Consider a two player game with Fred and Barney, who tals turns removing matchsticks from a pile. They start with 33 matchsticks, and Fred goes first. On each turn, each player may remove either one, two, three, four, or five matchsticks. The player to remove the last matchstick wins the game. What are the optimal strategies for each player? Who will win? b. Suppose now that they can remove up to six matchsticks, how will the optimal strategies change for- each player? a.
Q: The following payoff matrix represents a simultaneous-move game between two players: John and…
A: Game theory: It refers to the process of making strategies between two or more two players which…
Q: Aang and Bolin are playing a simultaneous-move game where they seek to maximiz their utility…
A: An essential concept in economics, the utility function attempts to quantify a person's level of…
Q: Find the value of the following game in mixed strategies and all the optimal strategies of 2). both…
A: The pure strategy Nash equilibrium is the strategy profile such that for each player given the…
Q: Suppose Clancy and Eileen are playing a game in which both must simultaneously choose the action…
A: Clancy When Eileen plays left, best response of Clancy is to play left(6>4) When Eileen plays…
Q: One day, Sam and Ryan play odds/evens to see who gets the last doughnut. On command, they each…
A: Disclaimer: Since it is a multiple part question, I am providing you with the answer to the first…
Q: In the following game, Player 1 makes a low bid or high bid, and Player 2 reacts in an easygoing or…
A: The correct option is b) High and Easy in both rounds.
Q: lesse and Janie are playing a game. On the table in front of them, there are 50 coins. They take…
A: Game theory is a topic of economics in which we analyze the different game strategy or its show the…
Q: In the following game, Player 1 makes a low bid or high bid, and Player 2 reacts in an easygoing or…
A: Introduction: Concept within game theory where the optimal outcome of a game is where there is…
Q: Suppose this is a one-shot game played by City Potato Farm and Country Potato Farm. What is the…
A: Game theory is a branch of applied mathematics and economics. It studies the decisions of players in…
Q: game Player 2 C D…
A: We will solve this game using the backward induction. That is firts solve for player 2 and then for…
Q: Suppose Andrew and Beth are playing a game in which both must simultaneously choose the action Left…
A: Game theory is the study of how interacting choices of economic agents produce outcomes with respect…
Q: There are two players, A and B. When A and B meet, each can decide to fight (F) or cave (C).…
A: Given, Two Players : A and BStrategies of both the Players : Fight and CaveIf both players choose…
Q: Consider the game shown below. In this game, players 1 and 2 must move at the same time without…
A: In the mentioned question we have been asked the best payoff where both will get their best.
Q: Suppose Charles and Dina are playing a game in which both must simultaneously choose the action Left…
A: The Nash equilibrium is a game theory decision-making theorem that argues that if a player sticks to…
Q: 9. In the game played in the class, "Guess 2/3 of the average", assume there are 3 students, each…
A: Introduction Each players names as integer between 0-100. Each player chooses best response to other…
Q: The following game is repeated infinitely many times. Suppose both players decide to play a grim…
A: Following game is repeated infinitely many times. Player 2 L C R U 4,4 -1,5 0,0…
Q: Consider a two-player, sequential-move game where each player can choose to play right or left.…
A: Nash Equilibrium:- The Nash equilibrium can be explained as a game theory decision-making hypothesis…
Q: Use the following payoff matrix for a one-shot game to answer the accompanying questions. a.…
A: Nash equilibrium is the optimal outcome of a game is one where no player has an incentive to deviate…
Q: Back to the "Battle of the Sexes" example, imagine that Brian is mad at Anna for some silly reason.…
A: We can use the backward induction after drawing the game tree for the player.
Q: Suppose Carlos and Deborah are playing a game in which both must simultaneously choose the action…
A: ANSWER STEP-1 When Carlos chooses Left. Deborah chooses right gives payoff of 4 which is higher than…
Q: Suppose Felix and Janet are playing a game in which both must simultaneously choose the action Left…
A: Nash Equilibrium is the optimal strategy where the players have no incentive to deviate from their…
Q: Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom,…
A: Answer: (D). Maximin strategy: A maximin strategy is the best strategy out of the worst strategies…
Q: Capturesque Pricing High Low High 11, 11 2, 18 eing Low 18, 2 10, 10 ower-left cell shows that if…
A: The supply function shows arranged reactions to contrasting level of cost. Assuming either the…
Q: Three politicians are voting on whether to allow themselves a salary increase of$3,500per a year. If…
A: The Nash equilibrium allows us to view the outcome of a one-shot game when each player plays their…
Q: PLAYER B LEFT…
A: Nash Equilibrium is a concept which exists in the subject Game Theory, wherein the outcome that is…
Q: Team 2 plays A Team 2 plays B Team 2 plays C Team 1 plays A 9, 9 8, 12 6, 6 Team 1 plays B 6, 6 0, 7…
A: n game theory, a Nash Equilibrium is a set of strategies, one for each player in a social game,…
Q: When you are with a young child and want to show them something fun and new, there is the risk that,…
A: Answer -
Q: Jesse and Janie are playing a game. On the table in front of them, there are 50 coins. They take…
A: Game Theory is a part of economics that studies the different ways the various choices of economic…
Q: What is the Nash equilibrium of this game, or what are the Nash equilibria of this game? (b) Does…
A: Nash equilibrium refers to a situation in a game theory when all the players choose the strategy…
Q: An incumbent can commit to producing a large quantity of output before the potential rival decides…
A: In Nash equilibrium, each person chooses their best strategy from the given strategies that the…
Q: Suppose now we alter the game so that whenever Colin chooses "paper" the loser pays the winner 3…
A: Game xT=13,13,13 yT=13,13,13
Q: Consider a two-player, sequential-move game where each player can choose to play right or left.…
A: (a) The extensive form of the game is shown below.
