CH_asInvoice

please  if you can teach explain

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on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.

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Consider the following game between Visa and Mastercard. They are trying to decide whether to invest in "Chip" technology. Which of the following statements is true about the outcome of the game? (Visa's payoffs are given to the left of the comma, and Mastercard's payoffs are given to the right of the comma.) Mastercard Invest Don't Invest Visa Invest -100, -100 450, 50 Don't Invest 50, 450 50, 50 O The game has two Nash Equilibria and neither firm has a dominant strategy. O The game has two Nash Equilibria and the game is an example of a prisoner's dilemma. O None of the answer choices are consistent with the game's outcome. O The game has one Nash equilibrium and is an example of a prisoner's dilemma. O The game has one Nash equilibrium and neither firm has a dominant strategy.

a) Write out the extensive form of a game between a farmer (playing in the first round) and nature (playing a mixed strategy in the second round).  Assume that the farmer can either pay a cash rent of $1500 for land (English system) or 1/2 of crop production to the landlord (sharecropping).  Assume the farmer is planting corn and will produce 2 tons of corn.  Assume that nature has a 50% chance of playing a strategy in which the price of corn is $3500/ton and a 50% chance of playing a strategy in which the price of corn is $500/ton.  The farmer keeps any money left after paying cash rent and sells any corn left after paying the landlord in sharecropping. b)What is the most that a risk neutral farmer would be willing to pay for an accurate prediction of the price of corn in problem 1 before choosing whether to pay cash rent or sharecrop?

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4). The following is a payoff matrix showing profit in millions of dollars when two companies simultaneously decide on various advertising budgets ($1 million, $2 million, or $3 million): a.   In the first round of strategy elimination (when all three possible budgets are under consideration), which ad budget would the companies exclude? b.   After the first round of elimination (previous question), would either company make a second-round elimination? c.   What would be the likely outcome of this simultaneous advertising decision (i.e. what ad budget would each company end up choosing)?

Please try to solve in 2 hours

Write out the extensive form of a game between a farmer (playing in the first round) and nature (playing a mixed strategy in the second round).  Assume that the farmer can either pay a cash rent of $1500 for land (English system) or 1/2 of crop production to the landlord (sharecropping).  Assume the farmer is planting corn and will produce 2 tons of corn.  Assume that nature has a 50% chance of playing a strategy in which the price of corn is $3500/ton and a 50% chance of playing a strategy in which the price of corn is $500/ton.  The farmer keeps any money left after paying cash rent and sells any corn left after paying the landlord in sharecropping. What is the most that a risk neutral farmer would be willing to pay for an accurate prediction of the price of corn in problem 1 before choosing whether to pay cash rent or sharecrop?

sub question : a, b, c

You and I play the following game. Hidden from you, I put a coin in my hand: with probability p it is a 10 pence coin and otherwise it is a 20 pence coin. You now guess which coin is in my hand: you guess it is 20 pence with probability s and otherwise you guess it is a 10 pence coin. You get to win the coin if you guess correctly and otherwise win nothing. What (in terms of p and s) is your expected gain in pence from playing this game once with me? Challenge: suppose we are going to play repeatedly and you want to maximise your gain and I wish to minimise my loss. What value of p should I choose and what value of s should you choose? (This question is somewhat ill-defined, but it does have an interesting possible answer.) (Note: anything labelled "challenge" will not be part of the hand-in.)

3. BP and ExxonMobil are engaged in negotiations regarding a new exploration. Simultaneously BP can choose to play Tough (T) or soft (S), while ExxonMobil can opt for Intransigent (I) or Acquiesce (A). The payoffs are as follows. If the choices are T and I, the payoffs are (5, 1) to BP and ExxonMobil, respectively. If the choices are S and I the payoffs are (6, 2) for BP and ExxonMobil, respectively. If the actions of the firms are T and A, the payoffs are (3, 3), and if the actions are S and A, then the payoffs are (4, 4). Which of the following statements are true? BP has a dominant strategy play S.   The Nash equilibrium is (S, A)   ExxonMobil has a dominant strategy to play A.   The dominant strategy equilibrium is (S, A)   These negotiations resemble a prisoners’ dilemma.

In a small isolated town, there are two types of people, saints and crooks. In business dealings between any two residents of this town, the payoffs are below. Saint Crook Saint 7,7 0, 10 Crook 10, 0 -5,-5 What percentage of this town's residents would be saints in an evolutionary stable strategy? a) 62.50% b) 0% c) 15.30% d) 100% e) 87.50%

Last answer was incorrect.

