Suppose Charles and Dina are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows showsthe payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Charles chooses Right and Dinachooses Right, Charles will receive a payoff of 5 and Dina will receive a payoff of 3.DinaLeftRightLeft4, 46, 3CharlesRight5, 45, 3The only dominant strategy in this game is forto chooseThe outcome reflecting the unique Nash equilibrium in this game is as follows: Charles choosesand Dina chooses

The Nash equilibrium is a game theory decision-making theorem that argues that if a player sticks to…

Suppose Charles and Dina are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows sh the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Charles chooses Right and Dit chooses Right, Charles will receive a payoff of 5 and Dina will receive a payoff of 3. Dina Left Right Left 4, 4 6, 3 Charles Right 5, 4 5, 3 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Charles chooses and Dina chooses

Suppose Charles and Dina are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows sh the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Charles chooses Right and Dit chooses Right, Charles will receive a payoff of 5 and Dina will receive a payoff of 3. Dina Left Right Left 4, 4 6, 3 Charles Right 5, 4 5, 3 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Charles chooses and Dina chooses

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 15.1IP

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Suppose Rashard and Alyssa are playing a game that requires both to simultaneously choose an action: Up or Down. The payoff matrix that follows shows the earnings of each person as a function of both of their choices. For example, the upper-right cell shows that if Rashard chooses Up and Alyssa chooses Down, Rashard will receive a payoff of 4 and Alyssa will receive a payoff of 5. Alyssa Up Down Rashard Up 8, 4 4, 5 Down 5, 4 6, 5 In this game, the only dominant strategy is for to choose . The outcome reflecting the unique Nash equilibrium in this game is as follows: Rashard chooses and Alyssa chooses.
Consider the following two-player game.First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously andindependently, player 1 selects a number y1 and player 2 selects a number y2, at which pointthe game ends.Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8xPlayer 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.
Theo and Addy are deciding what toys to pick out at the toy store. Depending on what toys they pick, they can play different games together, but they can’t coordinate their choices. They can’t talk to one another at all until after that make their choice. Below is their payout matrix which shows their utility for each choice. All the bold figures are for Theo and all the non bold figures are for Addy. Addy Strategies Theo Strategies Toy Gas Pump Jump Rope Toy food 20 10 10 3 Ball 7 3 9 4 a) If Theo chooses Toy Food, what would be the possible outcomes for Addy? What would be best for Addy? b) If Addy chose a Toy Gas Pump, what are the possible outcomes for Theo? What would be best for Theo? c) Does Addy have a dominant strategy? If yes, what is her strategy? If not how can you tell? d) Does Theo have a dominant strategy? If yes, what is her strategy? If not how…
Consider the payoff matrix for a game depicted below. Player 1 selects the row and Player 2 selects the column. Up Down Left 1, -1 -1, 1 Right -1, 1 1, -1 What is (are) the Nash equilibrium (equilibria)? Question 18Answer a. Player 1 plays right; Player 2 plays down b. Player 1 plays left; Player 2 plays down c. Player 1 plays down; Player 2 plays left d. Player 1 plays right; Player 2 plays up e. Player 1 plays up; Player 2 plays left f. There is no Nash equilibrium g. Player 1 plays down; Player 2 plays right h. Player 1 plays up; Player 2 plays right i. Player 1 plays left; Player 2 plays up
Consider the following game. There are two payers, Player 1 and Player 2. Player 1 chooses a row (10, 20, or 30), and Player 2 chooses a column (10/20/30). Payoffs are in the cells of the table, with those on the left going to Player 1 and those on the right going to player 2. Suppose that Player 1 chooses his strategy (10, 20 or 30), first, and subsequently, and after observing Player 1’s choice, Player 2 chooses his own strategy (of 10, 20 or 30). Which of the following statements is true regarding this modified game? I. It is a simultaneous move game, because the timing of moves is irrelevant in classifying games.II. It is a sequential move game, because Player 2 observes Player 1’s choice before he chooses his own strategy.III. This modification gives Player 1 a ‘first mover advantage’. A) I and IIB) II and IIIC) I and IIID) I onlyE) II only
. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that
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Suppose that Teresa and Caroline are both in the public eye. They get offers to sell secrets of the other to tabloids. If both keep the secrets, they are both better off than if they get exposed. If only one is exposed, the other person is better off than if no one was exposed. Their payoffs from each option are given in the payoff matrix. Suppose that Caroline and Teresa play the game over four television seasons, where each season is a new game. Consider the scenarios. Remember, a tit‑for‑tat strategy is one where the person starts by cooperating and then plays whatever strategy the other firm played last. Over four seasons, how much will Caroline make if she and Teresa both play tit‑for‑tat? $_______ Over four seasons, how much does Caroline make if she always exposes and Teresa plays tit‑for‑tat? $________
Suppose that Teresa and Caroline are both in the public eye. They get offers to sell secrets of the other to tabloids. If both keep the secrets, they are both better off than if they get exposed. If only one is exposed, the other person is better off than if no one was exposed. Their payoffs from each option are given in the payoff matrix. Suppose that Caroline and Teresa play the game over four television seasons, where each season is a new game. Consider the scenarios. Remember, a tit‑for‑tat strategy is one where the person starts by cooperating and then plays whatever strategy the other firm played last. Over four seasons, how much will Caroline make if she plays a tit‑for‑tat strategy and Teresa always exposes? $_______ Over four seasons, how much will Caroline make if she and Teresa both always expose? $_________ Does Caroline have a dominant strategy when she and Teresa play for four seasons? No, there is no dominant strategy…
True or False?Please Explain Thoroughly: In a Nash equilibrium of a strategic game, each player must best respond to her opponents’ actions, therefore, no other action profile can be unanimously preferredby all the players to a Nash equilibrium.
Consider the following game played by four individuals, players 1, 2, 3, and 4. Each individual has $10,000. Each player can donate between $0 and $10,000 to build a public park that costs $20,000. If they collect enough money, they construct the park, which is worth $9,000 to each of them. However, if they collect less than $20,000, they cannot build a park. Furthermore, regardless of whether the park is built or not, individuals lose any donations that they make. a) Describe the Nash equilibria for a simultaneous game. What makes them equilibria? Hint: There are many equilibria, so you may want to use a mathematical expression! b) Suppose that players 1, 2, and 3, each donate $4,000 for the park. How much will player 4 donate and why. What are the resulting payoffs for the players? c) Suppose instead that player 1 donated first, player 2 second, player 3 third, and player 4 last. Furthermore, players could only donate in intervals of 1,000 (0, $1,000, $2,000, etc.). How much will…
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?