Q: In the following game, Player 1 makes a low bid or high bid, and Player 2 reacts in an easygoing or…
A: The given game is a case of finite repeated game. The sub game perfect nash equilibrium for finite…
Q: Consider a two player game with Fred and Barney, who tal turns removing matchsticks from a pile.…
A: Player: It refers to the people who in the market plays together or in competition with one another.…
Q: 1. Draw the extensive form (tree) of the following game. 2. Find the perfect equilibrium. What are…
A: The question is related to Game Theory. Below is the solution.
Q: Imagine a two-player game that proceeds as follows. A pot of money is created with $6 in it…
A: A subgame perfect equilibrium ( that is also known as a subgame perfect Nash equilibrium) is…
Q: Keith and Blake play a simultaneous one-shot game given by the following table: Blake Left Right Top…
A: In game theory, players chooses their strategies and earns the payoffs. Payoff is the outcome of the…
Q: What is the SPNE of the following game, where Player 1 moves first and can play A or B, and player 2…
A: A subgame perfect equilibrium is a refinement of a Nash equilibrium that is used in dynamic /…
Q: Use the following game table to answer the question: Player 2 Y A 10, 5 6, 3 0,0 Player 1 В 2,6 1, 3…
A: Nash equilibrium is the optimal strategy of the two players in a non-cooperative game. It is the…
Q: 2. Consider the following "centipede game." The game starts with player 1 choosing be- tween…
A: There are two players : Player 1 & 2 Centipede games are those extensive form games in which…
Q: (The Beckhams' dilemma) Victoria and David are husband and wife. They both prefer ciean to dirty…
A: A Game can be referred to as an abstract model of the strategic situation. The pure strategy Nash…
Q: 19. Recall the following public goods game from the class, where two roommates are trying to figure…
A: Given information 2 players 2 strategy set for each
Q: Consider the following static, single-shot game played between two cyclists, Chico and Loco, who…
A: Nash Equilibrium is a concept in game theory that finds the best solution in a non-cooperative game…
Q: Consider the Sequential Matching Pennies Game. Now assume player 1 is allowed to quit the game in…
A: Matching Pennies is a simple game theory scenario that demonstrates how rational decision-makers…
Q: Suppose 2 players play the following game infinite times in the future. What should equilibrium…
A: An equilibrium strategy is the one in which each player performs the strategy that maximizes its own…
Q: John and Jane usually vote against each other’s party in the SSC elections resulting to negating or…
A: A. The diagram is as follows : Jane voting for her choice of party Jane voting against her…
Q: Consider the following 3-player static game with row player Batman (his choices are a and b), column…
A: There are three players : Batman , Catwoman & Joker Batman's Strategy set : { a , b } Catwoman's…
Q: Deborah Left Right Left 8, 4 4, 5 Carlos Right 5, 4 6, 5 Left Right The only dominant strategy in…
A: Given pay matrix:- As per given information:- When Carlos chooses 'Left', Deborah will choose…
2
Step by step
Solved in 2 steps
- H2. One day, Sam and Ryan play odds/evens to see who gets the last doughnut. On command, they each extend one or two fingers. If the sum is odd Sam wins the doughnut, if the sum is even Ryan wins the doughnut. Suppose the payoff from winning the doughnut is 1 and the payoff from losing is 0. a) Illustrate this interaction as a game in matrix form. b) Suppose that Sam thinks that Ryan will play one finger for sure? What will Sam play? Does Sam have reason to think that Ryan will play one finger for sure? c) Do either of them have a strictly dominated strategy? d) Find the pure strategy Nash equilibria of the game, if any. e) Suppose that Sam thinks that Ryan will play one finger or two fingers with even odds. Will Ryan play one finger for sure, play two fingers for sure or play each strategy with even odds? Does Sam have good reason to believe that Ryan will play one finger or two fingers with even odds?answer the ff: Suppose that each company cancharge either a high price for tickets or a low price. Ifone company charges $300, it earns low profit if theother company also charges $300 and high profit ifthe other company charges $600. On the other hand,if the company charges $600, it earns very low profit ifthe other company charges $300 and medium profitif the other company also charges $600.a. Draw the decision box for this game.b. What is the Nash equilibrium in this game?Explain.c. Is there an outcome that would be better than theNash equilibrium for both airlines? How could itbe achieved? Who would lose if it were achieved?1) Suppose that Player A can take two actions, either Up or Down. Player A is thinking to choose Up 50 percent of the time, and Down 50 percent of the time. This type of strategy is called a ____ ? 2) Consider a payoff matrix of a game shown below. In each cell, the number on the left is a payoff for Player A and the number on the right is a payoff for Player B. In order for (Down, Right) to be a unique pure strategy Nash equilibrium, a must be (greater, or smaller) than 3 and b must be (greater, or smaller) than 3. refer to image
