Suppose Yakov and Ana are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Yakov chooses Right and Ana chooses Right, Yakov will receive a payoff of 6 and Ana will receive a payoff of 6. Yakov Loft Right Left 2,3 3,7 Ana Right 4,4 6,6 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Yakov chooses and Ana chooses
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- Suppose Carlos and Deborah are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Carlos chooses Right and Deborah chooses Right, Carlos will receive a payoff of 6 and Deborah will receive a payoff of 5. Deborah Left Right Carlos Left 8, 4 4, 5 Right 5, 4 6, 5 The only dominant strategy in this game is for to choose . The outcome reflecting the unique Nash equilibrium in this game is as follows: Carlos chooses and Deborah chooses .Suppose Edison and Hilary are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that Edison chooses Right and Hilary chooses Right, Edison will receive a payoff of 3 and Hilary will receive a payoff of 7. Hilary Left Right Left 4, 6 6, 8 Edison Right 7, 5 3, 7 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Edison chooses and Hilary choosesSuppose Andrew and Beth are playing a game in which both must simultaneously choose the action Left or Right. The payoff matrix that follows shows the payoff each person will earn as a function of both of their choices. For example, the lower-right cell shows that if Andrew chooses Right and Beth chooses Right, Andrew will receive a payoff of 5 and Beth will receive a payoff of 5. Beth Left Right 6, 6 Right 4, 3 Left 6, 3 Andrew 5, 5 The only dominant strategy in this game is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Andrew chooses and Beth 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 shows 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 Dina 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 choosesSuppose 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.Suppose Antonio and Trinity 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 Antonio chooses Up and Trinity chooses Down, Antonio will receive a payoff of 7 and Trinity will receive a payoff of 5. Trinity Up Down Up 4,8 7,5 Antonio Down 3,2 5,6 In this game, the only dominant strategy is for to choose The outcome reflecting the unique Nash equilibrium in this game is as follows: Antonio chooses, and Trinity chooses Grade It Now Save & Continue Continue without saving @ 2 F2 #3 80 Q F3 MacBook Air 44 F7 Dll F8 44 F10 74 $ 4 05 Λ & % 5 6 7 8 * 0 Q W E R T Y U 1 A N S X 9 0 -O O D F G H J K L on را H command C > B N M Λ - - P [ H Λ command opti
- 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.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?Suppose that Kim and Nene 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 Nene and Kim 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 Nene make if she and Kim both play tit‑for‑tat? $ Over four seasons, how much does Nene make if she always exposes and Kim plays tit‑for‑tat? $ Over four seasons, how much will Nene make if she plays a tit‑for‑tat strategy and Kim always exposes? $ Over four seasons, how much will Nene make if she and…
- Alice and Julia want to spend time together but have different preferences for their activities. They can choose between two options: going to a soccer game or watching a football game. Alice prefers football and Julia prefers the football game, but they both prefer being together over being apart. If they both choose to attend a soccer game then Julia receives a payoff of 2 and Alice a payoff of 1. If they both choose to attend a football game, then Julia receive a payoff of 1 and Alice a payoff of 2. If one chooses a football game and the other a soccer game then they both receive a payoff of O. The payout matrix below illustrates these payoffs. Which of the following statements are true: I. There is a dominant strategy II. A nash equilibrium exists where Alice attends a football game and Julia attends a soccer game III. A nash equilibrium exists where both friends attend a soccer game IV. Both attending a football game is a stable outcome. Alice Soccer Football Julia Soccer Football…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…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? $________