Suppose you have $35,000 in wealth. You have the opportunity to play a game called "Big Bet/Small Bet." In this game, you first choose whether you would like to make a big bet of $15,000 of a small bet of $5,000. You then roll a fair die. If you roll a 4, 5, or 6, you win the game and earn $15,000 for the big bet or $5,000 for the small bet. If you roll a 1, 2, or 3, you lose and lose $15,000 for the big bet and $5,000 for the small bet the game Utility U₂ U₁ BEL 0 11 LATE EE ARTE Are the Small Bet and Big Bet considered fair bets? O Big Bet is fair, but Small Bet is not. No, both are not fair. Yes, both are fair. 20 OSmall Bet is fair, but Big Bet is not. G HA 1 35 D E 1 1 1 1 1 F 1 U 50 Income (thousands of dollars)

5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:ˆA writes down either number 1 or number 2, and B must guess which one.ˆIf the number that A has written down is i and B has guessed correctly, B receives i units from A.ˆIf B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.ˆSuppose B guesses 1 with probability p and 2 with probability 1 −p.ˆLet X1 denote B’s gain (or loss) in a game where A has written down 1.ˆLet X2 denote B’s gain (or loss) in a game where A has written down 2.(a)  Find the pmf of X1 and X2(b)  Find B’s expected gain for these two cases, E[X1] and E[X2].(c)  What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player AˆSuppose that A writes down 1 with probability q and 2 with probability 1 −q.ˆLet Y1 be A’s loss (or gain) if B chooses number 1.ˆLet Y2 be A’s loss (or gain) if B…

3:51 9 M 23 The mixed strategy Nash equilibrium of the following * game is Player 2 R. L Player 1 U 2,2 3,1 D 3.-1 0.0 U with 3/4 probability and D with 1/4 probability for player 1; L with1/2 probability and probability for player 2 with 1/2 U with 1/2 probability and D with 1/2 probability for player 1; L with1/4 probability and R with 3/4 probability for player 2 U with 1/4 probability and D with 3/4 probability for player 1; L with1/2 probability and R with 1/2 probability for player 2 O None of the above. U with 1/2 probability and D with 1/2 probability for player 1; L with3/4 probability and R with 1/4 probability for player 2

2. In this question, your goal will be to understand whether learning in games is always valuable for players. Consider the following incomplete-information game. First, nature chooses between one of the following two A and B tables, each with probability 0.5: A L R B L R U 0,0 6,-3 U-20,-20-7,-16 D -3,6 5,5 D -16,-7 -5,-5 Then, players 1 and 2 simultaneously choose U or D and L or R, respectively, and obtain payoffs according to the table chosen by nature. Parts I-III present variations of this game under different assumptions about what players know about nature's move. Part I: Suppose no player observes nature's move (and it is common knowledge). (a) Represent the game in extensive form. (b) Represent the game in Bayesian normal form. (c) Find the unique BNE.

Question is in the attachment section. Thank you in advance for your answer.

SOLVE PART D, E & F, please

Consider the attached game depicted in Normal Form. Find one Nash equilibrium and verify that it is a Nash equilibrium. Note: 1. Remember to express the Nash equilibrium in the form of a strategy profile. 2. Use the definition of Nash equilibrium to verify that the strategy profile you find is really a Nash equilibrium.

Question > Consider the following matrix game where Player 1 moves first then Player 2 observes player 1's move and responds. Draw the game tree for the sequential move game and then determine all the Nash equilibria. Player 1 Strategy A Strategy B Strategy C Strategy D -3, -2 10, 12 9, 20 Player 2 Please show each step on how to get the answer. Thank you! Strategy E 13,7 17, 17 12, 21 Strategy F 20,8 22, 16 19, 19

need help on question 7-13

i. ii. QUESTION ONE A. A Nash equilibrium is a strategy profile such that every player's strategy is the best response to all the other players. It requires that each player makes a best response and that expectations regarding the play of other players are correct. Below is the table showing strategies and payoff for Player 1 and Player 2. PLAYER 1 R1 R2 R3 R4 C1 0,7 5,2 7,0 6,6 C2 2,5 3,3 2,5 2,2 PLAYER 2 C3 7,0 5,2 0,7 4,4 CA 6,6 2,2 4,4 10,4 REQUIRED; Transform the normal form game above into an imperfect extensive game form Find the Nash equilibrium for the game above using iterative deletion of strictly dominated strategies. Find the Nash equilibrium using brute force or cell by cell inspection.