Suppose d = 1/4. Before the game starts, you tell the players that you will offer each of them money m > 0 at each period both of them cooperate. The new per period payoff matrix is as follows: C D C 2+m, 2+m 3, -3 D -3, 3 1, 1 At least how much should you offer to make the strategy described in part 6 a SPNE? (a) m≥ 1/15 (b) m≥ 0.2
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- Two friends, Khalid and Mahmood, are going to a watch a world cup football match. They play a simple game in which they hold out one or two fingers to decide who will pay for the other's ticket. Khalid wins if the fingers held out add up to an even number; Mahmood wins if the fingers held out add up to an odd number. The price of the ticket is 25 OMR. Construct a payoff matrix for the game. Is there a unique Nash equilibrium in this game? Which strategy should a player use to maximize her chances of winning the game?Paramter y = 0 What is the highest payoff any player can receive in any subgame perfect Nashequilibrium of the repeated game?Consider the game with the payoffs below. Which of the possible outcomes are MORE efficient than the Nash Equilibrium (NE)? Note, they do NOT need to be Nash equilibria themselves, they just need to be more efficient than the NE. Multiple answers are possible, but not necessary. You need to check ALL correct answers for full credit. JILL High Medium LowMAGGIE Left 3,4 2,3 2,2Center 4,8 9,7 8,7Right 7,6 8,5 9,4Group of answer choices (Left, Low) There is no strategy combination that is more efficient than the Nash equilibrium for this game. (Right, Medium) (Left, High) (Center, Medium) (Center, High) (Center, Low) (Left, Medium) (Right, Low) (Right, High)
- Push Not Push 4,2 2,3 Not 6,-1 0,0 Would any other solution other than Nash Equilbrium approach work? Why?Consider a game where there is a $2,520 prize if a player correctly guesses the outcome of a fair 7-sided die roll.Cindy will only play this game if there is a nonnegative expected value, even with the risk of losing the payment amount.What is the most Cindy would be willing to pay?Someone at a party pulls out a $100 bill and announces that he is going to auction it off. There are n=10 people at the partywho are potential bidders. The owner of the $100 bill puts forth the following procedure: All bidders simultaneously submit a written bid. Only the highest bidders pay their bid (assuming that the highest bid is positive). If m people submit the highest bid, then each receives 1/m of the $100. Each person’s strategy set is {0,1,2,...,1000}{0,1,2,...,1000} so bidding can go as high as $1,000. The payoff of a player bidding bi is:0 if bi < max{b1,b2,…,bn},and 100/m − bi if bi = max {b1,b2,…,bn}where,m is the number of bidders whose bid equals max{b1,...,bn}. How many pure-strategy Nash equilibria does this game have? 1) 0 2) 1 3) 4 4) More than 4.
- The first player can choose either U or D. If he chooses U, the second player has a choice of two strategies: L and R. If the second player moves L he obtains 1 and the first player gets 5. If the second player chooses R he obtains 2 units of payoff while the first player receives 1. Following a move D by the first player, both players engage in a simultaneous-move “Bach or Stravinsky” game (as it was described in class). Find the SPE of this game and write it down in a mixed and behavior form.Consider the game Ms. Bennet and Mr. Darcy play in ‘First Impressions’, Selected Set V. Suppose that Ms. Bennet prefers to meet Mr. Darcy (a = 0) with probability p. Further suppose that: - The ‘meeting Ms. Bennet’ plays Ball with probability q (and Dinner with probability 1 − q); - ‘avoiding Ms. Bennet’ plays Ball with probability r (and Dinner with probability 1 − r); M - r. Darcy plays Ball with probability s (and Dinner with probability 1 − s). Write down the strategic form game and find for all values of p ∈ (0, 1) the Bayesian-Nash equilibria in mixed strategies.You and a rival are engaged in a game in which there are three possible outcomes: you win, your rival wins (you lose), or the two of you tie. You get a payoff of 50 if you win, a payoff of 20 if you tie, and a payoff of 0 if you lose. What is your expected payoff in each of the following situations? (a) There is a 50% chance that the game ends in a tie, but only a 10% chance that you win. (There is thus a 40% chance that you lose.) (b) There is a 50–50 chance that you win or lose. There are no ties. (c) There is an 80% chance that you lose, a 10% chance that you win, and a 10% chance that you tie.
- Assume that the effective security level is now determined by the highest (not the lowest) security measures chosen by airlines. Letting max{s1, . . . , sn} denote the highest of the airlines’ strategies, we find that airline i’s payoff is now 50 + 20 x max{s1, . . . , sn} -10 si.Assuming the same strategy sets, find all Nash equilibria.Consider the following representation of a Normal form game. actions w a (45,22) (10,38) (42,13) (10,7) (p,28) (15,40) (q,10) (44,10) (20,22) (14,31) (27,13) (12,8) d. (20,41) (9,48) (28,24) (18,32) Here each cell in the table represents an ordered pair. First element is payoff of the first player and second element is payoff of the second player. The letters a, b, c, d, x, y, z, w represent the actions. Write down the table in your answer script too. Now answer the following questions: 1. What is the distinction between strictly dominant strategy and weakly dominant strategy? Is it reasonable for a player to play a strictly dominated strategy? Explain why. 2. What are the minimum values for p and q that will make ba strategy that strictly dominates all other strategies for player 1, assuming both p and q are natural numbers? 3. Does player 2 have any strictly dominated pure strategy? If yes, which pure strategy dominates that strategy? If the submit button is off it is beacuse the due…A strategy for player 1 is a value for x1 from the set X. Similarly, a strategyfor player 2 is a value for x2 from the set X. Player 1’s payoff is V1(x1, x2) =5 + x1 - 2x2 and player 2’s payoff is V2(x1, x2) = 5 + x2 - 2x1.a. Assume that X is the interval of real numbers from 1 to 4 (including 1and 4). (Note that this is much more than integers and includes such numbers as 2.648 and 1.00037). Derive all Nash equilibria.b. Now assume that the game is played infinitely often and a player’s payoff is the present value of his stream of single-period payoffs, where dis the discount factor.(i) Assume that X is composed of only two values: 2 and 3; thus, aplayer can choose 2 or 3, but no other value. Consider the followingsymmetric strategy profile: In period 1, a player chooses the value 2. In period t(≥2), a player chooses the value 2. In period a player chooses the value 2 if both players chose 2 in all previous periods; otherwise, she chooses the value 3. Derive conditions which ensure…