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Consider the extensive form game shown below. At each terminal node, the first payoff belongs to player 1, the second payoff belongs to player 2, and the third payoff belongs to player 3. How many strategies does player 3 have in this game? Numerical answer (12 (2,2,1) 2 b₂ (22, (2,4,2) (4,2,3) b₁ 2 (3,3,3) C1 02/ 03 b2 b3 (2,2,1) (4,2,0) (2,0,2) 03 3 b3 (0,3,4) image 1

Define a new game as a modified version of the game in Problem 1, which we will call the Matching Two Pennies game: each player choose heads (H) or tails (T) for two pennies. In this game, Player 1 wins if both coins show the same combination of heads and tails, while Player 2 wins if they do not. (a) Write the strategy sets S1 and S2 for this game. (b) Give the payoffs for each player in this Matching Two Pennies game, by defining T;(81, 82) for each player and for each strategy pair, either as a list or in matrix form.

Problem 4: Sequential Game Company A is considering whether to invest in infrastructure that will allow it to expand into a new market. Company B is considering whether to enter the market. Assume the companies know each other's payoffs. Use the decision tree below to answer the following questions. Result Enter B:2 A:2 Invest Company B B:0 A: 4 Don't enter Company A Enter B: 1 A: 1 Don't invest Company B B:0 A: 2 Don't enter Which company has the first-mover advantage in this game? [ Select] If Company A invests, Company B's best response is [ Select ] At this outcome, Company B receives a payoff of [ Select ] If Company A does not invest, Company B's best response is [ Select ] At this outcome, Company B receives a payoff of [Select ] Does Company B have a dominant strategy? If so, what is it? [ Select ] Given that the companies know each other's payoffs, Company A will choose to [ Select ] The outcome of the game will be that [ Select ]

PLAYER B COOPERATE DEFECT A: 1 year jailA: 10 years jail B:1 year jail B: 0 years jail A: 0 years jail A: 5 years jail B: 10 years jail B: 5 years jail If this game represents the results of two players who have been arrested and interrogated by police and offered a lower sentence if they cooperate with the investigation, what is the most likely outcome? neither player will cooperate Only player A will cooperate both players will cooperate with police Only player B will cooperate PLAYER A DEFECT COOPERATE

In a sideshow game. A player gets 3 balls to place into a Clown's mouth. Each ball is swallowed by the Clown and is then deposited into slots that can hold only 1 ball. Slots are numbered 1 to 9 and prizes are allocated to a player depending on the slot value of the three balls. If for example the first ball landed in slot 8, the second in slot 2 and the third in slot 1, the resulting prize number would be 821 as shown in Figure 3. 3rd 2nd 1st dol 1 2 3 4 5 6 7 8 9 Figure 3: A prize number of 821 is shown for a side show game. a) How many resulting prize numbers are possible in this game? b) How many resulting prize numbers are possible that end with the number 1?

Consider a game between player A with a choice between moves d₁, d2 and d3, and player B with a choice between 81, 82 and 83, and the following pay-off matrix: 81 82 83 d₁ (3,2) (2,0) (1,-1) d2 (1,0) (3,1) (2,-2) d3 (0,0) (2,3) (1,2) Is that game solvable? (We consider strong Pareto optimality for that question.) Oa. The game is solvable in the strict sense, with solutions (d₁, 1, (d2, 62) O b. The game is solvable in the strict sense, with solution (d₁, 81) О с. The game is solvable in the completely weak sense, with solutions (d₁, 1), (d2, 82) The game is solvable in the strict sense, with solutions (d1, 61), (d3, 82), (d2, 82) Od. O e. The game is solvable in the completely weak sense, with solutions (d₁, 81), (d3, 82), (d2, 62), (d3, 83) O f. The game is not solvable Og. The game is solvable in the completely weak sense, with solutions (d₁, 61), (d3, 62), (d2, 82) Oh. The game is solvable in the strict sense, with solutions (d1, 81), (d3, 82)

Question 19 Consider the following Extended Form Game: 05 02 06 O A' 7 (9,5) A P2 P1 B' A' B (5,2) (8,5) A (1,6) P2 Player 1 plays (B,B). Player 2 plays her best response. What is the payoff player 1 recieves? B' P1 B (6,7)

