre chooses 3 then DeAndre wins as his choice of 3 results in the sum equaling 10. Using SPNE, who wins?
When you are with a young child and want to show them something fun and new, there is the risk that, if they enjoy it, they'll ask for it over and over and over again, and if you ever say no they'll throw a fit, which you will then have to deal with. Consider the following game: First, you decide whether to show them an Old thing again, or a New thing. If you show them the Old thing, you get 2 points and the kid gets 2 points Then, If you showed them the New thing, the kid chooses whether to Ask for it to happen again, or Not Ask. If they choose Not Ask, you get 3 points and the kid gets 3 points If they choose to Ask, you can choose to say Yes, in which case you get 1 point and the kid gets 4 points, or No, in which case they throw a fit, and you get 0 points and the kid gets 2 points Draw the game tree for this game.
The following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff of
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.
Consider a sequential game where there are two players, Jake and Sydney. Jake really likes Sydney and is hoping to run in to her at a party this weekend. Sydney can't stand Jake. There are two parties going on this weekend and each player's payoffs are a function of whether they see one another at the party. The payoff matrix is as follows: Sydney Party 1 Party 2 Party 1 6, 18 18, 6 Jake Party 2 24,8 0,24 a) Does this game have a pure strategy Nash Equilibrium? b) What is the mixed strategy Nash Equilibrium? c) Now suppose Sydney decides what party she is going to first. Her roommate is friends with Jake and will call him to tell him which party they go to. Write the extensive form of this game (game tree). d) What is the subgame perfect Nash equilibrium from part c?
When two cats, Euclid and Jamie, play together, their game involves facing each other while several feet apart; each cat must then decide whether to pounce or to "freeze-to stay motionless und the other cat pounces. Euclid weighs 2 lb more than Jamie, so if they both pounce, Jamie is squashed and Euclid gains 6 points. If they both freeze, Euclid remains in control of the area and gains 2 points. If Euclid pounces while Jamie freezes, Jamie can put up a good defense, so Euclid gains only 1 point. Euclid is poor at defense, so if he freezes while Jamie pounces, he loses 1 point. Find the optimum strategy for each cat, and find the value of the game for Euclid. Construct the payoff matrix M = Euclid m11 12 M21 22 Jamie Pounce Freeze Pounce Freeze Euclid should pounce with probability (Type integers or simplified fractions.) and freeze with probability Jamie should pounce with probability and freeze with probability (Type integers or simplified fractions.) The value of the game for…
Keith and Blake play a simultaneous one-shot game given by the following table: Blake Left Right Keith Top Bottom 4.00, -5.00 0.00, -6.00 5.00, 0.00 -2.00, 7.00 As there is no unique pure strategy Nash equilibrium, assume that each player plays each of his choices half of the time. What is the average payoff for Keith? | What is the average payoff for Blake? (Round to two decimals if necessary.) (Round to two decimals if necessary.)
the Consider a simultaneous-move integer game between two players: Marilyn and Noah. Each of player is required to announce a positive integer between 1 to 4. In other words, a player can announce 1, 2, 3, or 4. Two players announce their integers simultaneously. Notice that this game is different from the games we learned in class in that each player has four actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both O. What is Marilyn's maximin strategy? 01 02 03 O
Consider the following game represented in normal form. Terry and Kerry are roommates who must make decisions about cleaning. Terry's payoff is the fiırst number in each cell and a higher number is a better outcome. Assume that Terry and Kerry make their decisions simultaneously. Kerry Clean Don't clean Terry Clean ( 8, 2 ) ( 3, 5 ) Don't ( 10, 3) ( 4, 1 ) clean The Nash equilibrium of this game is Terry will [ Select ] v and Kerry will [ [ Select ]
conside the following game There are two companies that sell Haitian coffee.Each company currently makes $5 million in revenue They need to determine whether they should engage in a social media advertising campaign Advertising costs $2 million for each company If one company advertises and the other does not, then the one that advertises captures $3 million from the company that does not. If both companies advertise they gain nothing. Draw the payoff matrix. What is this games Nash equilibrium
The Stag Hunt Game - A group of 10 hunters are hunting, where the games include a stag and several (>10) hares. Each hunter can choose whether to hunt the stag or go after a hare. It takes the joint effort of all 10 players to catch the stag, but each hunter on their own is able to catch a hare. Suppose that a stag is worth $100 and a hare is worth $9. Suppose also that when all 10 players together catch the stag, they each get $10 after the game is sold. (a) Formulate this situation as a strategic game and find the Nash equilibria. (b) Now suppose that there are still 10 hunters, who need to choose to either hunt the stag or catch a hare. However, suppose that only 6 hunters are needed to catch a stag. Assume further that after the stag is caught, it can still be sold for $100 and the money shall be divided evenly among the hunters who have chosen to join the stag hunt only. On the other hand, each hunter can always catch a hare on their own and sell it for $9. Formulate this…
Suppose that two firms, firm A and firm B, are competing in the market. Assume that each firm has two strategies available: “no promotion” and “extensive promotion”. If both firms choose “no promotion”, each firm will get a payoff of 8000. If both firms choose “extensive promotion”, each firm will get a payoff of 5000. If one firm chooses “no promotion” and the other firm chooses “extensive promotion”, the firm that chooses “no promotion” will get a payoff of 4000 and the firm that chooses “extensive promotion” will get a payoff of 10000.a. Assume the game is a 2-players one-shot simultaneous game, please develop the normal form of this game by showing the players, the strategies and the payoffs. b. Follow part (a), determine the dominant strategy of firm A. c. Follow part (a), determine the dominant strategy of firm B. d. Follow part (a), determine the equilibrium of this game. e. If the game becomes an infinitely repeated game, what do you expect to happen?