Consider a game in which two players simultaneously pick an integer from 1 through 10. Let s1 denote choice of player 1, and let s2 denote the choice of player 2. If s1 # 82 then player 1's payoff is: 81 + 82 2 and player 2's payoff is 81+ 82 10 – If s1 = 82 then each player gets 5. How many pure strategy Nash equilibria does the game have (you will get full points if you are within 2 of the correct answer)?
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- Consider the game of Chicken in which each player has the option to “get out of the way” and “hang tough” with payoffs: Get out of the way Hang tough Get out of the way 2,2 1,3 Hang tough 3,1 00 a. Find all pure strategy Nash equilibria, if they exist b. Let k be the probability that player 1 chooses “hang tough” and u be the probability that player two chooses “hang tough.” Find the mixed stragety Nash equilibria, if they existPLAYER B LEFT RIGHT UP 5 FOR A, 30 FOR B 10 FOR A, 12 FOR B PLAYER A DOWN -2 FOR A, 10 FOR B 8 FOR A, 15 FOR B In the above game, the players are seeking to maximize the number they recieve. They choose at the same time. What is the Nash equillibrium? Player A will choose UP and player B will choose LEFT Player A will UP and player B will choose RIGHT Player A will choose DOWN and player B will choose LEFT Player A will choose DOWN and player B will choose RIGHT Player A will choose LEFT and player B will choose UP Player A will choose LEFT and player B will choose DOWN Player A will choose RIGHT and player B will choose UP Player A will choose RIGHT and player B will choose DOWNConsider 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
- Please find herewith a payoff matrix. In each cell you find the payoffs of the players associated with a particular strategy combination: The first entry is the payoff of player 1, the second entry is the payoff of player2. Player 2 t1 t2 t3 Player 1 S1 3, 4 1, 0 5, 3 S2 0, 12 8, 12 4, 20 S3 2, 0 2, 11 1, 0 Suppose both players select their strategies (S1, S2 or S3 for player 1 and t1, t2 or t3 for player 2) simultaneously and that the game is played once. In your explanation to the questions below, please do refer to the figures in the matrix. Suppose player 2 could move before player 1 (i.e. has a first mover advantage). In your explanation to the questions below, please do refer to the figures in the matrix. What strategy would (s)he select? Is it really an ‘advantage’ for player 2 to move first? Or does player 2 benefit from being the second mover (and hence player 1 moving first)? I.e. for this question, do not make a comparison to the outcome of the…There are three players who must each choose an “effort” level from 1 to 7, that is, Si = {1, 2, 3, ..., 7}. The payoff for each player i is ui(si, s−i) = 10 max{s1, s2, s3} − si. How many pure- strategy Nash equilibria are there? Select one: a.2 b.4 c.none of the other answers d.3 e.110 1. Consider the game where initially She chooses between "Stay Home" and "Go Out". If She chooses "Stay Home" then She gets 2 and He gets 0. If She chooses "Go Out" then they each simultaneously choose "Movie" or "Concert" where the payoffs are 0,1 or 3 as in the Battle of the Sexes Game. What are the subgame perfect Nash Equilibria of this game ?
- Two players bargain over $20. Player 1 first proposes a split of(n, 20 - n), where n is an integer in {0, 1, ..., 20}. Player 2 can either accept or reject this proposal. If player accepts it, player 1 obtains $n and player 2 obtains $(20 - n). If player 2 rejects it, the money is taken away from them and both players will get $0. Question: Find two subgame perfect Nash equilibria of this game and state clearly each player's equilibrium strategies (recall that in a dynamic game, a player's strategy is a complete-contingent plan). Explain why the strategy profiles form a subgame perfect equilibrium.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…The count is three balls and two strikes, and the bases are empty. The batter wants to maximize the probability of getting a hit or a walk, while the pitcher wants to minimize this probability. The pitcher has to decide whether to throw a fast ball or a curve ball, while the batter has to decide whether to prepare for a fast ball or a curve ball. The strategic form of this game is shown here. Find all Nash equilibria in mixed strategies.
- Consider a game with two players (Alice and Bob) and payoffffs Bob Bob s1 s2 Alice, s1 3, 3 0, 0 Alice, s2 0, 0 2, 2 In the equilibrium in the above game, Alice should (A) always choose the fifirst strategy s1; (B) choose the fifirst strategy s1 with probability 40% ; (C) choose the fifirst strategy s1 with probability 50% ; (D) choose the fifirst strategy s1 with probability 60% .1.a) If the three executives of a fraudulent organization report nothing to the authorities, each gets a payoff of 100. If at least one of them blows the whistle, then those who reported the fraud get 28, while those who didn’t get -100. Suppose they play a symmetric mixed-strategy Nash equilibrium where each is silent (does not report fraud) with probability p. What is p?A, 0.1B, 0.28C, 0.5D, 0.8 b) In a two-player game, with strategies and (some known and some unknown) payoffs as shown below, suppose a mixed-strategy equilibrium exists where 1 plays C with probability 3/4, and Player 2 randomizes over X, Y, and Z with equal probabilities. What are the pure-strategy equilibria of this game? A, (A, Y) and (B, X)B, (A, Z) and (C, Y)C, (B, X) and (C, X)D, (C, X) and (C, Y)if Y = 4 (a) If ⟨a,d⟩ is played in the first period and ⟨b,e⟩ is played in the second period, what is the resulting (repeated game) payoff for the row player? (b) What is the highest payoff any player can receive in any subgame perfect Nash equilibrium of the repeated game?