5 3 (1,1) 4 2 (2,3) B (4,5) What is the payoff that player 1 derives from the strategy (B. (A'A')) P2 (6,7)
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![Consider the following Extended Form Game:
5
3
(1,1)
1
2
(2,3)
P1
A'
(4,5)
What is the payoff that player 1 derives from the strategy {B, (A,A')]?
P2
(6,7)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e8aa205-32aa-4f07-9b5c-13bb56a777db%2F9b16af40-6ca8-4c5f-a3f0-d83daa9057e2%2Fffwa9ks_processed.png&w=3840&q=75)
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- If you played the game in Exercise 1 many times, then you would expect your average payoff per game lo be about $ ____________.In 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 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…
- Consider a new card game between 2 players: Jim (player 1) and Angella (player 2) Jim is dealt two cards : ♡8 and ♠️9 . Angella is also dealt two cards: ♢6 and ♣️6 . Now, each of the players will play 1 card both at the same time. The payoff of Jim is 4 points if he plays a card of opposite color (red/black) than Angella, and otherwise his payoff is 10 points. The payoff of Angella is 3 points if the difference of the already played card numbers is greater than 4, otherwise her payoff is 2 points. 1. Find the Best Responses for Angella.2. Find all the Nash Equilibriums of the game (if any).Consider a two-player game that is set up with two piles of stones. The two players are taking turns removing stones from one of the two piles. In each turn, a player must choose a pile and remove one stone or two stones from it. The player who removes the last stone (making both piles empty) wins the game. Show that if the two piles contain the same number n ∈ Z+ of stones initially, then the second player can always guarantee a win.A has four shares in a lottery in which there are four prizes and five blanks. B has `3` shares in another lottery in which there are three prizes and four blanks.Which has the better chance of winning exactly one prize? Which will have better chance of winning exactly two prizes?
- 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.Suppose you and I play the game rock-paper-scissor twice. Assume mixed strategies (randomizing among the three actions) are not allowed. How many strategies do you have? Please show by table using the rock-paper-scissors game how the conclusion was arrived at.