Hello, please help me to solve part (d) and (e):Charlie finds two fifty-pence pieces on the floor. His friend Dylan is standing next to him when he finds them. Chris can offer Dylan nothing at all, one of the fifty-pence pieces, or both. Dylan observes the offer made by Charlie, and can either accept the offer (in which case they each receive the split specified by Charlie) or reject the offer.If he rejects the offer, each player gets nothing at all (because Charlie is embarassed and throws the moneyaway).(a) Formulate this interaction as an extensive-form game. To keep things simple, players’ payoff is equal to their monetary gain.(b) List all histories of the game. Split these into terminal and non-terminal histories.(c) What are the strategies available to Charlie? What are the strategies available to Dylan? Draw the strategic-form game.(d) Find the pure-strategy Nash equilibria of this game.(e) What do you think will happen?

Consider a sequential game between a shopkeeper and a haggling customer. The party who moves first chooses either a high price ($50) or low price ($20) and the second mover either agrees to the price or walks away from the deal and neither party gets anything. Ignore costs and assume the customer values the item at $60.​If the shopkeeper goes first and quotes a low price, what is the best response of the customer? Question 33 options: a)​Slam the storeowner's door on the way out b)​Laugh at the storeowner c)​Walk away from the deal d)​Accept the low price happily Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.

Economics Consider an infinitely repeated game played between two firms with the following payoffs (firm 1 is listed first): ·         (250, 290) if both firms deviate ·         (290, 330) if both firms cooperate ·         (230, 370) if only firm 2 deviates ·         (350, 270) if only firm 1 deviates a. What probability-adjusted discount factor would ensure that Firm 1 would cooperate in a Nash equilibrium if Firm 2 applied a trigger strategy in the event that Firm 1 deviated?  b. What probability-adjusted discount factor would ensure that Firm 2 would cooperate in a Nash equilibrium if Firm 1 applied a trigger strategy in the event that Firm 2 deviated?

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Firm B Q=5 Q=6 Q=5 (24, 24) (30, 10) Q=6 (10, 30) (19, 19) Firm A This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide how much output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A, Profit for Firm B). Refer to Table. The dominant strategy For Firm A is to produce 5 units and the dominant strategy for Firm B is to produce 6 units. 5 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 6 units.

Problem 4: Consider an infinitely repeated game, where the base game is the following 2-person 2x2 game: A A 0,0 10, 10 S1: choose A always S2: choose B always B 10, 10 0,0 Assume both players discount the future at the same rate of r, 0 < r < 1. Limiting each player's strategies to the following six possibilities, S3: Choose A then mimic the other player's previous choice S4: Choose B, then mimic the other player's previous choice S5: Choose A, then choose the opposite of the other player's previous choice S6: Choose B, then choose the opposite of the other player's previous choice a. present the strategic form of this game, b. identify all pure-strategy Nash equilibria c. does repetition with these strategies "solve" the coordination dilemma that confronts the players in the single play of the above game.

Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. The table below represents the choices available to Jane and Bill. If Jane trusts Bill to stay silent, what should she do? If Jane thinks that Bill will confess, what should she do? Does Jane have a dominant strategy?  A = Confess;  B = Stay Silent. (Each results entry lists Janes sentence first (in years), and Bill's sentence second.)            A A    (30,30)      A B  (35,15)        B A    (15, 35)   B B  (20, 20)

Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will be each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. The table below represents the choices available to Jane and Bill. If Jane trusts Bill to stay silent, what should she do? A = Confess; B = Stay Silent (Each results entry lists Janes's sentence first (in years), and Bill's sentence second.)   Jane A B Bill A (30, 30) (15, 35) B (35, 15) (20, 20)

Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will be each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. Table 10.7 below represents the choices available to Jane and Bill. If Jane trusts Bill to stay silent, what should she do? If Jane thinks that Bill will confess, what should she do? Does Jane have a dominant strategy? Does Bill have a dominant strategy? A = Confess; B = Stay Silent. (Each results entry lists Jane’s sentence first (in years), and Bill's sentence second.)

Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will be each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. The table below represents the choices available to Jane and Bill.   Which criminal(s) have a dominate strategy to cheat?  A = Confess; B = Stay Silent. (Each results entry lists Janes's sentence first (in years), and Bill's sentence second.)   Jane A B Bill A (30, 30) (15, 35) B (35, 15) (20, 20) Question 3 options:   Only Bill has a dominate strategy so he should cheat   Only Jane has a dominate strategy so she should cheat   Both Bill…

Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will be each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. Table 10.7 e below represents the choices available to Jane and Bill. A = Confess; B = Stay Silent. (Each results entry lists Bill's sentence fırst (in years), and Jane's sentence second). Answer the following: Jane A B A (30, 30) (15, 35) Bill (35, 15) (20, 20) Table 10.7 a) If Jane trusts Bill to stay silent, what should she do? b) If Jane thinks that Bill will confess, what should she do? c) Does Jane have a dominant strategy? Does Bill have a dominant strategy? Justify your answer.

Jane and Bill are apprehended for a bank robbery. They are taken into separate rooms and questioned by the police about their involvement in the crime. The police tell them each that if they confess and turn the other person in, they will receive a lighter sentence. If they both confess, they will be each be sentenced to 30 years. If neither confesses, they will each receive a 20-year sentence. If only one confesses, the confessor will receive 15 years and the one who stayed silent will receive 35 years. The table below represents the choices available to Jane and Bill.  If Jane thinks that Bill will confess, what should she do? A = Confess; B = Stay Silent. (Each results entry lists Janes's sentence first (in years), and Bill's sentence second.)

a) Return to the two-player game tree in part (a) of Exercise U2 in Chapter 3. (a) (b) Write the game in strategic form, making Albus the Row player and Minerva the Column player. Find all Nash equilibria. For those equilibria you found in part (a) of this exercise that are not subgame-perfect, identify the reason. 13,0 a MINERVA 12,1 N 1,1 a MINERVA ALBUS E S MINERVA 15,0 20 a 4,4 b 1,5

(d) Consider a simultaneous-move game between two firms choosing to sell their product at either £6, £7 or £8. The actions and payoffs are given in the matrix below. Firm 2's Prices £6 £7 £8 Firm 1's prices £6 4, 5 3, 5 2, 1 £7 0,4 2, 1 3,0 £8 -1, 1 4, 3 0, 2 What are the Nash equilibria of this game? Game theory is often used by firms competing under an oligopoly as a means of determining their best strategy. Why is game theory a useful tool and which characteristics of an oligopoly make it particularly useful for firms competing in this market structure? One outcome of an oligopoly is that firms may have an incentive to collude. Explain some of the conditions that make collusion more likely to occur and how game theory can explain why collusive agreements often break down.

QUESTION 2 In the game above, what is/are the sub-game perfect Nash equilibrium? (up, up) (up, down) ( down, up) (down, down) No equilibrium exists QUESTION 2 Up Down Player 1 No equilibrium exists Up In the game above, what is/are the sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) □ (down, down) Down Up Down Player 2 P1 gets $45 P2 gets $155 P1 gets $100 P2 gets $10 P1 gets $85 P2 gets $85 P1 gets $95 P2 gets $95

Use this information for questions 19-22. Consider the Acid Rain Game with new payoffs below. Total net benefits are given in the payoff matrix below. Country B $96 O $108 $90 Low $120 Abatement High Abatement Country A Low Abatement A: $20 B: $10 A: $21 B: $7 Imagine Country B discounts future profits at d=0.9. If you know that Country A will use the grim reaper punishment, what is the present value of net benefits from deviating for Country B? High Abatement A: $14 B: $18 A: $22 B: $12

A game involves two players: player A and player B. Player A has three strategies a1, a2 and a3 while player B has three strategies b1, b2 and b3.       Player B         b1 b2 b3     a1 -40,30 70,20 -10,120   Player A a2 40,60 80,80 60,20     a3 -30,40 -50,110 150, -70               Assuming that this is a one-time game, answer the following questions: Is there any dominant strategy for each player? What is the secure strategy of each player. What is the Nash equilibrium of the game?

