Which of the following is TRUE? O As is a dominant strategy for Player A. O The game has dominant equilibrium A3, B3. A3 dominates A₂. O B3 is a dominant strategy for Player B.
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- Consider the following sequential game. There are two players, Player 1 and Player 2, who alternate turns, Each turn, each player can choose one of two actions: Across (A) or Down (D). If either player chooses D on their turn, the game ends. Otherwise, it becomes the other player's turn, who may again play either A or D. The game ends after 100 turns for each player, if no player has played D previously. Payoffs in the game are represented by the following game tree, where nodes denote turns for each player, branches denote actions, and final payoffs are indicated at the end of each branch (Player 1's payoff is the first number, Player 2's payoff is the second): 100 100 ID D. D 98 98 97 100 99 99 98 101 Note that the sum of payoffs for each player is increasing by 1 each turn. However, a player claims a slightly larger payoff if the game ends on their turn, rather than their opponent's. Assuming that both players strictly apply the principle of backward induction, what payoffs will the…Consider the following game (anachronistically) called the battle of the sexes. Two brothers, Shahid and Jamil are spending their weekend in Philadelphia, but they have lost communication with each other and Shahid is coming from New York where Jamil is coming from Washington DC. They are trying to find out where they should meet when they arrive in Philadelphia: they want to meet up, and both know that Shahid prefers meeting at Reading Terminal Market (he's a foodie!) and Jamil prefers meeting at the Rocky Steps (he's a movie buff!). Not meeting up though would be the worst outcome as it's the city of brotherly love. Suppose the game is represented by the following payoff matrix with Jamil the row player: Rocky Steps Reading Terminal Market Rocky Steps 2,1 0,0 Reading Terminal Market 0,0 1,2 What is the expected value for each player in the mixed strategy Nash equilibria? 4/3 1.5 2 1 1/3A city police department and a gang of drug dealers play a game every day where the police must decide whether to focus their department resources on either street patrol or parks patrol, and the drug gang must make the same decision regarding where to focus their drug selling activities. If both focus on street sales the police make 90 arrests and the dealers avoid 10 arrests. If both focus on park selling. The police arrest 80 dealers and 20 dealers avoid capture. If the PD focuses on streets, while the DDs focus on parks, 5 arrests are made and 95 dealers escape arrest. If the PD focuses on parks while the DD focus on streets, then 10 arrests are made and 90 dealers get away. a) Find the Nash equilibrium in mixed strategies for the police department and for the drug dealers. b) Explain in simple terms what will play out in this game between the PD and the DDs. c) If the PD gets better at park patrol (measured by more arrests in parks than before), in which direction will the…
- Each Othello piece has a black side and a white side. Here is how Othello is played.A piece is considered to be caught when it is encircled by its rivals on both the left and right sides, or both the top and bottom, and when its colour is reversed. You must capture at least one throughout your turn. any of your adversary's pieces. When neither player has any further move options, the game is over. The player who has the most pieces is declared the winner. Put Othello's object-oriented design into practice.Consider the following scenarios. A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed, the student opens it. After all the students have taken turns, some of the lockers are open and some are closed. The program, when ran, will prompt the user to enter the number of lockers in the school. After the game is over, the program will output the number of lockers…Consider the following scenario: A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed, the student opens it. After all the students have taken turns, some of the lockers are open and some are closed. The program below, when ran, will prompt the user to enter the number of lockers in the school. After the game is over, the program will output the number of…
- 3. Construct your own two-player 2 x 3 game in which none of the actions of either player is weakly dominated by another action, but one of the (three) actions of player 2 is strictly dominated by a mixed strategy. Then find all mixed strategy Nash equilibria of your game.Find the Nash equilibria, including any mixed strategy equilibria that might exist, for the following strategic-form games. 1. Curve Slider 1, 2 0,3 2,1 Fast Early 3,0 2,1 1, 2 2,1 1, 2 3,0 Mid Late 2. Nice Mean 0,3 1,1 Nice 3,3 3,0 Mean 3. Beef Fish Red 3,3 White 1,2 0,1 2,0 Fight х, 2 1,1 2, x Train Fight Train 0,0 4.Raghu and Sayan both like to eat (a lot) but since they are also looking after their health, they can only eat a limited amount of calories per day. So when Kuldeep invites them to a party, both Raghu and Sayan decide to play a game. The game is simple, both Raghu and Sayan will eat the dishes served at the party till they are full, and the one who eats maximum number of distinct dishes is the winner. However, both of them can only eat a dishes if they can finish it completely i.e. if Raghu can eat only 50 kCal in a day and has already eaten dishes worth 40 kCal, then he can't eat a dish with calorie value greater than 10 kCal.Given that all the dishes served at the party are infinite in number, (Kuldeep doesn't want any of his friends to miss on any dish) represented by their calorie value(in kCal) and the amount of kCal Raghu and Sayan can eat in a day, your job is to find out who'll win, in case of a tie print “Tie” (quotes for clarity). Input:First line contains number of test…
- Write Algorithm FOR An iterative solution to Towers of Hanoi.in: triplet S = s0, s1, s2 representing the current game stateout: triplet R = r0, r1, r2 representing the new game stateConsider the following scenario:A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, thestudent opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed, the student opens it. After all the students have taken turns, some of the lockers are open and some are closed. The program see in the photo, when ran, should ask the user to enter the number of lockers in the school. The program will output the number of lockers and the…Colonel Blotto and Count Baloney are opposing commanders in a battle. There are three locations valued 1, 2, 3, and each comman- der has two military units to deploy (both to the same location or split to different locations). If one commander sends more units to a location than the other, that commander captures the location and wins its value. If both commanders send the same number of units to a location, it is not captured and nothing is won at this location. (a) Model this conflict as a zero-sum matrix game. (b) Use the method of eliminating dominated (not necessarily strictly dominated!) strategies to reduce this to a 1 ×1 game. (c) What strategy would you recommend to these commanders and why?