In your own words, and without using mathematical notation, provide an intuitive explanation of each of the following terms. a. A rationalizable strategy. b. A strategy in an extensive form game of perfect information. c. A Nash equilibrium in pure strategies.
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- 5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:A writes down either number 1 or number 2, and B must guess which one.If the number that A has written down is i and B has guessed correctly, B receives i units from A.If B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.Suppose B guesses 1 with probability p and 2 with probability 1 −p.Let X1 denote B’s gain (or loss) in a game where A has written down 1.Let 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 ASuppose that A writes down 1 with probability q and 2 with probability 1 −q.Let Y1 be A’s loss (or gain) if B chooses number 1.Let Y2 be A’s loss (or gain) if B…D A popular way of sharing a cake between two people is to have one of the two cut the cake and the other chooses the who gets what piece. A. Write down the extensive form representation of this game. B. Solve for the Nash equilibrium strategy equilibrium. 4What is the Nash Equilibrium in a game? A. A situation where all players cooperate for maximum gain B. A situation where no player can improve their outcome by changing their strategy unilaterally C. A situation where players always choose the same strategy D. A situation where players randomly select strategies
- What is Ann's maximin strategy? Game Bob R Ann U 10,-1 4, 4 D 4, 1 8, -1 Select one: a. none of the other answers b. 2/5 U+ 3/5 D c. 3/5 U + 2/5 D d. 4/7 U + 3/7 D e. 2/7 U + 5/7 DCostco Spend $1B on advertising Spend $1.5B on advertising Spend $1B on advertising $3.5B; $2.7B $4.2; $2.2B Target Spend $1.5B on advertising $3.2B; $3.4B $4B; $3B5. The Stag Hunt is a famous coordination game where two hunters must work together to hunt a stag but each one has the option to go solo and hunt a hare. The following payoff matrix depicts such a game: a. b. Hunter A Stag Hare Stag 5,5 4,0 Hunter B Hare 0,4 4,4 List any pure strategy Nash equilibria if they exist. Does the game have a mixed strategy Nash equilibrium? If so, solve for it.
- Table 1 shows the Matrix Representation of McDonalds and Burger King Companies game, A. Suppose that Burger King decides to advertise its new products. What is the best decision for McDonalds? B. Suppose that McDonalds decides to advertise its new products. What is the best decision for Burger King? C. Using Table 1, show the Nash Equilibrium and Explain.Aedri Quick Lesson in Game Theory A Nash Equilibrium is an outcome in which neither player is better off by changing their strategy. 2.7 Is a Dominant Strategy equilibrium also a Nash equilibrium? a) Yes b) No esc The Ice Cream Guys $3.99 $4.99 + Chucky's Chunky CCT: $20,000 $3.99 ICG: $20,000 CCT: $60,000 ICG: $10,000 tab Treats CCT: $10,000 $4.99 ICG: $60,000 CCT: $40,000 ICG: $40,000 The table above is the payoff matrix for the annual profit of the only two ice-cream-truck firms operating in Beach City. They are deciding the price of an ice cream cone. %3D caps lo 2.8 What is Chucky's dominant strategy? a) $3.99 b) $4.99 c) Not enough information hift 2.9 What is the dominant strategy equilibrium in this situation? a) Both charge $3.99 b) Both charge $4.99 c) CCT charges $3.99 and ICG charges $4.99 d) CCT charges $4.99 and ICG charges $3.99 2.10 Suppose these two firms engaged in collusion (which, of course, totally doesn't happen because it is against the law). Which outcome would…4.Use the following normal-form game to answer the questions below. Strategy D A 10, 10 60, -5 -5, 60 50, 50 (a) Identify the one-shot Nash equilibrium. (b) Suppose the game is infinitely repeated and the interest rate is 5%. Can the players achieve payoffs that are better than the one-shot Nash equilibrium? Explain.
- Which of the following statements about a Nash equilibrium is not correct? A. Each player plays a best response to opponents' Nash strategies. B. No player has a profitable unilateral deviation. C. For each finite noncoopertiave game there always exists a pure strategy Nash equilibrium. D. A game has at least two players. Which one of the following statements is incorrect? A. For dynamic games with complete information, not all subgame perfect Nash equilibrium points can be found by backward induction. B. A finite dynamic game with complete information may also have a normal form representation. C. A finite static game with complete information may not have a pure strategy Nash equilibrium. D. A finite static game with complete information cannot have an extensive form representation. Which one of the following statements is correct? A. A supergame cannot have any subgame perfect Nash equilibrium. B. A supergame can only have finite number of subgame perfect Nash…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, 19i. 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.