3. Consider the game represented by the payoff matrix below: R S (12, 12) (8,-5) (25, 14) (50, 12) (26,70) (-2.6) (20, 100) (22,75) C (11,0) (3,25) (24, 26) (50,26) D (5,-10) (16,-8) (13,-8) (50,-20) A B a. Find the Nash equilibria of the game using any suitable method. b. Apply Iterated Elimination of Strictly Dominated Actions (IESDA) to this game. Explain the steps as necessary. Do the Nash equilibria found in part a. survive IESDA? c. Apply Iterated Elimination of (Weakly) Dominated Actions (IEDA) to this game by elim- inating all whakly dominated actions in each round. Explain the steps as necessary. Do the Nash equilibria found in part a, survive IEDA

Final Quiz 2 Item 18 of 30 What is the best strategy in this game? Select the correct response: nts Japan's production is high = 40 M profit, China's production is low = 20 M profit Japan's production is low = 20 M profit, China's production is high = 40 M profit Japan's production is high = 30M profit, China's production is high = 30 M profit O Japan's production is low = 35 M profit, China's production is low = 35 M profit < Previous Type here to search O Ei

Consider the Stackelberg game depicted below in which you are the row player. R U 4,0 1,2 3,2 0,1 0,0 2,0 You may choose whether you want to be the leader (and commit to a possibly mixed strategy) or the follower in a game against the course staff (column player). You may trust that we maximize our expected payoff. The points awarded to you will equal one half of the expected payoff you obtain. If you want to be the leader, please submit your commitment strategy. For example, if you want to commit to [0.5: U, 0.2: M, 0.3: D], then submit: 0.5 0.2 0.3 If you want to be the follower instead, just submit: F

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

The following table contains the possible actions and payoffs of players 1 and 2. Player 2 Cooperate Player 1 Cooperate Not Cooperate 15, 15 20, -10 Not Cooperate -20, 20 10, 10 This game is infinitely repeated, and in each period both players must choose their actions simultaneously. If both players follow a tit-for-tat strategy, then they can Cooperate in equilibrium if the interest rate r is ✓. At an interest rate of r=0.5, If instead of playing an infinite number of times, the players play the game only 10 times, then in the first period player 1 receives a payoff of

Table 3. This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide how much output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A. Profit for Firm B). Firm A Q=5 Q=6 Firm B Q=5 (24, 24) (30, 10) Q=6 (10,30) (19, 19) Refer to Table 3. The dominant strategy For Firm A is to produce Select one: O a. 5 units and the dominant strategy for Firm B is to produce 5 units. b. 5 units and the dominant strategy for Firm B is to produce 6 units. c. 6 units and the dominant strategy for Firm B is to produce 5 units. d. 6 units and the dominant strategy for Firm B is to produce 6 units.

How many strategies does a player have in the repeated Prisoner's Dilemma Game with horizion 2 ?  How many strategies does a player have in the repeated Prisoner's Dilemma Game with horizion 3 ?

3. Two players play the following game for infinite times. Cooperate Betray Cooperate 10, 20 -25, 30 Betray 15, -23 -12, -19 For the player to continue to cooperate what would be the ranges of their discount factor, 8, and 82, respectively?

Question 16 Consider the following Extended Form Game: A' (9,5) O {(A,B), (A', B')} A P2 B' 'A' O {(B,B), (A', B')} P1 (5,2) (8,5) B A (1,6) P2 B' P1 B What is the Subgame Perfect Nash Equilibrium? (6,7) O {(A,A), (A', A)),((A,B), (A', A')), ((A,A), (A', B')).((A,B), (A', B'))} O (((B,A), (A', A')).((B,B), (A', A')), ((B,A), (A', B')), ((B,B), (A', B'))}

Question: Determine the set of rationalizable strategies for each of the following games. Player 2 Player 2 (0, 4) (3, 3) (4, 0) Player 2 (2,0) (3, 4) (1,3) (4, 2) (2, 3) (4,0) (3, 3) (0, 4) (1,1) Player 1 Player 1 (1,2) (0,2) | (3,0) Player 2 D D (5, 1) | (0, 2) | Player 1 (4, 6) (3, 5) (6, 3) (0, 1) (2,1) Player 2 (8, 6) (1,0) (0,8) (8, 2) (0, 1) (2, 6) (5, 1) (4, 4) (1,0) Player 1 (6,0) (2,8) D D Player 2 (8, 10) (6, 4) (2, 2) (0,0) (0,0) (3,3) (4, 1) (8, 5) Player 1 Player 1 B B Player 2 Player 2 (8, 10) (6, 4) (3, 10) (6, 4) (4, 1) (8, 5) (4, 1) (8, 5) Player 1 A Player 1 B B