Player 1 Player 2 L R U 2,4 D 6,2 4,2 2,4 why this game has no pure strategy Nash Equilibrium. e mixed strategy Nash Equilibrium. e now player 1 chooses his strategy first, player 2 observes this her choice. re any pure strategy Nash equilibria in this sequential game?
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- if Z = 3 (a) How many pure strategy profiles exist in this game? (b) In the unique subgame perfect Nash equilibrium, what is the sum of the payoffs to the two players?Consider a symmetric game with 10 players. Each player chooses among three strategies: x, y, and z. Let nx denote the number of players who choose x, ny denote the number of players who choose y, and nz denote the number of players who choose z. (So, nz = 10−nx−ny.) The payoff to a player from choosing strategy x is 10−nx (note that nx includes this player as well), strategy y is 13−2ny (again ny includes this player as well), and strategy z is 3. (a) Show that a Nash equilibrium must have at least one person choosing x and at least one person choosing y. (Hint: In a Nash equilibrium, no player can do better by doing something different.) b) Find all Nash equilibria.What is the pure strategy Nash equilibrium outcome if there is one Is this a socially optimal outcome? If not, which outcome is preferred
- Consider the following game. The first number (before the comma) is the payoff to the row player and the second number (after the comma) is the payoff to the column player. The Nash equilibrium(s) are: A B A 4,4 3,3 B 3,3 5,5 Group of answer choices: -(A,A) and (B,B) -(A,A) only -There are no Nash equilibriums. -(B,B) onlyIn a Stackelberg game, what is the best response that follower firm 2 can make to the choice y1 already made by the leader, firm 1?Consider the department store market in Sydney. Two players, David Jones and MYER, are deciding the prices for their new seasonal collection. They could choose either high or low pricing strategy. The payoffs are given by the following table. The first payoff is for David Jones. MYER David Jones Low High Low 6,6 7,4 High 4,8 8,9 5. If David Jones and MYER decide simultaneously, which of the following is true? a) There are two Nash equilibria in this game. b) There is no Nash equilibrium. c) Both shops have a dominant strategy to high pricing strategy. d) There is a unique Nash equilibrium. e) None of the other answers is correct.
- Consider the following normal form of the game with two players. What is the Nash Equilibrium of this game?In Hotelling's Ice Cream Truck game. Assume there are 9 spots: {-4, −3, −2, −1, 0, 1, 2, 3, 4}Assume there are two customers at each spot (18 in total). In a Nash equilibrium, each truck will locate at 0. How many customers would truck A lose by deviating and moving from position 0 to position 1. Select one: a.none of the other answers. b.3 c.1 d.0 e.2if w = 6 (a) This game has a unique (pure strategy) Nash equilibrium ⟨t*1 , t*2 ⟩ in which t*1 = t*2 Find the value of t*1 . (If your answer is a fraction, report it in lowest terms.) (b) To which strategy t2 is the strategy t1 = 4 a best response? (If your answer is a fraction, report it in lowest terms.)
- Consider a modified version of the board game RISK in which player A is attacking player B. At the beginning of each turn, player A rolls N 4-sided dice where N+1 is the number of armies that player A has (So if A has 3 armies, A starts by rolling 2 4-sided dice). Player B always rolls a single 6-sided die. If the biggest roll among the dice that A rolls is bigger than player B's roll, then player B loses an army. If all of player A's rolls are less than player B's roll, then player A loses an army. If it is a tie, neither player loses an army. The rolls are repeated until either B has no armies (A has captured the territory) or A has only one army (the attack has been repelled). If A has two armies and B has one army find the probability for each event: A loses an army, B loses an army and neither lose an army If A has three armies and B has one army find the find the probability for each event: A loses an army, B loses an army and neither lose an army If A has three armies and…A three-finger Morra game is a game in which two players simultaneously show one, two, or three fingers at each round. The outcome depends on a predetermined set of rules. Here is an interesting example: If the numbers of fingers shown by A and B differ by 1, then A loses one point. If they differ by more than 1, the round is a draw. If they show the same number of fingers, A wins an amount equal to the sum of the fingers shown. Determine the optimal strategy for each player. (Enter your probabilities as fractions.) Player A should show one finger with probability _____ , two fingers with probability _____ , and three fingers with probability ______ . Player B should show one finger with probability _______ , two fingers with probability ________ , and three fingers with probability ________ . Find the expected value of the game. The expected outcome is the player A will win __________ points per round, on average.Model the situation as a strategic game assuming that both ‘James’ and ‘Robert’ are altruistic, ranking outcomes according to the other person’s comfort and, out of politeness, prefer to stand than to sit if the other person stands. Model the situation as a strategic game and find any Nash equilibrium (equilibria) if it exists. Does a dominant strategy exist for either ‘James’ or ‘Robert’ with these preferences? Show all steps and working in support of the answerContext:The London Metro Bus is crowded for travel during peak hours. During such travel hours two daily passengers ‘James’ and ‘Robert’ enter the Metro. Luckily, two adjacent seats are free in the bus. Each of them must decide whether to sit or stand. For both, sitting alone is more comfortable than sitting next to the other person, which in turn is more comfortable than standing. consider james as "Row Player" and Robert as "Column Player"