- 12. Consider a game where each player picks a number from 0 to 60. The guess that is closest to half ofthe average of the chosen numbers wins a prize. If several peopleare equally close, then they share theprize. The game theory implies that (A) all players have dominant strategies to choose 0 (B) all players have dominant strategies to choose 30 (C) there is a Nash equilibrium where all players pick 0 (D) there is a Nash equilibrium where all players pick positive numbers 13. Behavioral data in such games suggests that (A) most subjects choose 0; (B) most subjects choose 30; (C) common answers include 30, 15, 7.5, and 0; (D) most subjects use randomization. Can you help me answer number 13 please?Consider the following game: Player 2 In Out Player 1 In -2,-2 2, 0 Out 0, 2 0, 0 (a) What is the Nash equilibrium of this game, or what are the Nash equilibriaof this game? (b) Does either firm have a dominate strategy (a strategy that is always abest response)? Which? (c) Suppose Player 1 could move before Player 2 and Player 2 could observe Player 1’s move. What do you think would happen?2. Consider a game that game theory people refer to as the “ultimatum game.”We will refer to our two players as the “offerer” and the “decider”. How the gameworks is that the offerer proposes a way to split $1000 between the two players.While this could be done in a variety of ways, we will assume that the offerersonly has two possible proposals: Either a 50-50 split, or she offers the decider$50 and keeps the rest. The decider can either accept or reject the offer. If the offer is accepted, the money is split as proposed. If the offer is rejected, themoney spontaneously combusts and nobody gets anything. a) List the strategies for each player and write an extensive form version of thegame with payouts. b) List all the Nash equilibria of this game. c) Explain which, if any of the Nash equilibrium are not sub-game perfect. d) Write the game out in normal form and find the pure strategy Nashequilibrium. Explain how this matches with your answers to (b) and (c) . Alsoexplain why there…
- 1. With nash equilibrium, do you always choose the optimal strategy? 2. Can a game have more than one nash equilibrium?Two farmers have unlimited access to a common plot of land and can let their cows graze on it. The matrix below shows the benefits they get from grazing either 1 or 2+ cows on the land. Farmer 2 Farmer1 1 cow 2+ cows 1 cow 8,8 2,10 2+cows 10,2 4,4 What kind of game is this? What is/are the Nash equilibrium/equilibria? What is/are the Pareto efficient outcome(s) in this game? (Hint: Remember that Pareto efficiency occurs when no one person can be made better off without someone else being made worse off) The government offers a reward or subsidy for communities where farmers only allow 1 cow to graze on the common field, resulting in a new payoff matrix:…Consider the following price game: Firm 1 Firm 2 High Low High 20, 20 12, 24 Low 24, 12 14, 14 Remark: In simultaneous move games (games with rows and columns) theconvention is to write the row player’s payoff first and the column player’spayoff second. (a) What is the Nash equilibrium of this game? Recall that for each playeryou should find the best response to each of the opponents’ strategies andunderline the associated payoff. Then look for a cell where both strategiesare best responses to each other. This is a Nash equilibrium. (b) Does either firm have a dominate strategy (a strategy that is always abest response)?
- 7. A farmer can either invest in irrigation for their farm or not. There's a 30% chance that they will receive adequate rain such that the irrigation is not necessary, and a 70% chance that the irrigation will be useful if acquired. Assume that the farmer will receive $5,000 if their crops are adequately watered, and $1,000 otherwise. Irrigation costs $3,000. For simplicity, assume this is a one-off game and that nature is not perverse.a. Draw the extensive form of this game, with the farmer acting first and nature second.b. What is the expected value of each strategy for the farmer?c. What is the expected value of perfect information on the weather?Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table: Player 1 Player 2 Left Right Top 6 1 9 4 Bottom 2 4 5 3 where the number on the left is the payoff to Player 1, and the number on the right is the payoff to Player 2. D) What is Player 1’s maximin strategy?E) What is Player 2’s maximin strategy?F) If the game were played with Player 1 moving first and Player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose?What is Ann's maximin strategy? Game Bob L RAnn U 10,-1 4, 4 D 4, 1 8, -1 Select one: a.none of the other answers b.4/7 U + 3/7 D c.2/5 U+ 3/5 D d.2/7 U + 5/7 D e.3/5 U + 2/5 D